[ { "path": ".github/workflows/docs.yml", "content": "name: Docs\n\non:\n push:\n branches:\n - main\n paths:\n - 'examples/**'\n - 'mkdocs.yml'\n - 'docs-mkdocs/**'\n - 'scripts/docs_*.sh'\n - 'scripts/sync_docs_notebooks.sh'\n - 'docs/**'\n - '.readthedocs.yml'\n - 'pyproject.toml'\n - 'pymdp/**'\n - '.github/workflows/docs.yml'\n pull_request:\n paths:\n - 'examples/**'\n - 'mkdocs.yml'\n - 'docs-mkdocs/**'\n - 'scripts/docs_*.sh'\n - 'scripts/sync_docs_notebooks.sh'\n - 'docs/**'\n - '.readthedocs.yml'\n - 'pyproject.toml'\n - 'pymdp/**'\n - '.github/workflows/docs.yml'\n\njobs:\n build-docs:\n runs-on: ubuntu-latest\n steps:\n - uses: actions/checkout@v4\n - name: Set up Python\n uses: actions/setup-python@v5\n with:\n python-version: '3.11'\n - name: Install uv\n uses: astral-sh/setup-uv@v6\n - name: Install dependencies\n run: |\n uv sync --no-default-groups --extra docs\n - name: Sync curated notebook docs\n run: |\n ./scripts/sync_docs_notebooks.sh\n - name: Build docs (strict)\n run: |\n uv run --no-default-groups --extra docs mkdocs build --strict\n" }, { "path": ".github/workflows/lint.yaml", "content": "name: Lint\n\non:\n pull_request:\n paths:\n - '**.py'\n - '.github/workflows/lint.yaml'\n - 'pyproject.toml'\n\n\njobs:\n build:\n runs-on: ubuntu-latest\n strategy:\n matrix:\n python-version: [\"3.11\"]\n steps:\n - uses: actions/checkout@v4\n - name: Set up Python ${{ matrix.python-version }}\n uses: actions/setup-python@v3\n with:\n python-version: ${{ matrix.python-version }}\n - name: Install dependencies\n run: |\n python -m pip install --upgrade pip\n pip install ruff\n - name: Analysing the code with ruff\n run: |\n ruff check\n" }, { "path": ".github/workflows/manual-branch-nightly.yaml", "content": "name: Manual Branch Nightly\n\non:\n workflow_dispatch:\n inputs:\n ref:\n description: Branch, tag, or SHA to validate\n required: true\n default: main\n type: string\n python_version:\n description: Python version to use\n required: true\n default: \"3.12\"\n type: string\n\nconcurrency:\n group: manual-branch-nightly-${{ inputs.ref }}\n cancel-in-progress: false\n\njobs:\n nightly:\n runs-on: ubuntu-latest\n permissions:\n contents: read\n steps:\n - uses: actions/checkout@v4\n with:\n ref: ${{ inputs.ref }}\n\n - name: Set up Python ${{ inputs.python_version }}\n uses: actions/setup-python@v3\n with:\n python-version: ${{ inputs.python_version }}\n\n - name: Install uv\n uses: astral-sh/setup-uv@v6\n\n - name: Verify nightly validation files exist\n run: |\n test -f scripts/run_notebook_manifest.py\n test -f test/notebooks/nightly_notebooks.txt\n\n - name: Install system dependencies\n run: |\n sudo apt-get update\n sudo apt-get install -y ffmpeg graphviz libgraphviz-dev pkg-config build-essential python3-dev\n\n - name: Install dependencies\n run: |\n uv sync --group test\n\n - name: Run nightly-marked tests\n run: |\n uv run pytest test -n 2 -m nightly\n\n - name: Run nightly-tier notebook tests\n run: |\n uv run python scripts/run_notebook_manifest.py test/notebooks/nightly_notebooks.txt\n" }, { "path": ".github/workflows/nightly-tests.yaml", "content": "name: Nightly Tests\n\non:\n schedule:\n - cron: \"0 2 * * *\"\n workflow_dispatch:\n\njobs:\n nightly:\n runs-on: ubuntu-latest\n strategy:\n matrix:\n python-version: [\"3.12\"]\n steps:\n - uses: actions/checkout@v4\n with:\n ref: main\n - name: Set up Python ${{ matrix.python-version }}\n uses: actions/setup-python@v3\n with:\n python-version: ${{ matrix.python-version }}\n - name: Install uv\n uses: astral-sh/setup-uv@v6\n - name: Install system dependencies\n run: |\n sudo apt-get update\n sudo apt-get install -y ffmpeg graphviz libgraphviz-dev pkg-config build-essential python3-dev\n - name: Install dependencies\n run: |\n uv sync --group test\n - name: Running nightly-marked tests\n run: |\n uv run pytest test -n 2 -m nightly\n - name: Running nightly-tier notebook tests\n run: |\n uv run python scripts/run_notebook_manifest.py test/notebooks/nightly_notebooks.txt\n" }, { "path": ".github/workflows/python-package.yml", "content": "name: Python package\n\non:\n push:\n branches: [main]\n pull_request:\n branches: [main]\n\njobs:\n build:\n runs-on: ubuntu-latest\n permissions:\n contents: read\n strategy:\n matrix:\n python-version: [\"3.11\", \"3.12\"]\n\n steps:\n - uses: actions/checkout@v4\n\n - name: Set up Python ${{ matrix.python-version }}\n uses: actions/setup-python@v5\n with:\n python-version: ${{ matrix.python-version }}\n\n - name: Build source and wheel distributions\n run: |\n python -m pip install --upgrade pip build\n python -m build --sdist --wheel\n\n - name: Install built wheel\n run: |\n python -m pip install dist/*.whl\n\n - name: Import smoke test\n run: |\n cd /tmp\n python - <<'PY'\n import pymdp\n from pymdp.agent import Agent\n\n print(\"Imported pymdp from\", pymdp.__file__)\n assert \"site-packages\" in pymdp.__file__\n print(\"Agent symbol:\", Agent.__name__)\n PY\n" }, { "path": ".github/workflows/test.yaml", "content": "name: Test\n\non:\n push:\n branches: [main]\n pull_request:\n branches: [main]\n\njobs:\n build:\n runs-on: ubuntu-latest\n strategy:\n matrix:\n python-version: [\"3.12\"]\n steps:\n - uses: actions/checkout@v4\n - name: Set up Python ${{ matrix.python-version }}\n uses: actions/setup-python@v3\n with:\n python-version: ${{ matrix.python-version }}\n - name: Install uv\n uses: astral-sh/setup-uv@v6\n - name: Install system dependencies\n run: |\n sudo apt-get update\n sudo apt-get install -y ffmpeg graphviz libgraphviz-dev pkg-config build-essential python3-dev\n - name: Install dependencies\n run: |\n uv sync --group test\n - name: Running unit tests with coverage\n run: |\n uv run pytest test -n 2 -m \"not nightly\" --cov=pymdp --cov-report=xml --cov-report=html --cov-report=term\n - name: Upload coverage reports as artifact\n uses: actions/upload-artifact@v4\n with:\n name: pymdp-coverage\n path: |\n coverage.xml\n htmlcov/\n retention-days: 30\n - name: Running CI-tier notebook tests\n run: |\n uv run python scripts/run_notebook_manifest.py test/notebooks/ci_notebooks.txt\n" }, { "path": ".gitignore", "content": "*.pyc\n__pycache__\n.DS_Store\n.ipynb_checkpoints\n.rope*\n.vscode/\n.ipynb_checkpoints/\n.pytest_cache\nenv/\npymdp.egg-info\ninferactively_pymdp.egg-info\nvenv/\n.venv\n.jax_cache\n.ruff_cache\n.coverage\ncoverage.xml\nhtmlcov/\nsite/\nbuild/\ndist/\nuv.lock\ndocs-mkdocs/tutorials/notebooks/examples/**/*.ipynb\n" }, { "path": ".pre-commit-config.yaml", "content": "repos:\n - repo: local\n hooks:\n - id: sanitize-notebooks\n name: sanitize notebooks by tier\n entry: uv run --group dev python scripts/notebook_precommit.py sanitize\n language: system\n files: ^examples/(?!legacy/).+\\.ipynb$\n pass_filenames: true\n - id: validate-notebook-execution-counts\n name: validate manifest notebook execution counts\n entry: uv run --group dev python scripts/notebook_precommit.py validate-counts\n language: system\n files: ^examples/(?!legacy/).+\\.ipynb$\n pass_filenames: true\n" }, { "path": ".readthedocs.yml", "content": "version: 2\n\nbuild:\n os: \"ubuntu-22.04\"\n tools:\n python: \"3.11\"\n jobs:\n pre_build:\n - ./scripts/sync_docs_notebooks.sh\n\npython:\n install:\n - method: pip\n path: .\n extra_requirements:\n - docs\n\nmkdocs:\n configuration: mkdocs.yml\n\nformats:\n - htmlzip\n" }, { "path": "CONTRIBUTING.md", "content": "# pymdp\n\n*Borrowed below list from [here](https://github.com/netsiphds/netrd)*\n\nWelcome to `pymdp` and thanks for your interest in contributing!\nDuring development please make sure to keep the following checklists handy.\nThey contain a summary of all the important steps you need to take to contribute\nto the package. As a general statement, the more familiar you already are\nwith git(hub), the less relevant the detailed instructions below will be for you.\n\n\n## Types of Contribution\n\nThere are multiple ways to contribute to `pymdp` (borrowed below list from [here](https://github.com/uzhdag/pathpy/blob/master/CONTRIBUTING.rst)):\n\n#### Report Bugs\n\nTo report a bug in the package, open an issue at https://github.com/infer-actively/pymdp/issues.\n\nPlease include in your bug report:\n\n* Your operating system name and version.\n* Any details about your local setup that might be helpful in troubleshooting.\n* Detailed steps to reproduce the bug.\n\n#### Fix Bugs\n\nLook through the GitHub issues for bugs. Anything tagged with \"bug\" and \"help\nwanted\" is open to whoever wants to implement it.\n\n#### Implement Features or New Methods\n\nLook through the GitHub issues for features. Anything tagged with \"enhancement\"\nand \"help wanted\" is open to whomever wants to implement it. If you know of a \nmethod that is implemented in another programming language, feel free to \ntranslate it into python here. If you don't want to translate it yourself, feel \nfree to add an issue at https://github.com/infer-actively/pymdp/issues. If you have \nread through this document and still have questions, also open an issue. When \nin doubt, open an issue.\n\n#### Improve Documentation\n\nDocumentation is just as important as the code it documents. Please feel\nfree to submit PRs that are focused on fixing, improving, correcting, or\nrefactoring documentation.\n\n#### Submit Feedback\n\nThe best way to send feedback is to open an issue.\n\nIf you are proposing to implement a function, feature, etc.\nsee more details below. \n\nIf you are proposing a feature not directly related to implementing a new method:\n\n* Explain in detail why the feature is desirable and how it would work.\n* Keep the scope as narrow as possible, to make it easier to implement.\n* Remember that this is a volunteer-driven project, and that your contributions\n are welcome!\n\n##### A Brief Note On Licensing\nOften, python code for an algorithm of interest already exists. In the interest of avoiding repeated reinvention of the wheel, we welcome code from other sources being integrated into `pymdp`. If you are doing this, we ask that you be explicit and transparent about where the code came from and which license it is released under. The safest thing to do is copy the license from the original code into the header documentation of your file. For reference, this software is [licensed under MIT](https://github.com/tlarock/netrd/blob/master/LICENSE).\n\n## Setup\nBefore starting your contribution, you need to complete the following instructions once.\nThe goal of this process is to fork, download and install the latest version of `pymdp`.\n\n1. Log in to GitHub.\n\n2. Fork this repository by pressing 'Fork' at the top right of this\n page. This will lead you to 'github.com//infer-actively'. We refer\n to this as your personal fork (or just 'your fork'), as opposed to this repository\n (github.com/infer-actively/pymdp), which we refer to as the 'upstream repository'.\n\n3. Clone your fork to your machine by opening a console and doing\n\n ```\n git clone https://github.com//infer-actively.git\n ```\n\n Make sure to clone your fork, not the upstream repo. This will create a\n directory called 'infer-actively/'. Navigate to it and execute\n\n ```\n git remote add upstream https://github.com/infer-actively/pymdp.git\n ```\n\n In this way, your machine will know of both your fork (which git calls\n `origin`) and the upstream repository (`upstream`).\n\n4. During development, you will probably want to play around with your\n code. For this, you need to install the `pymdp` package and have it\n reflect your changes as you go along. For this, open the console and\n navigate to the `infer-actively/` directory, and execute\n\n\t```\n\tpip install -e .\n\t```\n\n\tFrom now on, you can open a Jupyter notebook, ipython console, or your\n favorite IDE from anywhere in your computer and type `import pymdp`.\n\n\nThese steps need to be taken only once. Now anything you do in the `infer-actively/`\ndirectory in your machine can be `push`ed into your fork. Once it is in\nyour fork you can then request one of the organizers to `pull` from your\nfork into the upstream repository (by submitting a 'pull request'). More on this later!\n\n## Recommended local hooks\n\nIf you edit notebooks, install the local hooks after syncing the dev tooling:\n\n```\nuv sync --group dev\nuv run --group dev pre-commit install\nuv run --group dev pre-commit run --all-files\n```\n\nThe notebook hook reads the manifests in `test/notebooks/`:\n\n* Manifest-tested notebooks keep saved outputs but also keep canonical execution counts for output-bearing code cells so `nbval` can execute them reliably.\n* Nightly-tier notebooks still run through `nbstripout --keep-output`, but the hook restores canonical execution counts afterwards so the saved notebooks remain valid test inputs.\n\n\n## Before you start coding\n\nOnce you have completed the above steps, you are ready to choose an algorithm to implement and begin coding.\n\n1. Choose which algorithm you are interested in working on.\n\n2. Open an issue at https://github.com/infer-actively/pymdp/issues by clicking the \"New Issue\" button. \n\n\t* Title the issue \"Implement XYZ method\", where XYZ method is a shorthand name for whatever function / method / environment class you plan to implement.\n\t* Leave a comment that includes a brief motivation for why you want to see this method in `pymdp`, as well as any key citations.\n\t* If such an issue already exists for the method you are going to write, it is not necessary to open another. However, it is a good idea to leave a comment letting others know you are going to work on it.\n\n2. In your machine, create the file where your algorithm is going to\n live. If you chose a softmax algorithm, copy\n an existing file, such as `/pymdp/functions.py`, into \n `/pymdp/.py`. Please keep in mind that\n will be used inside the code, so try to choose\n something that looks \"pythonic\". In particular, cannot\n include spaces, should not include upper case letters, and should use underscores \n rather than hyphens.\n\n3. Open the newly created file and edit as follows. At the very top you\n will find a string describing the algorithm. Edit this to describe the algorithm you\n are about to code, and preferably include a citation and link to any relevant papers. \n Also add your name and email address (optional).\n\n## After you finish coding\n\n1. After updating your local code, the first thing to do is tell git which files\n you have been working on. (This is called staging.) If you worked on a softmax\n function, for example, do\n\n ```\n git add pymdp/.py\n ```\n\n2. Next tell git to commit (or save) your changes:\n\n\t```\n\tgit commit -m 'Write a commit message here. This will be public and\n\tshould be descriptive of the work you have done. Please be as explicit\n\tas possible, but at least make sure to include the name of the method\n\tyou implemented. For example, the commit message may be: add\n\timplementation of SomeMethod, based on SomeAuthor and/or SomeCode.'\n\t```\n\n3. Now you have to tell git to do two things. First, `pull` the latest changes from\n the upstream repository (in case someone made changes while you were coding), \n then `push` your changes and the updated code from your machine to your fork:\n\n\t```\n\tgit pull upstream \n\tgit push origin \n\t```\n\n\tNOTE: If you edited already existing files, the `pull` may result in\n\tconflicts that must be merged. If you run in to trouble here, ask\n\tfor help!\n\n4. Finally, you need to tell this (the upstream) repository to include your\n contributions. For this, we use the GitHub web interface. At the top of\n this page, there is a 'New Pull Request' button. Click on it, and it\n will take you to a page titled 'Compare Changes'. Right below the title,\n click on the blue text that reads 'compare across forks'. This will show\n four buttons. Make sure that the first button reads 'base fork:\n infer-actively/pymdp', the second button reads the branch you intend to\n merge into (for example `v1.0.0_alpha` for release work), the third\n button reads 'head fork: /infer-actively', and the fourth button\n reads the branch from your fork that contains your changes. (If everything has gone according to plan, the\n only button you should have to change is the third one - make sure you\n find your username, not someone elses.) After you find your username,\n GitHub will show a rundown of the differences that you are adding to the\n upstream repository, so you will be able to see what changes you are\n contributing. If everything looks correct, press 'Create Pull\n Request'.\n\tNOTE: Advanced git users may want to develop on branches other\n\tthan the upstream target branch on their fork. That is totally\n\tfine; just make sure the PR points at the correct upstream branch.\n\n\nThat's it! After you've completed these steps, maintainers will be notified \nand will review your code and changes to make sure that everything is in place. \nSome automated tests will also run in the background to make sure that your \ncode can be imported correctly and other sanity checks. Once that is all done, \none of us will either accept your Pull Request, or leave a message requesting some\nchanges (you will receive an email either way).\n" }, { "path": "LICENSE", "content": "MIT License\n\nCopyright (c) 2019 Conor Heins and Alec Tschantz\n\nPermission is hereby granted, free of charge, to any person obtaining a copy\nof this software and associated documentation files (the \"Software\"), to deal\nin the Software without restriction, including without limitation the rights\nto use, copy, modify, merge, publish, distribute, sublicense, and/or sell\ncopies of the Software, and to permit persons to whom the Software is\nfurnished to do so, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in all\ncopies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\nAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\nLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\nOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\nSOFTWARE.\n" }, { "path": "README.md", "content": "\n

\n \n \n \n

\n\nA Python package for simulating Active Inference agents in Markov Decision Process environments.\nPlease see our companion paper, published in the Journal of Open Source Software: [\"pymdp: A Python library for active inference in discrete state spaces\"](https://joss.theoj.org/papers/10.21105/joss.04098) for an overview of the package and its motivation. For a more in-depth, tutorial-style introduction to the package and a mathematical overview of active inference in Markov Decision Processes, see the [longer arxiv version](https://arxiv.org/abs/2201.03904) of the paper.\n\n## Citing `pymdp`\nIf you use `pymdp` in your work or research, please cite:\n\n```\n@article{Heins2022,\n doi = {10.21105/joss.04098},\n url = {https://doi.org/10.21105/joss.04098},\n year = {2022},\n publisher = {The Open Journal},\n volume = {7},\n number = {73},\n pages = {4098},\n author = {Conor Heins and Beren Millidge and Daphne Demekas and Brennan Klein and Karl Friston and Iain D. Couzin and Alexander Tschantz},\n title = {pymdp: A Python library for active inference in discrete state spaces},\n journal = {Journal of Open Source Software}\n}\n```\n\nThis package is hosted on the [`infer-actively`](https://github.com/infer-actively) GitHub organization, which was built with the intention of hosting open-source active inference and free-energy-principle related software.\n\nMost of the low-level mathematical operations are [NumPy](https://github.com/numpy/numpy) ports of their equivalent functions from the `SPM` [implementation](https://www.fil.ion.ucl.ac.uk/spm/doc/) in MATLAB. We have benchmarked and validated most of these functions against their SPM counterparts.\n\n## Status\n\n![status](https://img.shields.io/badge/status-active-green)\n[![PyPI version](https://img.shields.io/pypi/v/inferactively-pymdp?cacheSeconds=300)](https://pypi.org/project/inferactively-pymdp/1.0.0/)\n[![Documentation Status](https://readthedocs.org/projects/pymdp-rtd/badge/?version=latest)](https://pymdp-rtd.readthedocs.io/en/latest/)\n[![DOI](https://joss.theoj.org/papers/10.21105/joss.04098/status.svg)](https://doi.org/10.21105/joss.04098)\n\n\n# ``pymdp`` in action\n\nHere's a visualization of ``pymdp`` agents in action. One of the defining features of active inference agents is the drive to maximize \"epistemic value\" (i.e. curiosity). Equipped with such a drive in environments with uncertain yet disclosable hidden structure, active inference can ultimately allow agents to simultaneously learn about the environment as well as maximize reward.\n\nThe simulation below (see associated JAX notebook [here](https://pymdp-rtd.readthedocs.io/en/latest/tutorials/notebooks/examples/envs/cue_chaining_demo/)) demonstrates what might be called \"epistemic chaining,\" where an agent (here, analogized to a mouse seeking food) forages for a chain of cues, each of which discloses the location of the subsequent cue in the chain. The final cue (here, \"Cue 2\") reveals the location a hidden reward. This is similar in spirit to \"behavior chaining\" used in operant conditioning, except that here, each successive action in the behavioral sequence doesn't need to be learned through instrumental conditioning. Rather, active inference agents will naturally forage the sequence of cues based on an intrinsic desire to disclose information. This ultimately leads the agent to the hidden reward source in the fewest number of moves as possible.\n\nYou can run the code behind simulating tasks like this one and others in the **Examples** section of the [official documentation](https://pymdp-rtd.readthedocs.io/en/latest/). The GIF generation script used for these animations is available [here](examples/envs/chained_cue_navigation.py).\n\n\n\n\n\n\n\n\n
\n

\n \n
\n Cue 2 in Location 1, Reward on Top\n

\n		 \n

\n \n
\n Cue 2 in Location 3, Reward on Bottom\n

\n
\n\n## Quick-start: Installation and Usage\n\nWe recommend installing `pymdp` using [`uv`](https://docs.astral.sh/uv/), with an explicit virtual environment:\n\n```bash\nuv venv .venv\nsource .venv/bin/activate\nuv pip install inferactively-pymdp\n```\n\nIf you prefer `pip`, use:\n\n```bash\npip install inferactively-pymdp\n```\n\nIf `uv sync --group test` or `uv sync --extra nb` fails while building `pygraphviz`, install Graphviz first and then retry. On macOS, install `graphviz` with Homebrew. On Ubuntu/Debian, install `graphviz libgraphviz-dev pkg-config build-essential python3-dev` (or the version-matched `python3.x-dev` package if needed). The full troubleshooting notes live in [`docs-mkdocs/getting-started/installation.md`](docs-mkdocs/getting-started/installation.md).\n\nOnce in Python, you can then directly import `pymdp`, its sub-packages, and functions.\n\n```python\nfrom jax import numpy as jnp, random as jr\nfrom pymdp import utils\nfrom pymdp.agent import Agent\n\nkey = jr.PRNGKey(0)\nkeys = jr.split(key, 3)\n\nnum_obs = [3, 5]\nnum_states = [3, 2]\nnum_controls = [3, 1]\n\nA = utils.random_A_array(keys[0], num_obs, num_states)\nB = utils.random_B_array(keys[1], num_states, num_controls)\nC = utils.list_array_uniform([[no] for no in num_obs])\n\nagent = Agent(A=A, B=B, C=C, batch_size=1)\nobservation = [jnp.array([1]), jnp.array([4])]\n\nqs, info = agent.infer_states(observation, empirical_prior=agent.D, return_info=True)\n# Optional diagnostic: current variational free energy for each batch element.\nvfe = info[\"vfe\"]\nq_pi, neg_efe = agent.infer_policies(qs)\n\naction_keys = jr.split(keys[2], agent.batch_size + 1)\naction = agent.sample_action(q_pi, rng_key=action_keys[1:])\n```\n\n## Getting started / introductory material\n\nWe recommend starting with the JAX-first [official documentation](https://pymdp-rtd.readthedocs.io/en/latest/) for the repository, which provides practical guides, curated notebooks, and generated API references.\n\nFor new users to `pymdp`, we specifically recommend stepping through following three Jupyter notebooks (can also be used on Google Colab):\n\n- [Quickstart (JAX)](https://pymdp-rtd.readthedocs.io/en/latest/getting-started/quickstart-jax/)\n- [NumPy/legacy to JAX migration guide](https://pymdp-rtd.readthedocs.io/en/latest/migration/numpy-to-jax/)\n- [`rollout()` active inference loop guide](https://pymdp-rtd.readthedocs.io/en/latest/guides/rollout-active-inference-loop/)\n\nWe also have (and are continuing to build) a series of notebooks that walk through active inference agents performing different types of tasks in the [Notebook Gallery](https://pymdp-rtd.readthedocs.io/en/latest/tutorials/notebooks/).\n\n## Contributing\n\nThis package is under active development. If you would like to contribute, please refer to [CONTRIBUTING.md](CONTRIBUTING.md).\n\nRecommended local setup:\n\n```bash\ncd \nuv venv .venv\nsource .venv/bin/activate\nuv sync --group test\n```\n\nRecommended contributor hooks:\n\n```bash\nuv sync --group dev\nuv run --group dev pre-commit install\n```\n\nUseful variants:\n\n```bash\n# tests + contributor hooks\nuv sync --group test --group dev\n\n# docs work\nuv sync --group test --extra docs\n\n# notebook/media extras\nuv sync --group test --extra nb\n\n# model fitting extras\nuv sync --group test --extra modelfit\n```\n\nRun tests:\n\n```bash\npytest test\n```\n\nBuild docs locally:\n\n```bash\n./scripts/docs_build.sh\n```\n\n## Contributors\n\n- Conor Heins [@conorheins](https://github.com/conorheins)\n- Tim Verbelen [@tverbele](https://github.com/tverbele)\n- Dimitrije Markovic [@dimarkov](https://github.com/dimarkov)\n- Riddhi Jain Pitliya [@riddhipits](https://github.com/riddhipits)\n- Arun Niranjan [@Arun-Niranjan](https://github.com/Arun-Niranjan)\n- Toon Van de Maele [@toonvdm](https://github.com/toonvdm)\n- Ozan Catal [@OzanCatalVerses](https://github.com/OzanCatalVerses)\n- Tommaso Salvatori [@salvatomm](https://github.com/salvatomm)\n- Aswin Paul [@aswinpaul](https://github.com/aswinpaul)\n- Lancelot Da Costa [@lancelotdacosta](https://github.com/lancelotdacosta)\n- Ran Wei [@ran-weii](https://github.com/ran-weii)\n- Alexander Tschantz [@alec-tschantz](https://github.com/alec-tschantz)\n- Miguel de Prado [@praesc](https://github.com/praesc)\n- Nikola Pižurica [@NIkolaPizurica](https://github.com/NIkolaPizurica)\n- Nikola Milović [@nikolamilovic-ft](https://github.com/nikolamilovic-ft)\n- Matteo Risso [@matteorisso](https://github.com/matteorisso)\n- Christopher Buckley [@clb27](https://github.com/clb27)\n- Beren Millidge [@BerenMillidge](https://github.com/BerenMillidge)\n- Daphne Demekas [@daphnedemekas](https://github.com/daphnedemekas)\n- Cooper Williams [@coopwilliams](https://github.com/coopwilliams)\n" }, { "path": "docs/Makefile", "content": "# Minimal makefile for Sphinx documentation\n#\n\n# You can set these variables from the command line, and also\n# from the environment for the first two.\nSPHINXOPTS ?=\nSPHINXBUILD ?= sphinx-build\nSOURCEDIR = .\nBUILDDIR = _build\n\n# Put it first so that \"make\" without argument is like \"make help\".\nhelp:\n\t@$(SPHINXBUILD) -M help \"$(SOURCEDIR)\" \"$(BUILDDIR)\" $(SPHINXOPTS) $(O)\n\n.PHONY: help Makefile\n\n# Catch-all target: route all unknown targets to Sphinx using the new\n# \"make mode\" option. $(O) is meant as a shortcut for $(SPHINXOPTS).\n%: Makefile\n\t@$(SPHINXBUILD) -M $@ \"$(SOURCEDIR)\" \"$(BUILDDIR)\" $(SPHINXOPTS) $(O)\n" }, { "path": "docs/agent.rst", "content": "Agent class\n=================================\n\n.. autoclass:: pymdp.agent.Agent\n :members:\n" }, { "path": "docs/algos/fpi.rst", "content": "FPI (Fixed Point Iteration)\n=================================\n\n.. automodule:: pymdp.algos.fpi\n :members:\n\n" }, { "path": "docs/algos/index.rst", "content": "Algos\n=================================\n\nThe ``algos.py`` library contains the functions for implementing message passing algorithms for variational inference on POMDP generative models\n\nSub-libraries\n---------------\n\n.. toctree::\n :maxdepth: 1\n\n fpi\n mmp" }, { "path": "docs/algos/mmp.rst", "content": "MMP (Marginal Message Passing)\n=================================\n\n.. automodule:: pymdp.algos.mmp\n :members:" }, { "path": "docs/conf.py", "content": "# Configuration file for the Sphinx documentation builder.\n#\n# This file only contains a selection of the most common options. For a full\n# list see the documentation:\n# https://www.sphinx-doc.org/en/master/usage/configuration.html\n\n# -- Path setup --------------------------------------------------------------\n\n# If extensions (or modules to document with autodoc) are in another directory,\n# add these directories to sys.path here. If the directory is relative to the\n# documentation root, use os.path.abspath to make it absolute, like shown here.\n#\nimport os\nimport sys\nsys.path.insert(0, os.path.abspath('..'))\n\n# -- Project information -----------------------------------------------------\n\nproject = 'pymdp'\ncopyright = '2021, infer-actively'\nauthor = 'infer-actively'\n\n# The full version, including alpha/beta/rc tags\nrelease = '0.0.7.1'\n\n# -- General configuration ---------------------------------------------------\n\n# Add any Sphinx extension module names here, as strings. They can be\n# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom\n# ones.\nextensions = ['sphinx.ext.autodoc', \n 'sphinx.ext.doctest',\n 'sphinx.ext.coverage', \n 'sphinx.ext.napoleon',\n 'sphinx.ext.autosummary',\n 'myst_nb'\n ]\n\nsource_suffix = {\n '.rst': 'restructuredtext',\n '.ipynb': 'myst-nb'\n }\n\n# Add any paths that contain templates here, relative to this directory.\ntemplates_path = ['_templates']\n\n# List of patterns, relative to source directory, that match files and\n# directories to ignore when looking for source files.\n# This pattern also affects html_static_path and html_extra_path.\nexclude_patterns = ['_build', 'Thumbs.db', '.DS_Store']\n\n\n# -- Options for HTML output -------------------------------------------------\n\n# The theme to use for HTML and HTML Help pages. See the documentation for\n# a list of builtin themes.\n#\nhtml_theme = 'sphinx_rtd_theme'\n\n# Theme options are theme-specific and customize the look and feel of a theme\n# further. For a list of options available for each theme, see the\n# documentation.\nhtml_theme_options = {\n 'logo_only': True,\n}\n\n# The name of an image file (relative to this directory) to place at the top\n# of the sidebar.\nhtml_logo = '_static/pymdp_logo_2-removebg.png'\n\nhtml_favicon = '_static/pymdp_logo_2-removebg.png'\n\n# Add any paths that contain custom static files (such as style sheets) here,\n# relative to this directory. They are copied after the builtin static files,\n# so a file named \"default.css\" will overwrite the builtin \"default.css\".\nhtml_static_path = ['_static']\n\n\n# -- Options for myst ----------------------------------------------\njupyter_execute_notebooks = \"cache\"\njupyter_cache = \"notebooks\"\n" }, { "path": "docs/control.rst", "content": "Control\n=================================\n\nThe ``control.py`` module contains the functions for performing inference of policies (sequences of control states) in POMDP generative models,\naccording to active inference.\n\n.. automodule:: pymdp.control\n :members:" }, { "path": "docs/env.rst", "content": "Env\n========\n\nThe OpenAIGym-inspired ``Env`` base class is the main API that represents the environmental dynamics or \"generative process\" with\nwhich agents exchange observations and actions\n\nBase class\n----------\n.. autoclass:: pymdp.envs.Env\n\nSpecific environment implementations\n----------\n\nAll of the following dynamics inherit from ``Env`` and have the\nsame general usage as above.\n\n.. autosummary::\n :nosignatures:\n\n pymdp.envs.GridWorldEnv\n pymdp.envs.DGridWorldEnv\n pymdp.envs.SceneConstruction\n pymdp.envs.TMazeEnv\n pymdp.envs.TMazeEnvNullOutcome\n" }, { "path": "docs/index.rst", "content": ".. pymdp documentation master file, created by\n sphinx-quickstart on Fri Oct 29 13:27:58 2021.\n You can adapt this file completely to your liking, but it should at least\n contain the root `toctree` directive.\n\nWelcome to pymdp's documentation!\n=================================\n\n``pymdp`` is a Python package for simulating active inference agents in\ndiscrete space and time, using partially-observed Markov Decision Processes\n(POMDPs) as a generative model class. The package is designed to be modular and flexible, to\nenable users to design and simulate bespoke active inference models with varying levels of\nspecificity to a given task.\n\nFor a theoretical overview of active inference and the motivations for developing this package, \nplease see our companion paper_: \"pymdp: A Python library for active inference in discrete state spaces\".\n\n.. toctree::\n :maxdepth: 1\n :caption: Installation & Usage\n\n installation\n notebooks/pymdp_fundamentals\n notebooks/active_inference_from_scratch\n notebooks/using_the_agent_class\n\n.. toctree::\n :maxdepth: 1\n :caption: Examples\n\n notebooks/tmaze_demo\n notebooks/cue_chaining_demo\n \n.. toctree::\n :maxdepth: 2\n :caption: Modules\n\n inference\n control\n learning\n algos/index\n\n.. toctree::\n :maxdepth: 2\n :caption: Agent and environment API\n\n agent\n env\n\n.. toctree::\n :maxdepth: 1\n :caption: Additional learning materials\n\n notebooks/free_energy_calculation\n\nIndices and tables\n==================\n\n* :ref:`genindex`\n* :ref:`modindex`\n* :ref:`search`\n\n.. _paper: https://joss.theoj.org/papers/10.21105/joss.04098\n" }, { "path": "docs/inference.rst", "content": "Inference\n=================================\n\nThe ``inference.py`` module contains the functions for performing inference of discrete hidden states (categorical distributions) in POMDP generative models.\n\n.. automodule:: pymdp.inference\n :members:" }, { "path": "docs/installation.rst", "content": "Installation\n=================================\n\nWe recommend installing ``pymdp`` using the package installer pip_, which will install the package locally as well as its dependencies.\nThis can also be done in a virtual environment (e.g. one created using ``venv`` or ``conda``). \n\nWhen pip installing ``pymdp``, use the full package name: ``inferactively-pymdp``:\n\n.. code-block:: console\n\n (.venv) $ pip install inferactively-pymdp\n \n.. _pip: https://pip.pypa.io/en/stable/" }, { "path": "docs/learning.rst", "content": "Learning\n=================================\n\nThe ``learning.py`` module contains the functions for updating parameters of Dirichlet posteriors (that paramaterise categorical priors and likelihoods) in POMDP generative models.\n\n.. automodule:: pymdp.learning\n :members:" }, { "path": "docs/make.bat", "content": "@ECHO OFF\r\n\r\npushd %~dp0\r\n\r\nREM Command file for Sphinx documentation\r\n\r\nif \"%SPHINXBUILD%\" == \"\" (\r\n\tset SPHINXBUILD=sphinx-build\r\n)\r\nset SOURCEDIR=.\r\nset BUILDDIR=_build\r\n\r\nif \"%1\" == \"\" goto help\r\n\r\n%SPHINXBUILD% >NUL 2>NUL\r\nif errorlevel 9009 (\r\n\techo.\r\n\techo.The 'sphinx-build' command was not found. Make sure you have Sphinx\r\n\techo.installed, then set the SPHINXBUILD environment variable to point\r\n\techo.to the full path of the 'sphinx-build' executable. Alternatively you\r\n\techo.may add the Sphinx directory to PATH.\r\n\techo.\r\n\techo.If you don't have Sphinx installed, grab it from\r\n\techo.https://www.sphinx-doc.org/\r\n\texit /b 1\r\n)\r\n\r\n%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%\r\ngoto end\r\n\r\n:help\r\n%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%\r\n\r\n:end\r\npopd\r\n" }, { "path": "docs/notebooks/active_inference_from_scratch.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"Lggo6pjkdPhS\"\n },\n \"source\": [\n \"# Tutorial 1: Active inference from scratch\\n\",\n \"\\n\",\n \"[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/infer-actively/pymdp/blob/main/docs/notebooks/active_inference_from_scratch.ipynb)\\n\",\n \"\\n\",\n \"*Author: Conor Heins*\\n\",\n \"\\n\",\n \"This tutorial guides you through the construction of an active inference agent \\\"from scratch\\\" in a simple grid-world environment. This tutorial is designed to walk you through the various mathematical operations required for running active inference in discrete state spaces, as well as introduce you to the way discrete probability distributions are represented in `pymdp` (through the use of numpy vectors and matrices). We also show you how to compute the expected free energy in terms of risk and ambiguity, and how to use it to plan sequences of actions.\\n\",\n \"\\n\",\n \"By the end of this tutorial, you should be able to write simple active inference models from scratch using the main components of any POMDP generative model: the `A`, `B`, `C`, and `D` arrays, as well as be able to write the active inference loop for an agent engaged in a perception-action exchange with its environment.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"*Note*: When running this notebook in Google Colab, you may have to run `!pip install inferactively-pymdp` at the top of the notebook, before you can `import pymdp`. That cell is left commented out below, in case you are running this notebook from Google Colab.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# ! pip install inferactively-pymdp\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Imports\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {\n \"id\": \"hk0kXw1RRmTf\"\n },\n \"outputs\": [],\n \"source\": [\n \"import numpy as np\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import seaborn as sns\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"iSS6oO3RWrwp\"\n },\n \"source\": [\n \"### Define some auxiliary functions\\n\",\n \"\\n\",\n \"Here are some plotting functions that will come in handy throughout the tutorial.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {\n \"id\": \"Y0QiIF8SWxot\"\n },\n \"outputs\": [],\n \"source\": [\n \"def plot_likelihood(matrix, xlabels = list(range(9)), ylabels = list(range(9)), title_str = \\\"Likelihood distribution (A)\\\"):\\n\",\n \" \\\"\\\"\\\"\\n\",\n \" Plots a 2-D likelihood matrix as a heatmap\\n\",\n \" \\\"\\\"\\\"\\n\",\n \"\\n\",\n \" if not np.isclose(matrix.sum(axis=0), 1.0).all():\\n\",\n \" raise ValueError(\\\"Distribution not column-normalized! Please normalize (ensure matrix.sum(axis=0) == 1.0 for all columns)\\\")\\n\",\n \" \\n\",\n \" plt.figure(figsize = (6,6))\\n\",\n \" sns.heatmap(matrix, xticklabels = xlabels, yticklabels = ylabels, cmap = 'gray', cbar = False, vmin = 0.0, vmax = 1.0)\\n\",\n \" plt.title(title_str)\\n\",\n \" plt.show()\\n\",\n \"\\n\",\n \"def plot_grid(grid_locations, num_x = 3, num_y = 3 ):\\n\",\n \" \\\"\\\"\\\"\\n\",\n \" Plots the spatial coordinates of GridWorld as a heatmap, with each (X, Y) coordinate \\n\",\n \" labeled with its linear index (its `state id`)\\n\",\n \" \\\"\\\"\\\"\\n\",\n \"\\n\",\n \" grid_heatmap = np.zeros((num_x, num_y))\\n\",\n \" for linear_idx, location in enumerate(grid_locations):\\n\",\n \" y, x = location\\n\",\n \" grid_heatmap[y, x] = linear_idx\\n\",\n \" sns.set(font_scale=1.5)\\n\",\n \" sns.heatmap(grid_heatmap, annot=True, cbar = False, fmt='.0f', cmap='crest')\\n\",\n \"\\n\",\n \"def plot_point_on_grid(state_vector, grid_locations):\\n\",\n \" \\\"\\\"\\\"\\n\",\n \" Plots the current location of the agent on the grid world\\n\",\n \" \\\"\\\"\\\"\\n\",\n \" state_index = np.where(state_vector)[0][0]\\n\",\n \" y, x = grid_locations[state_index]\\n\",\n \" grid_heatmap = np.zeros((3,3))\\n\",\n \" grid_heatmap[y,x] = 1.0\\n\",\n \" sns.heatmap(grid_heatmap, cbar = False, fmt='.0f')\\n\",\n \"\\n\",\n \"def plot_beliefs(belief_dist, title_str=\\\"\\\"):\\n\",\n \" \\\"\\\"\\\"\\n\",\n \" Plot a categorical distribution or belief distribution, stored in the 1-D numpy vector `belief_dist`\\n\",\n \" \\\"\\\"\\\"\\n\",\n \"\\n\",\n \" if not np.isclose(belief_dist.sum(), 1.0):\\n\",\n \" raise ValueError(\\\"Distribution not normalized! Please normalize\\\")\\n\",\n \"\\n\",\n \" plt.grid(zorder=0)\\n\",\n \" plt.bar(range(belief_dist.shape[0]), belief_dist, color='r', zorder=3)\\n\",\n \" plt.xticks(range(belief_dist.shape[0]))\\n\",\n \" plt.title(title_str)\\n\",\n \" plt.show()\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"5RsP7hVidcfn\"\n },\n \"source\": [\n \"## **The Basics: categorical distributions**\\n\",\n \"\\n\",\n \"Let's start by creating a simple categorical distribution $P(x)$. We will represent this distribution numerically with a 1-D `numpy` array (i.e. a `numpy.ndarray` where `ndim == 1`). The discrete entries of this vector can be thought of as the probabilities of seeing each of the $K$ alternative outcomes (the support of the distribution), if we were to sample once from the distribution. We can write the distribution as a vector of probabilities, follows:\\n\",\n \"\\n\",\n \"\\n\",\n \"$$\\n\",\n \"P(x) = \\\\begin{bmatrix} P(x = 0) \\\\\\\\\\\\ P(x = 1)\\\\\\\\\\\\ \\\\vdots \\\\\\\\\\\\ P(x = K) \\\\end{bmatrix}\\n\",\n \"$$ \\n\",\n \"\\n\",\n \"We can use `numpy` and the `norm_dist` function from `utils` library of `pymdp` to quickly create a random categorical distribution.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"from pymdp import utils\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\"\n },\n \"id\": \"P0RZ91Xb34GY\",\n \"outputId\": \"2a120bcb-82ca-4e6b-8146-a82eb42e6fcd\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[[0.16880278]\\n\",\n \" [0.51728256]\\n\",\n \" [0.31391466]]\\n\",\n \"Integral of the distribution: 1.0\\n\"\n ]\n }\n ],\n \"source\": [\n \"my_categorical = np.random.rand(3)\\n\",\n \"# my_categorical = np.array([0.5, 0.3, 0.8]) # could also just write in your own numbers\\n\",\n \"my_categorical = utils.norm_dist(my_categorical) # normalizes the distribution so it integrates to 1.0\\n\",\n \"\\n\",\n \"print(my_categorical.reshape(-1,1)) # we reshape it to display it like a column vector\\n\",\n \"print(f'Integral of the distribution: {round(my_categorical.sum(), 2)}')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"uJmzJ7tFdptc\"\n },\n \"source\": [\n \" We can sample a discrete outcome from this distribution using the `sample()` function from the `utils` module\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\"\n },\n \"id\": \"1LvlfKJ54ibe\",\n \"outputId\": \"491c96b5-4667-4f8c-8adb-0acf8f0fd5b8\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Sampled outcome: 1\\n\"\n ]\n }\n ],\n \"source\": [\n \"sampled_outcome = utils.sample(my_categorical)\\n\",\n \"print(f'Sampled outcome: {sampled_outcome}')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"x5co79ug4UVy\"\n },\n \"source\": [\n \"Now plot the beliefs using our `plot_beliefs()` function that we defined in the beginning. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {\n \"id\": \"13yT2uB_dzFc\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_beliefs(my_categorical, title_str = \\\"A random (unconditional) Categorical distribution\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"vfDpOZ25dzpG\"\n },\n \"source\": [\n \"Now let's move onto _conditional_ categorical distributions or likelihoods, i.e. how we represent the distribution of one discrete random variable X, conditioned on the settings of another discrete random variable Y.\\n\",\n \"\\n\",\n \"We would write these mathematically as:\\n\",\n \"\\n\",\n \"\\n\",\n \"$$ \\\\begin{align}\\n\",\n \"P(X | Y)\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"\\n\",\n \"And can represent them using 2-D `numpy.ndarrays` i.e. matrices\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\"\n },\n \"id\": \"_PZ8VMWc46kk\",\n \"outputId\": \"55e3edb7-8491-4a76-a751-d41a10bda960\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[[0.089 0.739 0.145 0.399]\\n\",\n \" [0.772 0.201 0.026 0.578]\\n\",\n \" [0.181 0.253 0.788 0.844]]\\n\"\n ]\n }\n ],\n \"source\": [\n \"# initialize it with random numbers\\n\",\n \"p_x_given_y = np.random.rand(3, 4)\\n\",\n \"print(p_x_given_y.round(3))\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\"\n },\n \"id\": \"G8HyWdgE48Ts\",\n \"outputId\": \"c5f3fb1f-b23a-4f8d-a62b-9f7968f08bb1\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[[0.086 0.619 0.151 0.219]\\n\",\n \" [0.741 0.168 0.027 0.318]\\n\",\n \" [0.174 0.212 0.821 0.463]]\\n\"\n ]\n }\n ],\n \"source\": [\n \"# normalize it\\n\",\n \"p_x_given_y = utils.norm_dist(p_x_given_y)\\n\",\n \"print(p_x_given_y.round(3))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"2doBWPTW5Lix\"\n },\n \"source\": [\n \"Now print the first column (i.e. $P(X | Y = 0)$) and show that it's a proper categorical distribution\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {\n \"id\": \"9mtgjyb1d7ht\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[[0.08555937]\\n\",\n \" [0.74093812]\\n\",\n \" [0.1735025 ]]\\n\",\n \"Integral of P(X|Y=0): 0.9999999999999999\\n\"\n ]\n }\n ],\n \"source\": [\n \"print(p_x_given_y[:,0].reshape(-1,1))\\n\",\n \"print(f'Integral of P(X|Y=0): {p_x_given_y[:,0].sum()}')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"fqsar3k5d8lm\"\n },\n \"source\": [\n \"So column `i` of the matrix `p_x_given_y` represents the conditional probability of $X$, given the `i`-th level of the random variable $Y$, i.e. $P(X | Y = i)$\\n\",\n \"\\n\",\n \"Next: taking expectations of random variables using matrix-vector products\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {\n \"id\": \"XKkJuevmd-7H\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[[0.75]\\n\",\n \" [0.25]]\\n\",\n \"[[0.6 0.5 ]\\n\",\n \" [0.15 0.41]\\n\",\n \" [0.25 0.09]]\\n\"\n ]\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Create a P(Y) and P(X|Y) using the same numbers from the slides \\\"\\\"\\\"\\n\",\n \"\\n\",\n \"p_y = np.array([0.75, 0.25]) # this is already normalized - you don't need to `utils.norm_dist()` it!\\n\",\n \"\\n\",\n \"# the columns here are already normalized - you don't need to `utils.norm_dist()` it!\\n\",\n \"p_x_given_y = np.array([[0.6, 0.5],\\n\",\n \" [0.15, 0.41], \\n\",\n \" [0.25, 0.09]])\\n\",\n \"\\n\",\n \"print(p_y.round(3).reshape(-1,1))\\n\",\n \"print(p_x_given_y.round(3))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"iGFLbNSteN5h\"\n },\n \"source\": [\n \"Calculate expected value of $X$, given our current _belief_ about $Y$, i.e. $P(Y)$ using a simple matrix-vector product, of the form $\\\\mathbf{A}\\\\mathbf{x}$.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {\n \"id\": \"JMUFrn0FeOMY\"\n },\n \"outputs\": [],\n \"source\": [\n \"\\\"\\\"\\\" Calculate the expectation using numpy's dot product functionality \\\"\\\"\\\"\\n\",\n \"\\n\",\n \"# first version of the dot product (using the method of a numpy array)\\n\",\n \"E_x_wrt_y = p_x_given_y.dot(p_y)\\n\",\n \"\\n\",\n \"# second version of the dot product (using the function np.dot with two arguments)\\n\",\n \"# E_x_wrt_y = np.dot(p_x_given_y, p_y)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"XGzohGsF5taF\"\n },\n \"source\": [\n \"Now print it and verify the result is a proper categorical distribution (integrates to 1.0)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {\n \"id\": \"aqq_fV165yqp\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[0.575 0.215 0.21 ]\\n\",\n \"Integral: 1.0\\n\"\n ]\n }\n ],\n \"source\": [\n \"print(E_x_wrt_y)\\n\",\n \"print(f'Integral: {E_x_wrt_y.sum().round(3)}')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"YxwopW4heRcb\"\n },\n \"source\": [\n \"## **A simple environment: Grid-world**\\n\",\n \"Now that we understand categorical distributions and how to take conditional expectations of random variables, with categorical conditional and prior distributions, let's move onto a worked example of Active Inference, so-called 'Grid-World'. \\n\",\n \"\\n\",\n \"Before we write down the generative model $P(o,s)$ of an active inference agent who will navigate Grid-World, let's start by establishing what exactly this environment is and how we're going to represent it mathematically.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {\n \"id\": \"rZYA7vDreRo5\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)]\\n\"\n ]\n }\n ],\n \"source\": [\n \"import itertools\\n\",\n \"\\n\",\n \"\\\"\\\"\\\" Create the grid locations in the form of a list of (Y, X) tuples -- HINT: use itertools \\\"\\\"\\\"\\n\",\n \"grid_locations = list(itertools.product(range(3), repeat = 2))\\n\",\n \"print(grid_locations)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {\n \"id\": \"HLr-vvmLefyb\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_grid(grid_locations)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"PQ1Rm_w23sLO\"\n },\n \"source\": [\n \"## **Building the generative model**: $\\\\mathbf{A}$, $\\\\mathbf{B}$, $\\\\mathbf{C}$, and $\\\\mathbf{D}$\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"0q32yTQEeiqw\"\n },\n \"source\": [\n \"### 1. The **A** matrix or $P(o\\\\mid s)$. \\n\",\n \"\\n\",\n \"---\\n\",\n \"\\n\",\n \"The generative model's \\\"prior beliefs\\\" about how hidden states relate to observations\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {\n \"colab\": {\n \"base_uri\": \"https://localhost:8080/\"\n },\n \"id\": \"uRUbpndA61Lg\",\n \"outputId\": \"e02d2149-884c-48a4-d2b3-a4151ec82a07\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Dimensionality of hidden states: 9\\n\",\n \"Dimensionality of observations: 9\\n\"\n ]\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Create variables for the storing the dimensionalities of the hidden states and the observations \\\"\\\"\\\"\\n\",\n \"\\n\",\n \"n_states = len(grid_locations)\\n\",\n \"n_observations = len(grid_locations)\\n\",\n \"\\n\",\n \"print(f'Dimensionality of hidden states: {n_states}')\\n\",\n \"print(f'Dimensionality of observations: {n_observations}')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 17,\n \"metadata\": {\n \"id\": \"3QLSmiYu67j4\"\n },\n \"outputs\": [],\n \"source\": [\n \"\\\"\\\"\\\" Create the A matrix \\\"\\\"\\\"\\n\",\n \"\\n\",\n \"A = np.zeros( (n_states, n_observations) )\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 18,\n \"metadata\": {\n \"id\": \"k-i2_Uxc6_QY\"\n },\n \"outputs\": [],\n \"source\": [\n \"\\\"\\\"\\\" Create an umambiguous or 'noise-less' mapping between hidden states and observations \\\"\\\"\\\"\\n\",\n \"\\n\",\n \"np.fill_diagonal(A, 1.0)\\n\",\n \"\\n\",\n \"# alternative:\\n\",\n \"# A = np.eye(n_observations, n_states)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"DuU1UHLTfAHo\"\n },\n \"source\": [\n \"Likelihood matrices show relationships between indices of the state space, which are indexed linearly. Remember the (Y, X) coordinates of the grid world don't necessarily neatly map onto to the locations in the matrix here, which has 'unwrapped' the Grid World's (Y, X) locations into columns/rows.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 19,\n \"metadata\": {\n \"id\": \"HdmHQ2l-fKhR\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A, title_str = \\\"A matrix or $P(o|s)$\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"xZx08e6YfL7r\"\n },\n \"source\": [\n \"How could we introduce uncertainty into this A matrix? I.e. how do we introduce ambiguity or uncertainty into the agent's model of the world? \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 20,\n \"metadata\": {\n \"id\": \"OQycm296fCZN\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": \"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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Remind yourself of the mapping between linear indices (0 through 8) and grid locations (Y, X) \\\"\\\"\\\"\\n\",\n \"plot_grid(grid_locations)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 21,\n \"metadata\": {\n \"id\": \"MboJWmdqfRX0\"\n },\n \"outputs\": [],\n \"source\": [\n \"A_noisy = A.copy()\\n\",\n \"\\n\",\n \"# this line says: the probability of seeing yourself in location 0, given you're in location 0, is 1/3, AKA P(o == 0 | s == 0) = 0.3333....\\n\",\n \"A_noisy[0,0] = 1 / 3.0 # corresponds to location (0,0)\\n\",\n \"\\n\",\n \"# this line says: the probability of seeing yourself in location 1, given you're in location 0, is 1/3, AKA P(o == 1 | s == 0) = 0.3333....\\n\",\n \"A_noisy[1,0] = 1 / 3.0 # corresponds to one step to the right from (0, 1)\\n\",\n \"\\n\",\n \"# this line says: the probability of seeing yourself in location 3, given you're in location 0, is 1/3, AKA P(o == 3 | s == 0) = 0.3333....\\n\",\n \"A_noisy[3,0] = 1 / 3.0 # corresponds to one step down from (1, 0)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 22,\n \"metadata\": {\n \"id\": \"7hh5dxG-fRva\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A_noisy, title_str = 'modified A matrix where location (0,0) is \\\"blurry\\\"')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 23,\n \"metadata\": {\n \"id\": \"2duo3znv8SQp\"\n },\n \"outputs\": [],\n \"source\": [\n \"\\\"\\\"\\\" Let's make ake one grid location \\\"ambiguous\\\" in the sense that it could be easily confused with neighbouring locations \\\"\\\"\\\"\\n\",\n \"my_A_noisy = A_noisy.copy()\\n\",\n \"\\n\",\n \"# locations 3 and 7 are the nearest neighbours to location 6\\n\",\n \"my_A_noisy[3,6] = 1.0 / 3.0\\n\",\n \"my_A_noisy[6,6] = 1.0 / 3.0\\n\",\n \"my_A_noisy[7,6] = 1.0 / 3.0\\n\",\n \"\\n\",\n \"# Alternatively: you could have the probability spread among locations 3, 4, 6, and 7. This is basically saying, that whole lower-left corner of grid-world is blurry, if you're in location 6\\n\",\n \"# Remember to make sure the A matrix is column normalized. So if you do it this way, with the probabilities spread among 4 perceived locations, then you'll have to make sure the probabilities sum to 1.0\\n\",\n \"# my_A_noisy[3,6] = 1.0 / 4.0\\n\",\n \"# my_A_noisy[4,6] = 1.0 / 4.0\\n\",\n \"# my_A_noisy[6,6] = 1.0 / 4.0\\n\",\n \"# my_A_noisy[7,6] = 1.0 / 4.0\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"e4eyxN618ZgW\"\n },\n \"source\": [\n \"Now plot the new A matrix, that now has two \\\"blurry\\\" locations\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 24,\n \"metadata\": {\n \"id\": \"CZDtd3u63Qn0\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(my_A_noisy, title_str = \\\"Noisy A matrix now with TWO ambiguous locations\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"VVh-pexGuwnh\"\n },\n \"source\": [\n \"### 2. The **B** matrix or $P(s_{t}\\\\mid s_{t-1}, u_{t-1})$.\\n\",\n \"\\n\",\n \"\\n\",\n \"---\\n\",\n \"\\n\",\n \"The generative model's \\\"prior beliefs\\\" about (controllable) transitions between hidden states over time. Namely, how do hidden states at time $t$ result from hidden states at some previous time $t-1$. These transition dynamics are further conditioned on some past action $u_t$.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 25,\n \"metadata\": {\n \"id\": \"ihPWs7X_fVw3\"\n },\n \"outputs\": [],\n \"source\": [\n \"actions = [\\\"UP\\\", \\\"DOWN\\\", \\\"LEFT\\\", \\\"RIGHT\\\", \\\"STAY\\\"]\\n\",\n \"\\n\",\n \"def create_B_matrix():\\n\",\n \" B = np.zeros( (len(grid_locations), len(grid_locations), len(actions)) )\\n\",\n \"\\n\",\n \" for action_id, action_label in enumerate(actions):\\n\",\n \"\\n\",\n \" for curr_state, grid_location in enumerate(grid_locations):\\n\",\n \"\\n\",\n \" y, x = grid_location\\n\",\n \"\\n\",\n \" if action_label == \\\"UP\\\":\\n\",\n \" next_y = y - 1 if y > 0 else y \\n\",\n \" next_x = x\\n\",\n \" elif action_label == \\\"DOWN\\\":\\n\",\n \" next_y = y + 1 if y < 2 else y \\n\",\n \" next_x = x\\n\",\n \" elif action_label == \\\"LEFT\\\":\\n\",\n \" next_x = x - 1 if x > 0 else x \\n\",\n \" next_y = y\\n\",\n \" elif action_label == \\\"RIGHT\\\":\\n\",\n \" next_x = x + 1 if x < 2 else x \\n\",\n \" next_y = y\\n\",\n \" elif action_label == \\\"STAY\\\":\\n\",\n \" next_x = x\\n\",\n \" next_y = y\\n\",\n \" new_location = (next_y, next_x)\\n\",\n \" next_state = grid_locations.index(new_location)\\n\",\n \" B[next_state, curr_state, action_id] = 1.0\\n\",\n \" return B\\n\",\n \"\\n\",\n \"B = create_B_matrix()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"njx3RFJS-H87\"\n },\n \"source\": [\n \"Let's now explore what it looks to \\\"take\\\" an action, using matrix-vector product of an action-conditioned \\\"slice\\\" of the $\\\\mathbf{B}$ array and a previous state vector\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 26,\n \"metadata\": {\n \"id\": \"I8wrEfF5-IR1\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": \"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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Define a starting location\\\"\\\"\\\" \\n\",\n \"starting_location = (1,0)\\n\",\n \"\\n\",\n \"\\\"\\\"\\\"get the linear index of the state\\\"\\\"\\\"\\n\",\n \"state_index = grid_locations.index(starting_location)\\n\",\n \"\\n\",\n \"\\\"\\\"\\\" and create a state vector out of it \\\"\\\"\\\"\\n\",\n \"starting_state = utils.onehot(state_index, n_states)\\n\",\n \"\\n\",\n \"plot_point_on_grid(starting_state, grid_locations)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 27,\n \"metadata\": {\n \"id\": \"mX5gdrUrMHgz\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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w5g/v376sOJLTdnkurt6xe3X6NjIxU97cePnyInJwcJCcna9zjKa6eV82YMQMffPAB5s2bh/nz58Pa2hpdu3bFkCFDJNdzQUEBoqKicOnSJcjlcty6dUt1MPHq+pB6D5bm1e22Ro0aan2kp6cDgMa+o0GDBqhbt26p827cuDGmT5+Ob7/9FqNHj0bt2rXh4uKCXr16wcfHB9WqVStx2urVq+PXX3/F7t27kZqaCrlcjqysLACa+46XlXedAToKCwMDAzg4OODixYsoLCws8ZpeVFQUMjIyEB4ejgYNGuDDDz/EwYMH4ejoCAcHB/j5+cHJyQnDhw8vtT/lxhMQEIDu3bsXO06rVq1Ub1blhvCyl6+vlxZMyo3n1XmUtsKVNUodcScmJiI0NBSNGjVCx44dVTf1jh49ihUrVpQ67asMDAyKvT5b2rIBgEwmw8aNG3Hu3DkkJyfj8OHD2LBhA2JiYhAZGYm+ffuWOr3U61AaZW2lzeN1zjq0WZ8vX/t+nR1vWfowMTGBu7s79uzZg9DQUCQmJqJOnTro0qULAO23Z6XyvOZKpS2zsp6ePXvC39+/2HFKe/y6devW2Lt3L44cOYKDBw/iyJEjWLx4MdasWYPY2NgSP+Nz+vRpjBo1CrVr10anTp0wcOBAtGnTBnK5XOMKhNQySJGaVhmcUvuOkowaNQp9+vTB/v37cejQIRw7dgwHDhxAfHw8Vq1aVeJ0X375JTZu3Ig2bdrA3t4e7733HhwcHPDll1+WurMv7zoDdPg5ix49euDUqVNISEgo9rnmZ8+eYevWrSgqKkK9evVw+vRpHDx4EB9++CEmTZqkGq+wsBCPHj0qdcGUCVutWjV06tRJbdj169dx69Yt1KpVSzWPmzdvasxDeeQAvDjKqF27NlJTUzXGS0tLAwC1Sw3aaNKkSbFPqRw6dAiJiYmYPn06vvnmG5ibm2Pbtm1qp8Q///xzmfoCgGbNmqktk5LUp67T0tKQk5MDe3t72NvbIzQ0FNevX0dAQADWrFkjGRbaevXMDHixXurUqaO6oWhoaKh64kOptEtBJVFuHxW5PsvbR9++fTFlyhRcvnwZ+/btg5eXl2pHpO32rCumpqaoVasWCgsLNeq5c+cOfv/99xLrKSoqwpUrVyCTydCtWzfV2W5iYiKmTJmCuLi4Ep8kWrx4MYyMjJCQkKB25L98+fIKWjLtvbzvsLS0VLXn5uaqjvRL8ujRI1y5cgXt2rVDYGAgAgMD8fTpU8ycORN79+7F1atXi/0U/e3bt7Fx40a89957iIyMVBsm9T4ozzpT0tmjs35+fmjatCkiIyNx7do1tWFFRUX47LPPkJmZiTFjxqB69ep49OgRAGg8ybFlyxb89ddfKCwsVLUpjwKUR3ONGjWCjY0NduzYgfv376vGKygowKxZszBx4kQUFhaifv36cHBwwO7du1WXt4AXO9DDhw+r/q5WrRrc3d1x7NgxtUcchRD44YcfYGBgoHZNWxseHh7IzMzE/v371drXrVuneuLi0aNHaNKkiVpQ3L17F/v27VO9btry8vLCH3/8obZcOTk52LlzZ6nTzZ07Fx9++CHy8vJUbe+88w7q1q2rdvRlaGhYrq9rOXLkiNq6unbtGo4ePYquXbuqzsAaNGiAK1euqB21JyYmasxLWVdJ9TRs2BA2NjbYtWuX2iPI+fn5WLNmDWrUqFHuD/GVtY+uXbvC2NgYixYtwoMHD9RCWNvtuaykXqeSvPXWW/Dw8MChQ4dw5coVtWELFixASEhIiU/ZFRUVITg4GPPmzVNrb9u2rVpNyrOjl2t79OgRTE1N1YIiJydH9ai0Nu+H8m6nSt27d4eBgQFiYmLU2jdt2iQ5/2PHjmH48OFq9zlr166tCh3lsr+6X1Puo17dJx46dAg3b94sdp+orKU860xJZ2cWNWvWxJIlSzBy5EgMGjQIffv2ha2tLR49eoQ9e/bg8uXL8Pb2Vt0wcnBwgEwmw/z583H79m2YmJjg5MmTSExMRM2aNdV2XsqNZ9WqVfDw8EC3bt0we/ZsDB8+HAMHDsTQoUNRr149JCQk4Pz585g2bZrqaDUsLAxBQUEYNGgQ/P39kZ+fjw0bNmis8NDQUJw8eRJBQUEICgpCw4YNsX//fpw4cQIjRowo9vHE0vj7+2Pbtm2YMmUKAgICYGFhgZSUFBw7dgzz5s1DtWrV4OHhgcTERMyZMwe2tra4deuWKiwBqL0GUkaMGIGff/4ZH330EYYPHw5TU1PExsZKXoYaMWIExowZg4CAAPTv3x81a9ZEcnIy5HK52s04U1NTXLlyBZs2bYKzszOMjIzK9HrUqFEDw4YNQ1BQEJ4+fYp169ahbt26mDx5smqcPn36YPXq1ZgwYQI8PT1x6dIlJCUlaVxfVv69ePFidOjQAS4uLhr9KbePQYMGYejQoTA2NsauXbtw6dIlzJ49W/K6szbK0oeRkRG8vLywY8cONGrUCB06dCh2XlLbc1koX6fNmzcjMzOzTGeJyvdDQEAAAgIC0KRJE6SkpODgwYPw8/Mr8XHnGjVqICgoCMuWLUNISAjc3d3x7NkzxMbGolatWhg4cCCA/913OXDgAJo0aQIvLy94eHjghx9+wKRJk+Dm5oYHDx5g69atqqNqbd4PpqamOHXqFLZs2QI3Nzetl/dVFhYWCAgIwMaNG5GVlYVOnTrhwoULqoOX0i4xd+nSBRYWFvj4449x6dIlNG/eHKmpqYiJiYGLi4tqX/Lqfs3d3R1NmjTB8uXL8fz5czRu3Bi//fYbduzYUeI+8eV1+7rrTKXUZ6Uqwb1798SCBQtEr169hL29vWjbtq0YMmSI2Lp1q8YjlqdPnxb+/v7C3t5eODs7Cz8/P5GQkCDmz58v3n33XfHgwQMhhBCPHz8W77//vrCxsRHe3t6q6S9evCjGjRsnHB0dRdu2bUX//v3F9u3bNWr6f//v/4khQ4YIGxsb4ebmJr7//nsxbdo0YWNjozbezZs3xeTJk4Wzs7Ows7MTAwYMEHFxcWrjFPfYphDFPwb38OFD8emnnwpXV1fV/BITE1XDHz16JGbNmqUa7uXlJRYsWCDOnDkjLC0txY8//ljivIvz559/iunTpwtnZ2fh6OgoPvnkE7F+/fpSH50VQoiDBw8Kf39/4eTkJOzs7MTAgQPF7t271eZ9+PBh0aVLF2FtbS2+//77Yh99VCru0dlvvvlGfPvtt6JDhw7C3t5ejBs3TqSlpalN99dff4m5c+cKFxcXYWdnJ4KCgsTly5dF79691eZ369YtMXDgQGFtbS1GjhwphNB8dFaIF9vH2LFjRbt27YS9vb3w9/cX+/fvVxunuOlKa3+VNn0oHT16VFhaWor58+eXOC+p7VnbuoR48Xj6pEmThJ2dnXBychLPnj0rcfstrv3mzZti6tSpokOHDsLW1lb06tVLrFmzRhQWFpbab1FRkVizZo3o06ePsLe3F46OjmLMmDHiwoULauOtWLFC9V47ceKEePbsmViwYIHw8PAQtra2olu3buLjjz8WN27cEK1btxZffPGFEKL4bVhp+/btwtXVVdjY2IgdO3aU+Ojsq9ttce2FhYUiOjpaeHp6CmtrazFw4EBx8uRJYWlpKT755JNSX4Pbt2+LsLAw0blzZ2FtbS08PT3F/PnzRU5Ojmqc4vZr165dEyNHjhTt27cXjo6OYsCAASImJkasW7dOWFpaql7D4tZtedaZEEIYCPEa39z3N5KZmYkGDRpotI8fPx5XrlxBSkqK7osiIr2mPIo3NjZWa3/48CE6duyoca/17+Af/3sWgwcPxqhRo9TaMjMzcfLkSdjZ2VVRVUSkzy5cuIB27dohISFBrV15GervuO/Q2T0LfdWvXz8sX74c06ZNQ4cOHfDkyRNs2bIFCoUCISEhVV0eEemhdu3awczMDF988QVu3LiBf//737h69SpiY2Ph5ORU4d+Wqw/+8ZehFAoFYmJisGXLFmRkZKBmzZpo164dJk2a9EZ8pTgRVY179+4hOjoax44dQ1ZWFho1agQfHx+EhITo9FFmXfnHhwUREUn7x9+zICIiaQwLIiKS9Ebc4H74MA8Khe6ultWvL0NWVq7O+tP3OgD9qUVf6gBYiz7XAehPLbquw9DQAG+/bSw9Yhm9EWGhUAidhoWyT32gL3UA+lOLvtQBsJbi6EsdgP7Uoi91lAcvQxERkSSGBRERSSpzWFy+fBnW1tZq36RZnLy8PHz++edwdXWFg4MDxowZU+xXgRMRkf4rU1jcuHED48aN0+rrkKdMmaL6MZeIiAjcv38fwcHByMnJee1iiYioamgVFoWFhYiJicHgwYPx/PlzyfFPnz6NQ4cOISIiAgMGDICXlxfWrl2LnJwcbN68udxFExGRbmkVFmfOnMHChQsxcuRIhIaGSo5/7NgxGBsbq/24i6mpKZycnNR+fIeIiN4MWoVFy5YtkZycjAkTJmj1+76pqakwNzfXGLd58+aqn5QkIqI3h1afsyju9x5Kk5ubC5lMptFubGyM3Nyyfzilfn3NeVW2hg3r6LzP4uhLHUDF16LIz4dhMT94Xxl1vG5flVFLZdGXWvSlDkB/atGXOsqjUj6UV9p3E778u83aysrK1emHWho2rIMHD6r+Rry+1AFUTi0NG9bBsfcGVug8S+K6c1ul1P93Xj9vch2A/tSi6zoMDQ0q5QC7Uj5nIZPJiv093Ly8vGLPOIiISL9VSlhYWFggIyND4wwjPT0dFhYWldElERFVokoJCzc3Nzx58gTHjx9XtWVnZ+P06dPo1KlTZXRJRESVqELCIjs7G+fOnVPdvHZycoKzszOmTp2KuLg47N+/H++//z7q1KmDoUOHVkSXRESkQxUSFikpKfDz88OlS5dUbUuWLEHXrl0RGRmJmTNnonHjxli7di1MTEwqoksiItKhN+JnVfk0VNXj01Ca/u7r502uA9CfWvg0FBER/WMwLIiISBLDgoiIJDEsiIhIEsOCiIgkMSyIiEgSw4KIiCQxLIiISBLDgoiIJDEsiIhIEsOCiIgkMSyIiEgSw4KIiCQxLIiISBLDgoiIJDEsiIhIEsOCiIgkMSyIiEgSw4KIiCQxLIiISBLDgoiIJDEsiIhIEsOCiIgkMSyIiEgSw4KIiCQxLIiISBLDgoiIJDEsiIhIktZhsXv3bvTu3Rt2dnbw8fFBfHx8qeNnZ2cjPDwcbm5ucHZ2xrhx43Dz5s1ylktERFVBq7BITExEaGgo3NzcsHTpUjg7OyMsLAx79uwpdnwhBEJCQnD48GGEhoYiMjISDx48QHBwMB4/flyhC0BERJXvLW1GioqKgo+PD8LDwwEA7u7uePz4MRYtWgRvb2+N8W/evImzZ88iIiIC/fv3BwC0bNkS3bt3xy+//IIBAwZU3BIQEVGlkzyzyMjIgFwuh5eXl1p7z549kZqaioyMDI1pnj9/DgAwNjZWtZmYmAAAHj16VJ56iYioCkiGRWpqKgDAwsJCrd3c3BwAkJaWpjFN69at0aFDByxduhQ3btxAdnY25s6di9q1a6N79+4VUTcREemQ5GWonJwcAIBMJlNrV5415ObmFjvdZ599htGjR6NXr14AgBo1amDp0qUwMzMrV8FERKR7kmEhhCh1uKGh5snJjRs34O/vj+bNm2PWrFkwMjLCli1bMHHiRKxatQrt27cvU5H168ukR6pgDRvW0XmfxdGXOgD9quV1VEb9+vSa6Est+lIHoD+16Esd5SEZFnXqvFjIvLw8tXblGYVy+MvWrl0LAFi9erXqXoWrqyuGDRuGefPmYfv27WUqMisrFwpF6aFVkRo2rIMHD3J01p++1wFUTi26fgNVRv1/5/XzJtcB6E8tuq7D0NCgUg6wJe9ZKO9VyOVytfb09HS14S+7c+cOWrZsqQoKADAwMICjoyOuX79eroKJiEj3JMPC3NwczZo10/hMxb59+9CiRQs0adJEYxoLCwv88ccfePLkiVr7+fPn0bRp03KWTEREuqbV5yxCQkIQHh4OExMTeHp64sCBA0hKSkJUVBSAF5/WlsvlaNWqFWQyGd5//33s2rULI0eOxNixY2FkZISdO3fi1KlTqmmIiOjNoVVY+Pr6Ij8/H6tXr0ZcXBzMzMwQERGhetIpJSUF4eHhWL9+PTp06IBmzZph8+bNWLhwIcLDw2FgYABLS0usWbMGnTp1qtQFIiKiiqdVWACAv78//P39ix3m6+sLX19ftbaWLVti2bJl5auOiIj0Ar91loiIJDEsiIhIEsOCiIgkMSyIiEgSw4KIiCQxLIiISBLDgoiIJDEsiIhIEsOCiIgkMSyIiEgSw4KIiCQxLIiISBLDgoiIJDEsiIhIEsOCiIgkMSyIiEgSw4KIiCQxLIiISBLDgoiIJDEsiIhIEsOCiIgkMSyIiEgSw4KIiCQxLIiISBLDgoiIJDEsiIhIEsOCiIgkMSyIiEiS1mGxe/du9O7dG3Z2dvDx8UF8fHyp4ysUCixbtgzdunWDnZ0d+vbti4SEhPLWS0REVeAtbUZKTExEaGgohg8fDjc3NyQnJyMsLAxGRkbw9vYudpp58+YhNjYWU6dORevWrZGQkIBp06ZBJpOhc+fOFboQRERUubQKi6ioKPj4+CA8PBwA4O7ujsePH2PRokXFhoVcLkdMTAy++OILDB48GADg4uKCmzdv4siRIwwLIqI3jGRYZGRkQC6XY+rUqWrtPXv2RFJSEjIyMmBmZqY2LDk5GUZGRujfv79a+8aNG8tfMRER6ZzkPYvU1FQAgIWFhVq7ubk5ACAtLU1jmqtXr8LCwgLHjx9Hv3790KZNG3h5eSExMbEiaiYiIh2TDIucnBwAgEwmU2s3NjYGAOTm5mpMk52djbt372LWrFkIDAzEqlWrYG1tjSlTpuDEiRMVUTcREemQ5GUoIUSpww0NNfOmoKAA2dnZWL58Obp06QIA6NixI1JTU7FkyRJ07NixTEXWry+THqmCNWxYR+d9Fkdf6gD0q5bXURn169Nroi+16EsdgP7Uoi91lIdkWNSp82Ih8/Ly1NqVZxTK4S8zNjZGtWrV4OrqqmozNDREp06dsHXr1jIXmZWVC4Wi9NCqSA0b1sGDBzk660/f6wAqpxZdv4Eqo/6/8/p5k+sA9KcWXddhaGhQKQfYkpehlPcq5HK5Wnt6erra8JeZm5tDoVCgsLBQrb2goAAGBgavXSwREVUNybAwNzdHs2bNsGfPHrX2ffv2oUWLFmjSpInGNO7u7hBCICkpSdVWWFiII0eOwNHRsQLKJiIiXdLqcxYhISEIDw+HiYkJPD09ceDAASQlJSEqKgrAixvacrkcrVq1gkwmg4uLCzp37oy5c+fi6dOnaNGiBTZt2oTbt2/jm2++qdQFIiKiiqdVWPj6+iI/Px+rV69GXFwczMzMEBERgV69egEAUlJSEB4ejvXr16NDhw4AgMWLF2PRokVYuXIlHj9+jDZt2mD16tWwsbGpvKUhIqJKYSCkHnfSA7zBXfUq6wb3sfcGVug8S+K6cxtvcP+D6gD0p5Z/zA1uIiIihgUREUliWBARkSSGBRERSWJYEBGRJIYFERFJYlgQEZEkhgUREUliWBARkSSGBRERSWJYEBGRJIYFERFJYlgQEZEkhgUREUliWBARkSSGBRERSWJYEBGRJIYFERFJYlgQEZEkhgUREUliWBARkSSGBRERSWJYEBGRJIYFERFJYlgQEZEkhgUREUliWBARkSSGBRERSWJYEBGRJK3DYvfu3ejduzfs7Ozg4+OD+Ph4rTu5e/cuHB0d8f33379OjUREVMW0CovExESEhobCzc0NS5cuhbOzM8LCwrBnzx7JaYUQmDVrFnJzc8tdLBERVY23tBkpKioKPj4+CA8PBwC4u7vj8ePHWLRoEby9vUuddtOmTUhNTS1/pUREVGUkzywyMjIgl8vh5eWl1t6zZ0+kpqYiIyOj1GkXLlyIL7/8svyVEhFRlZEMC+VZgYWFhVq7ubk5ACAtLa3Y6RQKBWbOnAkfHx94eHiUt04iIqpCkpehcnJyAAAymUyt3djYGABKvBexbt063Lp1C8uXLy9vjahfXyY9UgVr2LCOzvssjr7UAehXLa+jMurXp9dEX2rRlzoA/alFX+ooD8mwEEKUOtzQUPPk5MaNG/juu++wePFi1KlT/hcpKysXCkXpdVSkhg3r4MGDHJ31p+91AJVTi67fQJVR/995/bzJdQD6U4uu6zA0NKiUA2zJy1DKnX1eXp5au/KM4tUwKCoqQnh4OLy9veHq6orCwkIUFhYCeHFpSvl/IiJ6c0iGhfJehVwuV2tPT09XG6509+5dnD9/HvHx8bC2tlb9A4Do6GjV/4mI6M0heRnK3NwczZo1w549e9CjRw9V+759+9CiRQs0adJEbfxGjRph69atGvMZNGgQhg4dioEDB1ZA2UREpEtafc4iJCQE4eHhMDExgaenJw4cOICkpCRERUUBALKzsyGXy9GqVSvIZDLY2toWO59GjRqVOIyIiPSXVp/g9vX1xeeff46jR48iJCQEv/76KyIiItCrVy8AQEpKCvz8/HDp0qVKLZaIiKqGVmcWAODv7w9/f/9ih/n6+sLX17fU6a9evVq2yoiISG/wW2eJiEgSw4KIiCQxLIiISBLDgoiIJDEsiIhIEsOCiIgkMSyIiEgSw4KIiCQxLIiISBLDgoiIJDEsiIhIEsOCiIgkMSyIiEgSw4KIiCQxLIiISBLDgoiIJDEsiIhIEsOCiIgkMSyIiEgSw4KIiCQxLIiISBLDgoiIJDEsiIhIEsOCiIgkMSyIiEgSw4KIiCQxLIiISBLDgoiIJGkdFrt370bv3r1hZ2cHHx8fxMfHlzr+gwcPMHv2bHTp0gUODg7w9fVFUlJSeeslIqIq8JY2IyUmJiI0NBTDhw+Hm5sbkpOTERYWBiMjI3h7e2uMn5+fj9GjRyMnJwcTJ05Eo0aNsHfvXkyePBlFRUXo06dPhS8IERFVHq3CIioqCj4+PggPDwcAuLu74/Hjx1i0aFGxYXH48GFcuXIFcXFxsLOzAwC4urrizp07+OGHHxgWRERvGMnLUBkZGZDL5fDy8lJr79mzJ1JTU5GRkaExjbGxMfz8/GBra6vW/s4770Aul5ezZCIi0jXJM4vU1FQAgIWFhVq7ubk5ACAtLQ1mZmZqw1xcXODi4qLWVlBQgEOHDuE///lPuQomIiLdkzyzyMnJAQDIZDK1dmNjYwBAbm6uVh19/fXXuHnzJsaOHVvWGomIqIpJnlkIIUodbmhYet4IIfD1119j3bp1GDVqFLp37162CgHUry+THqmCNWxYR+d9Fkdf6gD0q5bXURn169Nroi+16EsdgP7Uoi91lIdkWNSp82Ih8/Ly1NqVZxTK4cXJz8/HzJkzkZCQgFGjRmHGjBmvVWRWVi4UitJDqyI1bFgHDx7k6Kw/fa8DqJxadP0Gqoz6/87r502uA9CfWnRdh6GhQaUcYEuGhfJehVwuh5WVlao9PT1dbfircnNzMW7cOJw9exazZs3C8OHDK6JeIiKqApL3LMzNzdGsWTPs2bNHrX3fvn1o0aIFmjRpojFNUVERPvjgA5w/fx5RUVEMCiKiN5xWn7MICQlBeHg4TExM4OnpiQMHDiApKQlRUVEAgOzsbMjlcrRq1QoymQw//fQTTp06BT8/PzRu3Bjnzp1TzcvAwABt27atlIUhIqLKoVVY+Pr6Ij8/H6tXr0ZcXBzMzMwQERGBXr16AQBSUlIQHh6O9evXo0OHDti7dy8AIDY2FrGxsWrzqlatGn7//fcKXgwiIqpMWoUFAPj7+8Pf37/YYb6+vvD19VX9vX79+vJXRkREeoPfOktERJIYFkREJIlhQUREkhgWREQkiWFBRESSGBZERCSJYUFERJIYFkREJIlhQUREkhgWREQkiWFBRESSGBZERCSJYUFERJIYFkREJIlhQUREkhgWREQkiWFBRESSGBZERCSJYUFERJIYFkREJIlhQUREkhgWREQkiWFBRESSGBZERCSJYUFERJIYFkREJIlhQUREkhgWREQkiWFBRESStA6L3bt3o3fv3rCzs4OPjw/i4+NLHT8vLw+ff/45XF1d4eDggDFjxuDmzZvlLJeIiKqCVmGRmJiI0NBQuLm5YenSpXB2dkZYWBj27NlT4jRTpkzBnj17EBoaioiICNy/fx/BwcHIycmpsOKJiEg33tJmpKioKPj4+CA8PBwA4O7ujsePH2PRokXw9vbWGP/06dM4dOgQfvjhB3h4eAAA2rdvj27dumHz5s0YO3ZsBS4CERFVNskzi4yMDMjlcnh5eam19+zZE6mpqcjIyNCY5tixYzA2Noarq6uqzdTUFE5OTjh8+HAFlE1ERLokeWaRmpoKALCwsFBrNzc3BwCkpaXBzMxMYxpzc3NUq1ZNrb158+ZISkoqc5GGhgZlnqa8qqLP4uhLHYB+1fI6KqN+fXpN9KUWfakD0J9adFlHZfUlGRbKewwymUyt3djYGACQm5urMU1ubq7G+MppihtfyttvG5d5mvKqX1+z/qqgL3UAlVOL685tFT7PklRG/X/39fM69KUOQH9q0Zc6ykPyMpQQovQZGGrOorRpihufiIj0m+Seu06dOgBePAr7MuUZgnL4y2Qymcb4ynkUd8ZBRET6TTIslPcq5HK5Wnt6erra8FenycjI0DjDSE9PL3Z8IiLSb5JhYW5ujmbNmml8pmLfvn1o0aIFmjRpojGNm5sbnjx5guPHj6vasrOzcfr0aXTq1KkCyiYiIl3S6nMWISEhCA8Ph4mJCTw9PXHgwAEkJSUhKioKwIsgkMvlaNWqFWQyGZycnODs7IypU6ciNDQU9erVQ3R0NOrUqYOhQ4dW6gIREVHFMxBSd7D/z08//YTVq1fj7t27MDMzw9ixY9G/f38AwPbt2xEeHo7169ejQ4cOAIDHjx9jwYIFSE5OhkKhgKOjI2bOnIl33nmn0haGiIgqh9ZhQURE/1x8jpWIiCQxLIiISBLD4iVl/Rr2ynb58mVYW1vj3r17VdK/QqHA5s2b0bdvXzg4OKB79+6YP3/+a30Kv7yEEFi7di169uwJOzs79OvXDz///LPO63jVhAkT0KNHjyrpu7CwEHZ2drCyslL75+DgoPNafv31VwwdOhRt27aFm5sbvvzyy2I/a1WZTp48qfFavPxvx44dOq1n8+bN8PHxgb29Pfr27Ytdu3bptP+KptXTUP8Eyq9hHz58ONzc3JCcnIywsDAYGRkV+826le3GjRsYN24cCgsLdd630qpVq/Ddd99h1KhRcHFxQVpaGhYvXozr16/jxx9/1GktK1aswOLFi/HRRx/B3t4ehw8fRmhoKKpVq4ZevXrptBalnTt3Yv/+/WjevHmV9J+Wlobnz58jIiICLVq0ULXr+lsSzp07hxEjRqBr165YtmwZ0tPT8e233yI7O1v1xKQuWFtbIzY2Vq1NCIGPP/4YT58+RefOnXVWS2xsLD777DOMHDkS7u7uOHToEKZPn47q1avDx8dHZ3VUKEFCCCG6d+8uJk+erNY2adIk4e3trdM6CgoKxMaNG4WDg4NwdnYWlpaW4u7duzqtQQghFAqFcHJyEp999plae0JCgrC0tBS///67zmrJz88XTk5O4osvvlBrDwwMFEOHDtVZHS+7d++ecHJyEh4eHqJ79+5VUsOuXbtE69atxdOnT6ukf6WAgAAREBAgFAqFqm3jxo2iW7duVV7b2rVrRevWrcW5c+d02q+fn58ICgpSaxs2bJgIDAzUaR0ViZeh8Hpfw15Zzpw5g4ULF2LkyJEIDQ3VWb+vysvLQ79+/dCnTx+1duWjz69+or8yVatWDRs2bND4HZTq1avj+fPnOqvjZbNnz4arqytcXFyqpH/gxWXK5s2bo1atWlVWg/LDtkOHDoWBwf++7TQgIADJyclVWtuDBw+waNEi1eUxXXr+/Lnqy1aV6tWrh0ePHum0jorEsIB2X8OuKy1btkRycjImTJig8RXvuiSTyTB79mw4OjqqtScnJwMAWrVqpbNaDA0NYWVlhX/9618QQiAzMxMrV67E8ePH4efnp7M6lOLi4nDp0iV88sknOu/7ZVevXkWNGjUwatQoODg4wMnJCXPmzNHpPaVr165BCAETExNMnjwZ9vb2cHR0xKeffopnz57prI7iREdHw9DQEJMnT9Z538HBwThy5AiSkpKQm5uLPXv2ICUlBe+9957Oa6kovGeB1/sa9srSoEEDnfVVVufPn8fKlSvRvXt3tGzZskpq2LdvHyZOnAgA8PT0RL9+/XTa/+3btzF//nzMnz8fpqamOu37VVeuXEFubi4GDx6M8ePH4+LFi4iOjkZaWhrWr1+vdqRfWbKzswEAM2fORI8ePbBs2TJcvXoV3333HZ4/f44FCxZUeg3FycrKQnx8PEaOHIm6devqvP/evXvjxIkTakE1YMAAjB49Wue1VBSGBV7va9j/ac6cOYPx48ejWbNmmDt3bpXV0aZNG2zcuBFXr17FokWLMHbsWKxbt04nO0YhBGbNmoXOnTujZ8+eld6flKioKJiYmMDKygoA4OTkhPr162P69Ok4fvy42i9VVpaCggIAQLt27fDpp58CAFxcXCCEQEREBEJCQjR+HE0X4uLioFAoEBwcrPO+AeCDDz7Af//7X4SHh6NNmzY4f/48vv/+e9UZ+5uIYYHX+xr2f5LExETMnDkTLVq0wKpVq/D2229XWS1mZmYwMzODk5MTZDIZwsLC8N///hft2rWr9L5jYmJw9epV/Pzzz6qn1JQHGoWFhahWrZpOQkvJ2dlZo83T0xPAi7MOXYSF8uzbw8NDrd3NzQ0LFizA1atXqyQs9u7dC3d39yo5+zt79iyOHj2K+fPnw9fXF8CLdVW3bl3MmTMHQ4YMgaWlpc7rKi8eMuP1vob9n2LNmjWYOnUq7O3tERMTg0aNGum8hkePHiE+Ph73799Xa2/Tpg0A4M8//9RJHXv37sXDhw/h5uYGa2trWFtbIz4+HnK5HNbW1jp9jj8rKwtxcXEaD18o7xPoKtCVj+zm5+ertSvPOHQZnkr379/H77//XmWPqN65cwcANA5g2rdvDwC4fv26zmuqCAwLvN7XsP8TxMXFYcGCBfDx8cGqVauq7AxLoVBg5syZGs/QHzt2DAB0dpT2+eefY+vWrWr/unTpgsaNG6v+rysGBgaYM2cONm7cqNaemJiIatWqaTyYUFlatmyJpk2bIjExUa394MGDeOutt6rkA4Lnz58HAJ29Bq9SHlyeOXNGrf3cuXMAgKZNm+q6pArBy1D/R+pr2P9psrKy8NVXX6Fp06YICAjA77//rja8efPmOjvFNzU1xbBhw7By5UoYGRnB1tYWZ86cwYoVKzB48GCdfZNxcf3Uq1cPNWrUgK2trU5qUDI1NUVAQAA2bNgAmUyG9u3b48yZM1i+fDkCAgJUT/JVNgMDA4SGhqp+jsDX1xcXL17EsmXLEBgYWCWXga5du4ZatWpV2U7Z2toa3bt3x1dffYWcnBy8++67uHjxIpYuXQoPDw+dP8ZbURgW/8fX1xf5+flYvXo14uLiYGZmhoiIiCr7dHBVO3LkCP766y/cvn0bAQEBGsMjIyN1+hhgeHg4/v3vf2Pr1q2Ijo5G48aNMXHiRIwaNUpnNeibsLAw/Otf/8K2bduwcuVK/Otf/8LEiRN1/sRNr169UKNGDSxduhTjxo1D/fr1ERISgnHjxum0DqXMzMwqeQLqZVFRUViyZAnWrl2LrKwsNG3aFCNHjtT4rNCbhF9RTkREknjPgoiIJDEsiIhIEsOCiIgkMSyIiEgSw4KIiCQxLIiISBLDgoiIJDEsiIhIEsOCiIgk/X+1DMRFpFIDMAAAAABJRU5ErkJggg==\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_beliefs(starting_state, \\\"Categorical distribution over the starting state\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"k1hodf-fI02_\"\n },\n \"source\": [\n \"Now let's imagine we're moving **\\\"RIGHT\\\"** - write the conditional expectation, that will create the state vector corresponding to the new state after taking a step to the right.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 28,\n \"metadata\": {\n \"id\": \"D8Q_dTRSMSje\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": \"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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Redefine the action here, just for reference \\\"\\\"\\\"\\n\",\n \"actions = [\\\"UP\\\", \\\"DOWN\\\", \\\"LEFT\\\", \\\"RIGHT\\\", \\\"STAY\\\"]\\n\",\n \"\\n\",\n \"\\\"\\\"\\\" Generate the next state vector, given the starting state and the B matrix\\\"\\\"\\\"\\n\",\n \"right_action_idx = actions.index(\\\"RIGHT\\\") \\n\",\n \"next_state = B[:,:, right_action_idx].dot(starting_state) # input the indices to the B matrix\\n\",\n \"\\n\",\n \"\\\"\\\"\\\" Plot the next state, after taking the action \\\"\\\"\\\"\\n\",\n \"plot_point_on_grid(next_state, grid_locations)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"0h9yH5ARJI-E\"\n },\n \"source\": [\n \"Now let's imagine we're moving **\\\"DOWN\\\"** from where we just landed - write the conditional expectation, that will create the state vector corresponding to the new state after taking a step down.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 29,\n \"metadata\": {\n \"id\": \"nXaYlJElNRAO\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": \"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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Generate the next state vector, given the previous state and the B matrix\\\"\\\"\\\"\\n\",\n \"prev_state = next_state.copy()\\n\",\n \"down_action_index = actions.index(\\\"DOWN\\\")\\n\",\n \"next_state = B[:,:,down_action_index].dot(prev_state)\\n\",\n \"\\n\",\n \"\\\"\\\"\\\" Plot the new state vector, after making the movement \\\"\\\"\\\"\\n\",\n \"plot_point_on_grid(next_state, grid_locations)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"YkxsKuonRbjX\"\n },\n \"source\": [\n \"### 3. The prior over observations: the $\\\\mathbf{C}$ vector or $\\\\tilde{P}(o)$\\n\",\n \"\\n\",\n \"---\\n\",\n \"\\n\",\n \"The (biased) generative model's prior preference for particular observations, encoded in terms of probabilities.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 30,\n \"metadata\": {\n \"id\": \"3jSjRkyoPt1w\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Create an empty vector to store the preferences over observations \\\"\\\"\\\"\\n\",\n \"C = np.zeros(n_observations)\\n\",\n \"\\n\",\n \"\\\"\\\"\\\" Choose an observation index to be the 'desired' rewarding index, and fill out the C vector accordingly \\\"\\\"\\\"\\n\",\n \"desired_location = (2,2) # choose a desired location\\n\",\n \"desired_location_index = grid_locations.index(desired_location) # get the linear index of the grid location, in terms of 0 through 8\\n\",\n \"\\n\",\n \"C[desired_location_index] = 1.0 # set the preference for that location to be 100%, i.e. 1.0\\n\",\n \"\\n\",\n \"\\\"\\\"\\\" Let's look at the prior preference distribution \\\"\\\"\\\"\\n\",\n \"plot_beliefs(C, title_str = \\\"Preferences over observations\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"syuovouSRmQe\"\n },\n \"source\": [\n \"### 3. The prior over hidden states: the $\\\\mathbf{D}$ vector or $P(s)$\\n\",\n \"\\n\",\n \"---\\n\",\n \"\\n\",\n \"The generative model's prior belief over hidden states at the first timestep.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 31,\n \"metadata\": {\n \"id\": \"ElcxKHl_QHpv\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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m3Mzc3x7lz5/DNN9/A09MT/fr1w9GjRxEVFQU/Pz8UFhYiKSlJvV5fXFysMffq1av46quv4ObmBltbW0RERGDr1q14+PAhfHx88PDhQ2zbtg0mJiaYNm0aAGD48OHYuHEjJk2ahLCwMLRp0waXLl1CUlISgoKC+Oa52mq4C4eoLqkuU8zOztZq+xcvp1N58fJHIYS4dOmSmDhxoujZs6fo0aOHCA0NLXcpYkXzKjN69GgRGhoq9u/fLwYPHiwcHBxEcHBwucsAVceOiooSLi4uonv37mL48OFi9+7dVR77xUs2hRDixo0bYsaMGaJ3797C0dFRBAQEiI0bN4qysjL1NhVdsvn06VOxceNG8cYbb4gePXoIFxcXMWHCBPHLL79Uez9zc3PFBx98IPr27SscHByEv7+/WL9+vcYxVQoLC4Wjo6MICgqqdF///Oc/hYeHh3BwcBBDhgwRy5cvF48ePVJvo7pkU9t/A3v27BFBQUHqv9fRo0eLH374QWOb3bt3q4+5Z88eoVQqxdq1a8WgQYOEg4ODGDBggJg+fbrIysoSvXv3FlFRUeq5J06cEAMHDhT29vbi888/F0I8u1R2+/btIjAwUDg4OAh3d3cRHR0tfvvtN43j/vbbb2LKlCnCw8ND2NvbiyFDhojVq1erL9OlmjMQgl+MTkQkFVwcIyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJyF/izVkPHhRDqdTdlaUtW8qQl1eks+Ppew5Af7LoSw6AWfQ5B6A/WXSdw9DQAC1aVP4Gtr9E6SuVQqelrzqmPtCXHID+ZNGXHACzVERfcgD6k0VfcgBc3iEikhSWPhGRhLx06f/666+wt7fX+NTFihQXF2PBggXqL2ieMGGC+qNziYioYbxU6V+/fh1RUVFafaTte++9h5SUFMTExCAuLg737t3DmDFjUFhYWOOwRERUO1qVfllZGbZv344RI0bgyZMn1W5//vx5HD9+HHFxcQgKCsKQIUOwadMmFBYWYseOHbUOTURENaNV6aenp2Pp0qUYN24cYmJiqt3+1KlTMDEx0fiCDXNzc7i6uuLEiRM1T0tERLWiVenb2NggNTUVU6ZM0ep7UDMzM2FlZVVu244dO1b4FXJERKQbWl2n36pVq5faaVFRkfr7Lp9nYmKCoqKXf5NCy5bl96UNZUkJDI2MajTXwuLlvoOzNseqyxz1SV+y6EsOgFkqoi85AP3Joi85gHp6c1ZV38tSk++3zMsrqtGbGywsTHHqzcq/0q4ueez9Frm5dfsitYWFaZ3vs6b0JYu+5ACYRZ9zAPqTRdc5DA0NqjxRrpfr9GUymcZ3ZaoUFxdX+AyAiIh0o15K39raGtnZ2eXO+G/evAlra+v6OCQREWmhXkrf09MTf/75J06fPq0ey8/Px/nz59G3b9/6OCQREWmhTko/Pz8fFy5cUL9I6+rqCjc3N8yYMQOJiYk4cuQI3nnnHZiamiIsLKwuDklERDVQJ6V/7NgxhISE4PLly+qx1atXw9vbG0uWLEFsbCzatm2LTZs2wczMrC4OSURENWAgqrrURk/w6p2Gpy9Z9CUHwCz6nAPQnyySuHqHiIj0E0ufiEhCWPpERBLC0icikhCWPhGRhLD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEJY+kREEsLSJyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikhCtS3///v0YOnQonJyc4O/vj6SkpCq3z8/Ph1wuh6enJ9zc3BAVFYUbN27UMi4REdWGVqV/8OBBxMTEwNPTEwkJCXBzc8Ps2bORkpJS4fZCCERHR+PEiROIiYnBkiVLkJubizFjxqCgoKBO7wAREWmvsTYbxcfHw9/fH3K5HADg5eWFgoICrFixAn5+fuW2v3HjBn766SfExcVh+PDhAAAbGxv4+Pjg6NGjCAoKqrt7QEREWqv2TD87OxsKhQJDhgzRGPf19UVmZiays7PLzXny5AkAwMTERD1mZmYGAHj48GFt8hIRUS1UW/qZmZkAAGtra41xKysrAEBWVla5OV26dEHv3r2RkJCA69evIz8/H5988gn+67/+Cz4+PnWRm4iIaqDa5Z3CwkIAgEwm0xhXncUXFRVVOG/+/PkYP348AgICAABGRkZISEiApaVlrQITEVHNVVv6Qogqbzc0LP9k4fr16wgNDUXHjh0xZ84cGBsb45tvvsHUqVOxfv169OrV66VCtmwpq34jPWBhYfqX2GdN6UsWfckBMEtF9CUHoD9Z9CUHoEXpm5o+C1tcXKwxrjrDV93+vE2bNgEANmzYoF7L9/DwwKhRo7Bw4ULs3r37pULm5RVBqaz6h09FdP1A5+YW1un+LCxM63yfNaUvWfQlB8As+pwD0J8sus5haGhQ5YlytWv6qrV8hUKhMX7z5k2N2593584d2NjYqAsfAAwMDODi4oJr165pl5yIiOpctaVvZWWFDh06lLsm//Dhw+jUqRPatWtXbo61tTV+//13/PnnnxrjFy9eRPv27WsZmYiIakqr6/Sjo6Mhl8thZmaGAQMGIC0tDcnJyYiPjwfw7N23CoUCnTt3hkwmwzvvvIN9+/Zh3LhxmDhxIoyNjbF3716cO3dOPYeIiHRPq9IPDg5GSUkJNmzYgMTERFhaWiIuLk59Zc6xY8cgl8uxZcsW9O7dGx06dMCOHTuwdOlSyOVyGBgYwNbWFhs3bkTfvn3r9Q4REVHltCp9AAgNDUVoaGiFtwUHByM4OFhjzMbGBmvWrKldOiIiqlP8lE0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEJY+kREEsLSJyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikhCWPhGRhLD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSonXp79+/H0OHDoWTkxP8/f2RlJRU5fZKpRJr1qzBoEGD4OTkhMDAQBw4cKC2eYmIqBYaa7PRwYMHERMTg7Fjx8LT0xOpqamYPXs2jI2N4efnV+GchQsXYufOnZgxYwa6dOmCAwcO4P3334dMJkP//v3r9E4QEZF2tCr9+Ph4+Pv7Qy6XAwC8vLxQUFCAFStWVFj6CoUC27dvx0cffYQRI0YAANzd3XHjxg2cPHmSpU9E1ECqLf3s7GwoFArMmDFDY9zX1xfJycnIzs6GpaWlxm2pqakwNjbG8OHDNca3bdtW+8RERFRj1a7pZ2ZmAgCsra01xq2srAAAWVlZ5eZkZGTA2toap0+fxrBhw9CtWzcMGTIEBw8erIvMRERUQ9WWfmFhIQBAJpNpjJuYmAAAioqKys3Jz89HTk4O5syZg9GjR2P9+vWwt7fHe++9hzNnztRFbiIiqoFql3eEEFXebmhY/udGaWkp8vPzsXbtWgwcOBAA0KdPH2RmZmL16tXo06fPS4Vs2VJW/UZ6wMLC9C+xz5rSlyz6kgNgloroSw5Af7LoSw5Ai9I3NX0Wtri4WGNcdYavuv15JiYmaNSoETw8PNRjhoaG6Nu3L3bt2vXSIfPyiqBUVv3DpyK6fqBzcwvrdH8WFqZ1vs+a0pcs+pIDYBZ9zgHoTxZd5zA0NKjyRLna5R3VWr5CodAYv3nzpsbtz7OysoJSqURZWZnGeGlpKQwMDKpPTURE9aLa0reyskKHDh2QkpKiMX748GF06tQJ7dq1KzfHy8sLQggkJyerx8rKynDy5Em4uLjUQWwiIqoJra7Tj46Ohlwuh5mZGQYMGIC0tDQkJycjPj4ewLMXbhUKBTp37gyZTAZ3d3f0798fn3zyCR49eoROnTrhq6++wu3bt7Fs2bJ6vUNERFQ5rUo/ODgYJSUl2LBhAxITE2FpaYm4uDgEBAQAAI4dOwa5XI4tW7agd+/eAICVK1dixYoVWLduHQoKCtCtWzds2LABDg4O9XdviIioSgaiustz9EBtXsg99eZb9ZCoPI+93/KFXAnlAJhFn3MA+pPlL/dCLhER/X2w9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEJY+kREEsLSJyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikhCWPhGRhLD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUmI1qW/f/9+DB06FE5OTvD390dSUpLWB8nJyYGLiws+//zzmmQkIqI6olXpHzx4EDExMfD09ERCQgLc3Nwwe/ZspKSkVDtXCIE5c+agqKio1mGJiKh2GmuzUXx8PPz9/SGXywEAXl5eKCgowIoVK+Dn51fl3K+++gqZmZm1T0pERLVW7Zl+dnY2FAoFhgwZojHu6+uLzMxMZGdnVzl36dKl+Pjjj2uflIiIaq3a0ledpVtbW2uMW1lZAQCysrIqnKdUKhEbGwt/f3/069evtjmJiKgOVLu8U1hYCACQyWQa4yYmJgBQ6Vr95s2bcevWLaxdu7a2GdGypaz6jfSAhYXpX2KfNaUvWfQlB8AsFdGXHID+ZNGXHIAWpS+EqPJ2Q8PyTxauX7+O5cuXY+XKlTA1rf2dzcsrglJZdY6K6PqBzs0trNP9WViY1vk+a0pfsuhLDoBZ9DkHoD9ZdJ3D0NCgyhPlapd3VKVdXFysMa46w3+x1J8+fQq5XA4/Pz94eHigrKwMZWVlAJ4t+ah+T0REuldt6avW8hUKhcb4zZs3NW5XycnJwcWLF5GUlAR7e3v1LwBYtWqV+vdERKR71S7vWFlZoUOHDkhJScHgwYPV44cPH0anTp3Qrl07je1bt26NXbt2ldvP22+/jbCwMLz11lt1EJuIiGpCq+v0o6OjIZfLYWZmhgEDBiAtLQ3JycmIj48HAOTn50OhUKBz586QyWRwdHSscD+tW7eu9DYiIqp/Wr0jNzg4GAsWLMAPP/yA6Oho/Otf/0JcXBwCAgIAAMeOHUNISAguX75cr2GJiKh2tDrTB4DQ0FCEhoZWeFtwcDCCg4OrnJ+RkfFyyYiIqM7xUzaJiCSEpU9EJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikhCWPhGRhLD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEJY+kREEsLSJyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJiNalv3//fgwdOhROTk7w9/dHUlJSldvn5uZi7ty5GDhwIJydnREcHIzk5OTa5iUiolporM1GBw8eRExMDMaOHQtPT0+kpqZi9uzZMDY2hp+fX7ntS0pKMH78eBQWFmLq1Klo3bo1Dh06hOnTp+Pp06d444036vyOEBFR9bQq/fj4ePj7+0MulwMAvLy8UFBQgBUrVlRY+idOnMDVq1eRmJgIJycnAICHhwfu3LmDL7/8kqVPRNRAql3eyc7OhkKhwJAhQzTGfX19kZmZiezs7HJzTExMEBISAkdHR43x1157DQqFopaRiYiopqo908/MzAQAWFtba4xbWVkBALKysmBpaalxm7u7O9zd3TXGSktLcfz4cbz++uu1CkxERDVX7Zl+YWEhAEAmk2mMm5iYAACKioq0OtBnn32GGzduYOLEiS+bkYiI6ki1Z/pCiCpvNzSs+ueGEAKfffYZNm/ejMjISPj4+LxcQgAtW8qq30gPWFiY/iX2WVP6kkVfcgDMUhF9yQHoTxZ9yQFoUfqmps/CFhcXa4yrzvBVt1ekpKQEsbGxOHDgACIjIzFr1qwahczLK4JSWfUPn4ro+oHOzS2s0/1ZWJjW+T5rSl+y6EsOgFn0OQegP1l0ncPQ0KDKE+VqS1+1lq9QKGBnZ6cev3nzpsbtLyoqKkJUVBR++uknzJkzB2PHjn2p4EREVPeqXdO3srJChw4dkJKSojF++PBhdOrUCe3atSs35+nTp5g8eTIuXryI+Ph4Fj4RkZ7Q6jr96OhoyOVymJmZYcCAAUhLS0NycjLi4+MBAPn5+VAoFOjcuTNkMhm+/vprnDt3DiEhIWjbti0uXLig3peBgQG6d+9eL3eGiIiqplXpBwcHo6SkBBs2bEBiYiIsLS0RFxeHgIAAAMCxY8cgl8uxZcsW9O7dG4cOHQIA7Ny5Ezt37tTYV6NGjXDlypU6vhtERKQNrUofAEJDQxEaGlrhbcHBwQgODlb/ecuWLbVPRkREdY6fsklEJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikhCWPhGRhLD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEJY+kREEsLSJyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJCEufiEhCWPpERBKidenv378fQ4cOhZOTE/z9/ZGUlFTl9sXFxViwYAE8PDzg7OyMCRMm4MaNG7WMS0REtaFV6R88eBAxMTHw9PREQkIC3NzcMHv2bKSkpFQ657333kNKSgpiYmIQFxeHe/fuYcyYMSgsLKyz8ERE9HIaa7NRfHw8/P39IZfLAQBeXl4oKCjAihUr4OfnV2778+fP4/jx4/jyyy/Rr18/AECvXr0waNAg7NixAxMnTqzDu0BERNqq9kw/OzsbCoUCQ4YM0Rj39fVFZmYmsrOzy805deoUTExM4OHhoR4zNzeHq6srTpw4UQexiYioJqo908/MzAQAWFtba4xbWVkBALKysmBpaVlujpWVFRo1aqQx3rFjRyQnJ790SENDg5ee0xDqI6c+3Xd9yaIvOQBmqYi+5AD0J4suc1R3rGpLX7UGL5PJNMZNTEwAAEVFReXmFBUVldteNaei7avTooXJS89R8dj7bY3nvqyWLcvfZ33cZ03pSxZ9yQEwS0X0JQegP1n0JQegxfKOEKLqHRiW30VVcyranoiIdKPaBjY1NQXw7BLM56nO2FW3P08mk5XbXrWPip4BEBGRblRb+qq1fIVCoTF+8+ZNjdtfnJOdnV3ujP/mzZsVbk9ERLpRbelbWVmhQ4cO5a7JP3z4MDp16oR27dqVm+Pp6Yk///wTp0+fVo/l5+fj/Pnz6Nu3bx3EJiKimtDqOv3o6GjI5XKYmZlhwIABSEtLQ3JyMuLj4wE8K3SFQoHOnTtDJpPB1dUVbm5umDFjBmJiYtC8eXOsWrUKpqamCAsLq9c7RERElTMQ1b1S+3++/vprbNiwATk5ObC0tMTEiRMxfPhwAMDu3bshl8uxZcsW9O7dGwBQUFCAxYsXIzU1FUqlEi4uLoiNjcVrr71Wb3eGiIiqpnXpExHRXx+vnyQikhCWPhGRhLD0n/OyHx9d33799VfY29vj7t27DXJ8pVKJHTt2IDAwEM7OzvDx8cGiRYtq9K7q2hJCYNOmTfD19YWTkxOGDRuG7777Tuc5XjRlyhQMHjy4QY5dVlYGJycn2NnZafxydnbWeZZ//etfCAsLQ/fu3eHp6YmPP/64wvfq1KezZ8+Weyye/7Vnzx6d5tmxYwf8/f3Ro0cPBAYGYt++fTo9fmW0unpHClQfHz127Fh4enoiNTUVs2fPhrGxcYWfJFrfrl+/jqioKJSVlen82Crr16/H8uXLERkZCXd3d2RlZWHlypW4du0a/vd//1enWb744gusXLkS//3f/40ePXrgxIkTiImJQaNGjRAQEKDTLCp79+7FkSNH0LFjxwY5flZWFp48eYK4uDh06tRJPa7rd71fuHAB7777Lry9vbFmzRrcvHkT//M//4P8/Hz1FX66YG9vj507d2qMCSHwwQcf4NGjR+jfv7/OsuzcuRPz58/HuHHj4OXlhePHj2PmzJlo0qQJ/P39dZajQoKEEEL4+PiI6dOna4xNmzZN+Pn56TRHaWmp2LZtm3B2dhZubm7C1tZW5OTk6DSDEEIolUrh6uoq5s+frzF+4MABYWtrK65cuaKzLCUlJcLV1VV89NFHGuOjR48WYWFhOsvxvLt37wpXV1fRr18/4ePj0yAZ9u3bJ7p06SIePXrUIMdXCQ8PF+Hh4UKpVKrHtm3bJgYNGtTg2TZt2iS6dOkiLly4oNPjhoSEiIiICI2xUaNGidGjR+s0R0W4vIOafXx0fUlPT8fSpUsxbtw4xMTE6Oy4LyouLsawYcPwxhtvaIyrLrl98R3a9alRo0bYunVrue9haNKkCZ48eaKzHM+bO3cuPDw84O7u3iDHB54t/3Xs2BFNmzZtsAyqN12GhYXBwOD/f7pjeHg4UlNTGzRbbm4uVqxYoV520qUnT56oP5RSpXnz5nj48KFOc1SEpQ/tPj5aV2xsbJCamoopU6aU+2hqXZLJZJg7dy5cXFw0xlNTUwEAnTt31lkWQ0ND2NnZoU2bNhBC4P79+1i3bh1Onz6NkJAQneVQSUxMxOXLl/HPf/5T58d+XkZGBoyMjBAZGQlnZ2e4urpi3rx5On3N5bfffoMQAmZmZpg+fTp69OgBFxcXfPjhh3j8+LHOclRk1apVMDQ0xPTp03V+7DFjxuDkyZNITk5GUVERUlJScOzYMbz55ps6z/IirumjZh8fXV9atWqls2O9rIsXL2LdunXw8fGBjY1Ng2Q4fPgwpk6dCgAYMGAAhg0bptPj3759G4sWLcKiRYtgbm6u02O/6OrVqygqKsKIESMwadIkXLp0CatWrUJWVha2bNmiceZdX/Lz8wEAsbGxGDx4MNasWYOMjAwsX74cT548weLFi+s9Q0Xy8vKQlJSEcePGoVmzZjo//tChQ3HmzBmNHzhBQUEYP368zrO8iKWPmn18tNSkp6dj0qRJ6NChAz755JMGy9GtWzds27YNGRkZWLFiBSZOnIjNmzfrpOCEEJgzZw769+8PX1/fej9edeLj42FmZgY7OzsAgKurK1q2bImZM2fi9OnTGt9cV19KS0sBAD179sSHH34IAHB3d4cQAnFxcYiOji73JUu6kJiYCKVSiTFjxuj82AAwefJk/Pzzz5DL5ejWrRsuXryIzz//XP0MuiGx9FGzj4+WkoMHDyI2NhadOnXC+vXr0aJFiwbLYmlpCUtLS7i6ukImk2H27Nn4+eef0bNnz3o/9vbt25GRkYHvvvtOfVWV6oShrKwMjRo10skPHxU3N7dyYwMGDADw7FmALkpf9WxY9V3YKp6enli8eDEyMjIapPQPHToELy+vBnk29tNPP+GHH37AokWLEBwcDODZ31WzZs0wb948jBw5Era2tjrPpcJTWNTs46OlYuPGjZgxYwZ69OiB7du3o3Xr1jrP8PDhQyQlJeHevXsa4926dQMA/PHHHzrJcejQITx48ACenp6wt7eHvb09kpKSoFAoYG9vr9PrwPPy8pCYmFjuIgPVOrqufjCrLhUtKSnRGFc9A9DlD0GVe/fu4cqVKw12aeSdO3cAoNyJSK9evQAA165d03mm57H0UbOPj5aCxMRELF68GP7+/li/fn2DPeNRKpWIjY0tdw32qVOnAEBnZ00LFizArl27NH4NHDgQbdu2Vf9eVwwMDDBv3jxs27ZNY/zgwYNo1KhRuRfg64uNjQ3at2+PgwcPaox///33aNy4cYO8UezixYsAoLPH4EWqk8T09HSN8QsXLgAA2rdvr+tIGri883+q+/hoqcnLy8Onn36K9u3bIzw8HFeuXNG4vWPHjjp76mxubo5Ro0Zh3bp1MDY2hqOjI9LT0/HFF19gxIgROvvk1oqO07x5cxgZGcHR0VEnGVTMzc0RHh6OrVu3QiaToVevXkhPT8fatWsRHh6uvvKsvhkYGCAmJkb9MerBwcG4dOkS1qxZg9GjRzfI8spvv/2Gpk2bNli52tvbw8fHB59++ikKCwvRtWtXXLp0CQkJCejXr5/OLx99EUv//wQHB6OkpAQbNmxAYmIiLC0tERcX12Dv9mxoJ0+exH/+8x/cvn0b4eHh5W5fsmSJTi8/k8vlePXVV7Fr1y6sWrUKbdu2xdSpUxEZGamzDPpm9uzZaNOmDb799lusW7cObdq0wdSpU3V+hUhAQACMjIyQkJCAqKgotGzZEtHR0YiKitJpDpX79+83yBU7z4uPj8fq1auxadMm5OXloX379hg3bly595o0BH60MhGRhHBNn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEL+H6EU66swNRmSAAAAAElFTkSuQmCC\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Create a D vector, basically a belief that the agent has about its own starting location \\\"\\\"\\\"\\n\",\n \"\\n\",\n \"# create a one-hot / certain belief about initial state\\n\",\n \"D = utils.onehot(0, n_states)\\n\",\n \"\\n\",\n \"# demonstrate hwo belief about initial state can also be uncertain / spread among different possible initial states\\n\",\n \"# alternative, where you have a degenerate/noisy prior belief\\n\",\n \"# D = utils.norm_dist(np.ones(n_states))\\n\",\n \"\\n\",\n \"\\\"\\\"\\\" Let's look at the prior over hidden states \\\"\\\"\\\"\\n\",\n \"plot_beliefs(D, title_str = \\\"Prior beliefs over states\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"OT9qqFTqRrvv\"\n },\n \"source\": [\n \"## **Hidden state inference**\\n\",\n \"\\n\",\n \"Hidden state inference proceeds by finding the setting of the optimal variational posterior $q(s_t)$ that minimizes the variational free energy. For the simple POMDP generative model and posterior we're considering here, this update reduces to a remarkably simple update rule, that is essentially proportional to Bayes` rule:\\n\",\n \"\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"q(s_t) = \\\\sigma\\\\left(\\\\ln \\\\mathbf{A}[o,:] + \\\\ln\\\\mathbf{B}[:,:,u] \\\\cdot q(s_{t-1})\\\\right) \\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"YCtY7o4bpGTq\"\n },\n \"source\": [\n \"Import the `softmax` function and a numerically-stable version of `np.log` from `pymdp.maths`\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 32,\n \"metadata\": {\n \"id\": \"UIJgNbv_RsFV\"\n },\n \"outputs\": [],\n \"source\": [\n \"from pymdp.maths import softmax\\n\",\n \"from pymdp.maths import spm_log_single as log_stable\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"ugPbd0lXpOED\"\n },\n \"source\": [\n \"Below we implement the `infer_states()` function\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 33,\n \"metadata\": {\n \"id\": \"7gtv82kiQhJF\"\n },\n \"outputs\": [],\n \"source\": [\n \"\\\"\\\"\\\" Create an infer states function that implements the math we just discussed\\\"\\\"\\\"\\n\",\n \"\\n\",\n \"def infer_states(observation_index, A, prior):\\n\",\n \"\\n\",\n \" \\\"\\\"\\\" Implement inference here -- NOTE: prior is already passed in, so you don't need to do anything with the B matrix. \\\"\\\"\\\"\\n\",\n \" \\\"\\\"\\\" This function has already been given P(s_t). The conditional expectation that creates \\\"today's prior\\\", using \\\"yesterday's posterior\\\", will happen *before calling* this function\\\"\\\"\\\"\\n\",\n \" \\n\",\n \" log_likelihood = log_stable(A[observation_index,:])\\n\",\n \"\\n\",\n \" log_prior = log_stable(prior)\\n\",\n \"\\n\",\n \" qs = softmax(log_likelihood + log_prior)\\n\",\n \" \\n\",\n \" return qs\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's do a simulated single timestep of hidden state inference\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 34,\n \"metadata\": {\n \"id\": \"YPaAhj-2nv5c\"\n },\n \"outputs\": [],\n \"source\": [\n \"qs_past = utils.onehot(4, n_states) # agent believes they were at location 4 -- i.e. (1,1) one timestep ago\\n\",\n \"\\n\",\n \"last_action = \\\"UP\\\" # the agent knew it moved \\\"UP\\\" one timestep ago\\n\",\n \"action_id = actions.index(last_action) # get the action index for moving \\\"UP\\\"\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"V7yvEyGgRhn4\"\n },\n \"source\": [\n \"Get \\\"today's prior\\\" using the past posterior and the past action, i.e. calculate:\\n\",\n \"\\n\",\n \"\\n\",\n \"$$ \\\\begin{align}\\n\",\n \"P(s_t) = \\\\mathbf{E}_{q(s_{t-1})}\\\\left[P(s_t | s_{t-1}, u_{t-1})\\\\right]\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"\\n\",\n \"and choose an observation that is consistent with the new location \\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 35,\n \"metadata\": {\n \"id\": \"sbtcFip-SOI6\"\n },\n \"outputs\": [],\n \"source\": [\n \"prior = B[:,:,action_id].dot(qs_past)\\n\",\n \"\\n\",\n \"observation_index = 1\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"SGwNJDJdRXJ8\"\n },\n \"source\": [\n \"Now run the `infer_states()` function, using the observation, the $\\\\mathbf{A}$ matrix, and the prior we just calculated above\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 36,\n \"metadata\": {\n \"id\": \"YIDxVmMzmdrQ\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"qs_new = infer_states(observation_index, A, prior)\\n\",\n \"plot_beliefs(qs_new, title_str = \\\"Beliefs about hidden states\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"Juc77Bs8JwsI\"\n },\n \"source\": [\n \"Let's see what happens if observation and the prior \\\"disagree\\\" with eachother?\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 37,\n \"metadata\": {\n \"id\": \"TN0g4BnYKEyF\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Get an observation that 'conflicts' with the prior \\\"\\\"\\\"\\n\",\n \"observation_index = 2 # this is like the agent is seeing itself in location (0, 2)\\n\",\n \"qs_new = infer_states(observation_index, A, prior)\\n\",\n \"plot_beliefs(qs_new)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"DmAiGBsyLjk7\"\n },\n \"source\": [\n \"What happens if likelihood and prior are partially ambiguous?\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 38,\n \"metadata\": {\n \"id\": \"5JFCey-ShsQg\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[[0.254 0.093 0.093 0.093 0.093 0.093 0.093 0.093 0.093]\\n\",\n \" [0.093 0.254 0.093 0.093 0.093 0.093 0.093 0.093 0.093]\\n\",\n \" [0.093 0.093 0.254 0.093 0.093 0.093 0.093 0.093 0.093]\\n\",\n \" [0.093 0.093 0.093 0.254 0.093 0.093 0.093 0.093 0.093]\\n\",\n \" [0.093 0.093 0.093 0.093 0.254 0.093 0.093 0.093 0.093]\\n\",\n \" [0.093 0.093 0.093 0.093 0.093 0.254 0.093 0.093 0.093]\\n\",\n \" [0.093 0.093 0.093 0.093 0.093 0.093 0.254 0.093 0.093]\\n\",\n \" [0.093 0.093 0.093 0.093 0.093 0.093 0.093 0.254 0.093]\\n\",\n \" [0.093 0.093 0.093 0.093 0.093 0.093 0.093 0.093 0.254]]\\n\"\n ]\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Create an ambiguous A matrix \\\"\\\"\\\"\\n\",\n \"A_partially_ambiguous = softmax(A)\\n\",\n \"print(A_partially_ambiguous.round(3))\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 39,\n \"metadata\": {\n \"id\": \"w_altXG0hyYV\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" ... and a noisy prior \\\"\\\"\\\"\\n\",\n \"noisy_prior = softmax(prior) \\n\",\n \"plot_beliefs(noisy_prior)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 40,\n \"metadata\": {\n \"id\": \"v2tpfddELr_t\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Do inference with the new, partially-ambiguous A matrix and the noised-up prior \\\"\\\"\\\"\\n\",\n \"qs_new = infer_states(observation_index, A_partially_ambiguous, noisy_prior)\\n\",\n \"plot_beliefs(qs_new)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"xec2mpugs4rh\"\n },\n \"source\": [\n \"## **Action Selection and the Expected Free Energy** \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"n-3cHIUyqtfS\"\n },\n \"source\": [\n \"Now we'll write functions to compute the expected states $Q(s_{t+1}|u_t)$, expected observations $Q(o_{t+1}|u_t)$, the entropy of $P(o|s)$: $\\\\mathbf{H}\\\\left[\\\\mathbf{A}\\\\right]$, and the KL divergence between the expected observations and the prior preferences $\\\\mathbf{C}$.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 41,\n \"metadata\": {\n \"id\": \"hBtftGDwq2VO\"\n },\n \"outputs\": [],\n \"source\": [\n \"\\\"\\\"\\\" define component functions for computing expected free energy \\\"\\\"\\\"\\n\",\n \"\\n\",\n \"def get_expected_states(B, qs_current, action):\\n\",\n \" \\\"\\\"\\\" Compute the expected states one step into the future, given a particular action \\\"\\\"\\\"\\n\",\n \" qs_u = B[:,:,action].dot(qs_current)\\n\",\n \"\\n\",\n \" return qs_u\\n\",\n \"\\n\",\n \"def get_expected_observations(A, qs_u):\\n\",\n \" \\\"\\\"\\\" Compute the expected observations one step into the future, given a particular action \\\"\\\"\\\"\\n\",\n \"\\n\",\n \" qo_u = A.dot(qs_u)\\n\",\n \"\\n\",\n \" return qo_u\\n\",\n \"\\n\",\n \"def entropy(A):\\n\",\n \" \\\"\\\"\\\" Compute the entropy of a set of conditional distributions, i.e. one entropy value per column \\\"\\\"\\\"\\n\",\n \"\\n\",\n \" H_A = - (A * log_stable(A)).sum(axis=0)\\n\",\n \"\\n\",\n \" return H_A\\n\",\n \"\\n\",\n \"def kl_divergence(qo_u, C):\\n\",\n \" \\\"\\\"\\\" Compute the Kullback-Leibler divergence between two 1-D categorical distributions\\\"\\\"\\\"\\n\",\n \" \\n\",\n \" return (log_stable(qo_u) - log_stable(C)).dot(qo_u)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"oUoKd1s6PZbT\"\n },\n \"source\": [\n \"Now let's imagine we're in some starting state, like (1,1)\\n\",\n \"N.B. This is the generative process we're talking about -- i.e. the true state of the world\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 42,\n \"metadata\": {\n \"id\": \"H2hh-d6HNQ-R\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": \"iVBORw0KGgoAAAANSUhEUgAAAXUAAAEACAYAAABMEua6AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAAAKWklEQVR4nO3cX2iWBf/H8e9sRQ9uSH8s0825VpAUlQRJ0ANB09zW+ncQhkHYH4yWMM2yIBiRYkaS1UEQMyOIiEEMGrNsQpYHnuzADtKgNtzYr1ZmgfcIbHX/Dh6SVj77o9vup2+v1+F13bv9IPLm8rru3WXFYrEYAKQwp9QDAJg+og6QiKgDJCLqAImIOkAiog6QSHnJB5y3qNQTAP5Wvhk6EvPnV572nCt1gEREHSARUQdIRNQBEhF1gEREHSARUQdIRNQBEhF1gEREHSARUQdIRNQBEhF1gEREHSARUQdIRNQBEhF1gEREHSARUQdIRNQBEhF1gEREHSARUQdIRNQBEhF1gEREHSARUQdIRNQBEhF1gEREHSARUQdIpHyyLxwaGor+/v4oFAoxZ86cqKysjNra2liwYMFM7gNgCiaM+t69e+OVV16Jvr6+KBaLY86VlZVFTU1NtLa2xqpVq2ZsJACTM27UOzs74+mnn46GhoZYv3591NTUxNy5cyMiolAoxNGjR+Ojjz6KDRs2xC+//BLNzc2zMhqA0ysr/vny+w8aGxtj+fLl0dbWNu6btLW1RW9vb3R1dU15QPl5i6b8MwD/ZN8MHYn58ytPe27cB6VDQ0NRX18/4R9QX18fg4ODZ7YOgGkzbtSrq6vjwIEDE77JJ5984oEpwP+Ace+pP/roo/Hkk0/Gd999FytXroza2tqoqKiIiIiRkZFT99S7urriueeem5XBAPx3495Tj4jo7u6OnTt3xsDAQJSVlY05VywWo6qqKlpaWuLuu+8+owHuqQNMzXj31CeM+u8GBwejr68vCoVCFIvFU59TX7x48VmNE3WAqRkv6pP+5aPq6uqorq6etlEATD9fEwCQiKgDJCLqAImIOkAiog6QiKgDJCLqAImIOkAiog6QiKgDJCLqAImIOkAiog6QiKgDJCLqAImIOkAiog6QiKgDJCLqAImIOkAiog6QiKgDJCLqAImIOkAiog6QiKgDJCLqAImIOkAiog6QiKgDJFJe6gH8ff38f5+VegJn4V8L/13qCcwAV+oAiYg6QCKiDpCIqAMkIuoAiYg6QCKiDpCIqAMkIuoAiYg6QCKiDpCIqAMkIuoAiYg6QCKiDpCIqAMkIuoAiYg6QCKiDpCIqAMkIuoAiYg6QCKiDpCIqAMkIuoAiYg6QCKiDpCIqAMkIuoAiYg6QCKiDpCIqAMkIuoAiYg6QCLlE71geHh4Sm946aWXnvEYAM7OhFG/9dZb49dff530Gx4+fPisBgFw5iaMekdHR6xbty5OnjwZTzzxRJSXT/gjAJTIhIVeunRp7N69O+699974/vvv47HHHpuNXQCcgUk9KK2rq4uNGzdGe3t7HD9+fKY3AXCGJn0vZfXq1XHllVfO5BYAztKko37OOefEjTfeOJNbADhLPqcOkIioAyQi6gCJiDpAIqIOkIioAyQi6gCJiDpAIqIOkIioAyQi6gCJiDpAIqIOkIioAyQi6gCJiDpAIqIOkIioAyQi6gCJiDpAIqIOkIioAyQi6gCJiDpAIqIOkIioAyQi6gCJiDpAIqIOkIioAyQi6gCJlJd6AH9f/1r471JPAP7ElTpAIqIOkIioAyQi6gCJiDpAIqIOkIioAyQi6gCJiDpAIqIOkIioAyQi6gCJiDpAIqIOkIioAyQi6gCJiDpAIqIOkIioAyQi6gCJiDpAIqIOkIioAyQi6gCJiDpAIqIOkIioAyQi6gCJiDpAIqIOkIioAyQyqagfOXIkPv744+jv7z/t+R9//DE++OCDaR0GwNSVj3dyZGQkWltb48CBA1EsFqOsrCxWrFgRzz//fMybN+/U6wYGBuKpp56K5ubmGR8MwH837pX6a6+9Fp9//nns2LEjOjs7o6WlJfbv3x/3339/HDt2bLY2AjBJ40Z937590draGo2NjXHVVVfF448/Hm+//XYMDw/HI488EoVCYbZ2AjAJ40b92LFjsWTJkjHHrrvuunj99dejr68v1q9fH6OjozO5D4ApGDfq1dXVcfDgwb8cv+GGG2Lbtm1x8ODB2Lx5s7AD/I8Y90HpfffdF1u2bImRkZFoamqKZcuWnTrX2NgYw8PDsX379jh06NCMDwVgYuNGffXq1XHixInYtWtXlJWVjYl6RMTatWujoqIitm7dOqMjAZicsmKxWJzMCwuFQlRUVJz23PHjx+PTTz+Nu+66a8oDys9bNOWfAfgn+2boSMyfX3nac5OO+kwRdYCpGS/qviYAIBFRB0hE1AESEXWAREQdIBFRB0hE1AESEXWAREQdIBFRB0hE1AESEXWAREQdIBFRB0hE1AESEXWAREQdIBFRB0hE1AESEXWAREQdIBFRB0hE1AESEXWAREQdIBFRB0hE1AESEXWAREQdIBFRB0ikrFgsFks9AoDp4UodIBFRB0hE1AESEXWAREQdIBFRB0hE1AESEXWAREQdIBFRnyFdXV3R1NQU1157bTQ0NERnZ2epJzFFhw8fjquvvjq+/fbbUk9hkn777bd49913o7m5OZYtWxb19fWxbdu2KBQKpZ42a8pLPSCj7u7u2LRpUzzwwANx8803R09PT2zevDnOP//8WLVqVannMQlff/11rFu3LkZHR0s9hSlob2+PnTt3xkMPPRQ33XRT9Pf3x6uvvhpfffVV7Nq1q9TzZoXvfpkBK1asiGuuuSZefvnlU8daW1vjyy+/jD179pRwGRMZHR2N9957L3bs2BHnnntu/PTTT7F///5YsGBBqacxgWKxGMuXL4+mpqZoa2s7dby7uzs2bNgQnZ2dsXTp0hIunB1uv0yzwcHBGBgYiJUrV445ftttt0VfX18MDg6WaBmT0dvbGy+99FI8+OCDsWnTplLPYQpGRkbijjvuiNtvv33M8csvvzwiIgYGBkoxa9a5/TLN+vr6IiKitrZ2zPGampqIiOjv74/q6upZ38Xk1NXVRU9PT1x00UXx/vvvl3oOU1BRURHPPvvsX4739PRERMQVV1wx25NKQtSn2YkTJyLiP//A/mju3LkREf+oBzZ/RxdffHGpJzCNDh06FG+88UbU19dHXV1dqefMCrdfptlEjyjmzPFXDrOht7c3Hn744aiqqootW7aUes6sUZhpVllZGRH/ub/3R79fof9+Hpg53d3dsXbt2rjsssvirbfeigsuuKDUk2aNqE+z3++l//mhzNGjR8ecB2bG7t27Y+PGjXH99dfHO++8E5dcckmpJ80qUZ9mNTU1UVVVFR9++OGY43v37o0lS5bEwoULS7QM8uvo6IgXXnghGhoaor29/R/5P2MPSmdAS0tLPPPMMzFv3ry45ZZbYt++fbFnz54xn1sHptcPP/wQW7dujUWLFsWaNWviiy++GHN+8eLFceGFF5Zo3ewR9Rlwzz33xMmTJ+PNN9+Mjo6OqK6uju3bt0djY2Opp0Fan332Wfz8888xNDQUa9as+cv5F198Me68884SLJtdfqMUIBH31AESEXWAREQdIBFRB0hE1AESEXWAREQdIBFRB0hE1AES+X+Emhlu+AfupgAAAABJRU5ErkJggg==\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Get state index, create state vector for (1,1) \\\"\\\"\\\"\\n\",\n \"\\n\",\n \"state_idx = grid_locations.index((1,1))\\n\",\n \"state_vector = utils.onehot(state_idx, n_states)\\n\",\n \"plot_point_on_grid(state_vector, grid_locations)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"VOLwt7CgUW61\"\n },\n \"source\": [\n \"And let's furthermore assume we start with the (accurate) belief about our location, that we are in location (1,1). So let's just make our current $Q(s_t)$ equal to the true state vector. You could think of this as if we just did one 'step' of inference using our current observation along with precise `A`/`B` matrices.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 43,\n \"metadata\": {\n \"id\": \"Pv9UFpcuUY5F\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Make qs_current identical to the true starting state \\\"\\\"\\\" \\n\",\n \"qs_current = state_vector.copy()\\n\",\n \"plot_beliefs(qs_current, title_str =\\\"Where do we believe we are?\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"jBXAqRmNPv07\"\n },\n \"source\": [\n \"And we prefer to be in state (1,2). So we express that as high probability over the corresponding entry of the $\\\\mathbf{C}$ vector -- that happens to be index 5.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 44,\n \"metadata\": {\n \"id\": \"Ya77s9O9WlMs\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_grid(grid_locations)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 45,\n \"metadata\": {\n \"id\": \"IMD0HkBCPsXL\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Create a preference to be in (1,2) \\\"\\\"\\\"\\n\",\n \"\\n\",\n \"desired_idx = grid_locations.index((1,2))\\n\",\n \"\\n\",\n \"C = utils.onehot(desired_idx, n_observations)\\n\",\n \"\\n\",\n \"plot_beliefs(C, title_str = \\\"Preferences\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"JPg-sC00QCLI\"\n },\n \"source\": [\n \"Now to keep things simple, let's evaluate the expected free energies $\\\\mathbf{G}$ of just two actions that we could take from our current position -- either moving LEFT or moving RIGHT. Let's remind ourselves of what action indices those are\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 46,\n \"metadata\": {\n \"id\": \"ggCUDAf4QUQg\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action index of moving left: 2\\n\",\n \"Action index of moving right: 3\\n\"\n ]\n }\n ],\n \"source\": [\n \"left_idx = actions.index(\\\"LEFT\\\")\\n\",\n \"right_idx = actions.index(\\\"RIGHT\\\")\\n\",\n \"\\n\",\n \"print(f'Action index of moving left: {left_idx}')\\n\",\n \"print(f'Action index of moving right: {right_idx}')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"w3G4KPVyQhoF\"\n },\n \"source\": [\n \"And now let's use the functions we've just defined, in combination with our `A`, `B`, `C` arrays and our current posterior `qs_current`, to compute the expected free energies for the two actions\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 47,\n \"metadata\": {\n \"id\": \"FNeEYmIETAZh\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Expected free energy of moving left: 36.841361487904734\\n\",\n \"\\n\",\n \"Expected free energy of moving right: 0.0\\n\",\n \"\\n\"\n ]\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Compute the expected free energies for moving left vs. moving right \\\"\\\"\\\"\\n\",\n \"G = np.zeros(2) # store the expected free energies for each action in here\\n\",\n \"\\n\",\n \"\\\"\\\"\\\"\\n\",\n \"Compute G for MOVE LEFT here \\n\",\n \"\\\"\\\"\\\"\\n\",\n \"\\n\",\n \"qs_u_left = get_expected_states(B, qs_current, left_idx)\\n\",\n \"# alternative\\n\",\n \"# qs_u_left = B[:,:,left_idx].dot(qs_current)\\n\",\n \"\\n\",\n \"H_A = entropy(A)\\n\",\n \"qo_u_left = get_expected_observations(A, qs_u_left)\\n\",\n \"# alternative\\n\",\n \"# qo_u_left = A.dot(qs_u_left)\\n\",\n \"\\n\",\n \"predicted_uncertainty_left = H_A.dot(qs_u_left)\\n\",\n \"predicted_divergence_left = kl_divergence(qo_u_left, C)\\n\",\n \"G[0] = predicted_uncertainty_left + predicted_divergence_left\\n\",\n \"\\n\",\n \"\\\"\\\"\\\"\\n\",\n \"Compute G for MOVE RIGHT here \\n\",\n \"\\\"\\\"\\\"\\n\",\n \"\\n\",\n \"qs_u_right = get_expected_states(B, qs_current, right_idx)\\n\",\n \"# alternative\\n\",\n \"# qs_u_right = B[:,:,right_idx].dot(qs_current)\\n\",\n \"\\n\",\n \"H_A = entropy(A)\\n\",\n \"qo_u_right = get_expected_observations(A, qs_u_right)\\n\",\n \"# alternative\\n\",\n \"# qo_u_right = A.dot(qs_u_right)\\n\",\n \"\\n\",\n \"predicted_uncertainty_right = H_A.dot(qs_u_right)\\n\",\n \"predicted_divergence_right = kl_divergence(qo_u_right, C)\\n\",\n \"G[1] = predicted_uncertainty_right + predicted_divergence_right\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\\"\\\"\\\" Now let's print the expected free energies for the two actions, that we just calculated \\\"\\\"\\\"\\n\",\n \"print(f'Expected free energy of moving left: {G[0]}\\\\n')\\n\",\n \"print(f'Expected free energy of moving right: {G[1]}\\\\n')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"w8JbcjuMR5FU\"\n },\n \"source\": [\n \"Now let's use formula for the posterior over actions, i.e. \\n\",\n \"\\n\",\n \"\\n\",\n \"$$ \\\\begin{align}\\n\",\n \"Q(u_t) = \\\\sigma(-\\\\mathbf{G})\\n\",\n \"\\\\end{align} $$\\n\",\n \"\\n\",\n \"to compute the probabilities of each action\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 48,\n \"metadata\": {\n \"id\": \"tpY1lva_TwuM\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Probability of moving left: 9.999999999999965e-17\\n\",\n \"Probability of moving right: 1.0\\n\"\n ]\n }\n ],\n \"source\": [\n \"Q_u = softmax(-G)\\n\",\n \"\\n\",\n \"\\\"\\\"\\\" and print the probability of each action \\\"\\\"\\\"\\n\",\n \"print(f'Probability of moving left: {Q_u[0]}')\\n\",\n \"print(f'Probability of moving right: {Q_u[1]}')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"iLk1LqB9X3fC\"\n },\n \"source\": [\n \"For usefulness later on, let's wrap the expected free energy calculations into a function\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 49,\n \"metadata\": {\n \"id\": \"tkdwjTLPX2ti\"\n },\n \"outputs\": [],\n \"source\": [\n \"def calculate_G(A, B, C, qs_current, actions):\\n\",\n \"\\n\",\n \" G = np.zeros(len(actions)) # vector of expected free energies, one per action\\n\",\n \"\\n\",\n \" H_A = entropy(A) # entropy of the observation model, P(o|s)\\n\",\n \"\\n\",\n \" for action_i in range(len(actions)):\\n\",\n \" \\n\",\n \" qs_u = get_expected_states(B, qs_current, action_i) # expected states, under the action we're currently looping over\\n\",\n \" qo_u = get_expected_observations(A, qs_u) # expected observations, under the action we're currently looping over\\n\",\n \"\\n\",\n \" pred_uncertainty = H_A.dot(qs_u) # predicted uncertainty, i.e. expected entropy of the A matrix\\n\",\n \" pred_div = kl_divergence(qo_u, C) # predicted divergence\\n\",\n \"\\n\",\n \" G[action_i] = pred_uncertainty + pred_div # sum them together to get expected free energy\\n\",\n \" \\n\",\n \" return G\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"midF2HSEswHJ\"\n },\n \"source\": [\n \"## **Complete Recipe for Active Inference**\\n\",\n \"\\n\",\n \"1. Sample an observation $o_t$ from the current state of the environment\\n\",\n \"2. Perform inference over hidden states i.e., optimize $q(s)$ through free-energy minimization\\n\",\n \"3. Calculate expected free energy of actions $\\\\mathbf{G}$ \\n\",\n \"4. Sample action from the posterior over actions $Q(u_t) \\\\sim \\\\sigma(-\\\\mathbf{G})$.\\n\",\n \"5. Use the sampled action $a_t$ to perturb the generative process and go back to step 1.\\n\",\n \"\\n\",\n \"\\n\",\n \"---\\n\",\n \"\\n\",\n \"Let's start by creating a class that will represent the Grid World environment (i.e., _generative process_) that our active inference agent will navigate within. Note that we don't need to specify the generative process in terms of `A` and `B` matrices - the generative process will be as arbitrary and complex as the environment is. The `A` and `B` matrices are just the agent's _representation_ of the world and the task, which in this case happen to capture the Markovian, noiseless dynamics of the world perfectly.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 50,\n \"metadata\": {\n \"id\": \"az0jx39hsySI\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Starting state is (0, 0)\\n\"\n ]\n }\n ],\n \"source\": [\n \"class GridWorldEnv():\\n\",\n \" \\n\",\n \" def __init__(self,starting_state = (0,0)):\\n\",\n \"\\n\",\n \" self.init_state = starting_state\\n\",\n \" self.current_state = self.init_state\\n\",\n \" print(f'Starting state is {starting_state}')\\n\",\n \" \\n\",\n \" def step(self,action_label):\\n\",\n \"\\n\",\n \" (Y, X) = self.current_state\\n\",\n \"\\n\",\n \" if action_label == \\\"UP\\\": \\n\",\n \" \\n\",\n \" Y_new = Y - 1 if Y > 0 else Y\\n\",\n \" X_new = X\\n\",\n \"\\n\",\n \" elif action_label == \\\"DOWN\\\": \\n\",\n \"\\n\",\n \" Y_new = Y + 1 if Y < 2 else Y\\n\",\n \" X_new = X\\n\",\n \"\\n\",\n \" elif action_label == \\\"LEFT\\\": \\n\",\n \" Y_new = Y\\n\",\n \" X_new = X - 1 if X > 0 else X\\n\",\n \"\\n\",\n \" elif action_label == \\\"RIGHT\\\": \\n\",\n \" Y_new = Y\\n\",\n \" X_new = X +1 if X < 2 else X\\n\",\n \"\\n\",\n \" elif action_label == \\\"STAY\\\":\\n\",\n \" Y_new, X_new = Y, X \\n\",\n \" \\n\",\n \" self.current_state = (Y_new, X_new) # store the new grid location\\n\",\n \"\\n\",\n \" obs = self.current_state # agent always directly observes the grid location they're in \\n\",\n \"\\n\",\n \" return obs\\n\",\n \"\\n\",\n \" def reset(self):\\n\",\n \" self.current_state = self.init_state\\n\",\n \" print(f'Re-initialized location to {self.init_state}')\\n\",\n \" obs = self.current_state\\n\",\n \" print(f'..and sampled observation {obs}')\\n\",\n \"\\n\",\n \" return obs\\n\",\n \" \\n\",\n \"env = GridWorldEnv()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"N9dSgKgkNXWp\"\n },\n \"source\": [\n \"Now equipped with an environment and a generative model (our `A`, `B`, `C`, and `D`), we can code up the entire active inference loop\\n\",\n \"\\n\",\n \"---\\n\",\n \"\\n\",\n \"To have everything in one place, let's re-create the whole generative model\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 51,\n \"metadata\": {\n \"id\": \"ML3UMFXlNNXA\"\n },\n \"outputs\": [],\n \"source\": [\n \"\\\"\\\"\\\" Fill out the components of the generative model \\\"\\\"\\\"\\n\",\n \"\\n\",\n \"A = np.eye(n_observations, n_states)\\n\",\n \"\\n\",\n \"B = create_B_matrix()\\n\",\n \"\\n\",\n \"C = utils.onehot(grid_locations.index( (2, 2) ), n_observations) # make the agent prefer location (2,2) (lower right corner of grid world)\\n\",\n \"\\n\",\n \"D = utils.onehot(grid_locations.index( (1,2) ), n_states) # start the agent with the prior belief that it starts in location (1,2) \\n\",\n \"\\n\",\n \"actions = [\\\"UP\\\", \\\"DOWN\\\", \\\"LEFT\\\", \\\"RIGHT\\\", \\\"STAY\\\"]\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"S_cDKHlJQpxl\"\n },\n \"source\": [\n \"Now let's initialize the environment with starting state `(1,2)`, so that the agent has accurate beliefs about where it's starting.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 52,\n \"metadata\": {\n \"id\": \"wLq3n2bDQwRh\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Starting state is (1, 2)\\n\"\n ]\n }\n ],\n \"source\": [\n \"env = GridWorldEnv(starting_state = (1,2))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"bYSh6_UPRKuS\"\n },\n \"source\": [\n \"Let's write a function that runs the whole active inference loop, and then run it for `T = 5` timesteps.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 53,\n \"metadata\": {\n \"id\": \"AhC96iFoRENl\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Re-initialized location to (1, 2)\\n\",\n \"..and sampled observation (1, 2)\\n\",\n \"Time 0: Agent observes itself in location: (1, 2)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 1: Agent observes itself in location: (2, 2)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 2: Agent observes itself in location: (2, 2)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 3: Agent observes itself in location: (2, 2)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 4: Agent observes itself in location: (2, 2)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Write a function that, when called, runs the entire active inference loop for a desired number of timesteps\\\"\\\"\\\"\\n\",\n \"\\n\",\n \"def run_active_inference_loop(A, B, C, D, actions, env, T = 5):\\n\",\n \"\\n\",\n \" \\\"\\\"\\\" Initialize the prior that will be passed in during inference to be the same as `D` \\\"\\\"\\\"\\n\",\n \" prior = D.copy() # initial prior should be the D vector\\n\",\n \"\\n\",\n \" \\\"\\\"\\\" Initialize the observation that will be passed in during inference - hint use env.reset()\\\"\\\"\\\"\\n\",\n \" obs = env.reset() # initialize the `obs` variable to be the first observation you sample from the environment, before `step`-ing it.\\n\",\n \"\\n\",\n \" for t in range(T):\\n\",\n \"\\n\",\n \" print(f'Time {t}: Agent observes itself in location: {obs}')\\n\",\n \"\\n\",\n \" # convert the observation into the agent's observational state space (in terms of 0 through 8)\\n\",\n \" obs_idx = grid_locations.index(obs)\\n\",\n \"\\n\",\n \" # perform inference over hidden states\\n\",\n \" qs_current = infer_states(obs_idx, A, prior)\\n\",\n \"\\n\",\n \" plot_beliefs(qs_current, title_str = f\\\"Beliefs about location at time {t}\\\")\\n\",\n \"\\n\",\n \" # calculate expected free energy of actions\\n\",\n \" G = calculate_G(A, B, C, qs_current, actions)\\n\",\n \" \\n\",\n \" # compute action posterior\\n\",\n \" Q_u = softmax(-G)\\n\",\n \"\\n\",\n \" # sample action from probability distribution over actions\\n\",\n \" chosen_action = utils.sample(Q_u)\\n\",\n \"\\n\",\n \" # compute prior for next timestep of inference\\n\",\n \" prior = B[:,:,chosen_action].dot(qs_current) \\n\",\n \"\\n\",\n \" # update generative process\\n\",\n \" action_label = actions[chosen_action]\\n\",\n \"\\n\",\n \" obs = env.step(action_label)\\n\",\n \" \\n\",\n \" return qs_current\\n\",\n \"\\n\",\n \"\\\"\\\"\\\" Run the function we just wrote, for T = 5 timesteps \\\"\\\"\\\"\\n\",\n \"qs = run_active_inference_loop(A, B, C, D, actions, env, T = 5)\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"W9V2E_DwWhBl\"\n },\n \"source\": [\n \"## **Planning**\\n\",\n \"\\n\",\n \"But there's a problem. Imagine we started the agent at the top left corner (coordinate `(0,0)`) rather than one step away from the target location\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 54,\n \"metadata\": {\n \"id\": \"2w4TX0q2WcFl\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Starting state is (0, 0)\\n\",\n \"Re-initialized location to (0, 0)\\n\",\n \"..and sampled observation (0, 0)\\n\",\n \"Time 0: Agent observes itself in location: (0, 0)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 1: Agent observes itself in location: (0, 1)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 2: Agent observes itself in location: (0, 0)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 3: Agent observes itself in location: (0, 0)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 4: Agent observes itself in location: (0, 0)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"D = utils.onehot(grid_locations.index((0,0)), n_states) # let's have the agent believe it starts in location (0,0)\\n\",\n \"\\n\",\n \"env = GridWorldEnv(starting_state = (0,0))\\n\",\n \"qs = run_active_inference_loop(A, B, C, D, actions, env, T = 5)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"r0sC3oyIW_f7\"\n },\n \"source\": [\n \"Because the expected free energy of each action is only evaluated for one timestep in the future, the agent has no way of knowing which action to initially take, to get closer to its final \\\"goal\\\" of `(2,2)`. This is because the expected divergence term for all actions $\\\\operatorname{D}_{KL}(Q(o|u) \\\\parallel \\\\mathbf{C})$ is identical for all considered actions (which are just 1-step moves away from starting from `(0,0)` ). This speaks to the importance of planning, or _multiple timestep policies_. \\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"SQoxPD7g3VtT\"\n },\n \"source\": [\n \"Now let's do active inference with multi-step policies\\n\",\n \"\\n\",\n \"We can rely on a useful function from `pymdp`'s `control` module called `construct_policies()` to automatically generate a list of all the policies we want to entertain, for a given number of control states (actions) and a desired temporal horizon. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 55,\n \"metadata\": {\n \"id\": \"DPuFHY1kW4K2\"\n },\n \"outputs\": [],\n \"source\": [\n \"from pymdp.control import construct_policies\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 56,\n \"metadata\": {\n \"id\": \"EsL5zFC93oCC\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Total number of policies for 5 possible actions and a planning horizon of 4: 625\\n\"\n ]\n }\n ],\n \"source\": [\n \"policy_len = 4\\n\",\n \"n_actions = len(actions)\\n\",\n \"\\n\",\n \"# we have to wrap `n_states` and `n_actions` in a list for reasons that will become clear in Part II\\n\",\n \"all_policies = construct_policies([n_states], [n_actions], policy_len = policy_len)\\n\",\n \"\\n\",\n \"print(f'Total number of policies for {n_actions} possible actions and a planning horizon of {policy_len}: {len(all_policies)}')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"QKA_YdDS5Qo2\"\n },\n \"source\": [\n \"Let's re-write our expected free energy function, but now we loop over policies (sequences of actions), rather than actions (1-step policies)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {\n \"id\": \"gtv6cvy2qvtT\"\n },\n \"outputs\": [],\n \"source\": [\n \"def calculate_G_policies(A, B, C, qs_current, policies):\\n\",\n \"\\n\",\n \" G = np.zeros(len(policies)) # initialize the vector of expected free energies, one per policy\\n\",\n \" H_A = entropy(A) # can calculate the entropy of the A matrix beforehand, since it'll be the same for all policies\\n\",\n \" qs_pi_t = None\\n\",\n \" for policy_id, policy in enumerate(policies): # loop over policies - policy_id will be the linear index of the policy (0, 1, 2, ...) and `policy` will be a column vector where `policy[t,0]` indexes the action entailed by that policy at time `t`\\n\",\n \"\\n\",\n \" t_horizon = policy.shape[0] # temporal depth of the policy\\n\",\n \"\\n\",\n \" G_pi = 0.0 # initialize expected free energy for this policy\\n\",\n \"\\n\",\n \" for t in range(t_horizon): # loop over temporal depth of the policy\\n\",\n \"\\n\",\n \" action = policy[t,0] # action entailed by this particular policy, at time `t`\\n\",\n \"\\n\",\n \" # get the past predictive posterior - which is either your current posterior at the current time (not the policy time) or the predictive posterior entailed by this policy, one timstep ago (in policy time)\\n\",\n \" if t == 0:\\n\",\n \" qs_prev = qs_current \\n\",\n \" else:\\n\",\n \" qs_prev = qs_pi_t\\n\",\n \" \\n\",\n \" qs_pi_t = get_expected_states(B, qs_prev, action) # expected states, under the action entailed by the policy at this particular time\\n\",\n \" qo_pi_t = get_expected_observations(A, qs_pi_t) # expected observations, under the action entailed by the policy at this particular time\\n\",\n \"\\n\",\n \" kld = kl_divergence(qo_pi_t, C) # Kullback-Leibler divergence between expected observations and the prior preferences C\\n\",\n \"\\n\",\n \" G_pi_t = H_A.dot(qs_pi_t) + kld # predicted uncertainty + predicted divergence, for this policy & timepoint\\n\",\n \"\\n\",\n \" G_pi += G_pi_t # accumulate the expected free energy for each timepoint into the overall EFE for the policy\\n\",\n \"\\n\",\n \" G[policy_id] += G_pi\\n\",\n \" \\n\",\n \" return G\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"kYYRyszL9L00\"\n },\n \"source\": [\n \"Let's write a function for computing the action posterior, given the posterior probability of each policy:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 58,\n \"metadata\": {\n \"id\": \"VvxYGhuwsSp9\"\n },\n \"outputs\": [],\n \"source\": [\n \"def compute_prob_actions(actions, policies, Q_pi):\\n\",\n \" P_u = np.zeros(len(actions)) # initialize the vector of probabilities of each action\\n\",\n \"\\n\",\n \" for policy_id, policy in enumerate(policies):\\n\",\n \" P_u[int(policy[0,0])] += Q_pi[policy_id] # get the marginal probability for the given action, entailed by this policy at the first timestep\\n\",\n \" \\n\",\n \" P_u = utils.norm_dist(P_u) # normalize the action probabilities\\n\",\n \" \\n\",\n \" return P_u\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"Do8CftUd6Vq2\"\n },\n \"source\": [\n \"Now we can write a new active inference function, that uses temporally-deep planning\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 59,\n \"metadata\": {\n \"id\": \"d4YrbkGWslC-\"\n },\n \"outputs\": [],\n \"source\": [\n \"def active_inference_with_planning(A, B, C, D, n_actions, env, policy_len = 2, T = 5):\\n\",\n \"\\n\",\n \" \\\"\\\"\\\" Initialize prior, first observation, and policies \\\"\\\"\\\"\\n\",\n \" \\n\",\n \" prior = D # initial prior should be the D vector\\n\",\n \"\\n\",\n \" obs = env.reset() # get the initial observation\\n\",\n \"\\n\",\n \" policies = construct_policies([n_states], [n_actions], policy_len = policy_len)\\n\",\n \"\\n\",\n \" for t in range(T):\\n\",\n \"\\n\",\n \" print(f'Time {t}: Agent observes itself in location: {obs}')\\n\",\n \"\\n\",\n \" # convert the observation into the agent's observational state space (in terms of 0 through 8)\\n\",\n \" obs_idx = grid_locations.index(obs)\\n\",\n \"\\n\",\n \" # perform inference over hidden states\\n\",\n \" qs_current = infer_states(obs_idx, A, prior)\\n\",\n \" plot_beliefs(qs_current, title_str = f\\\"Beliefs about location at time {t}\\\")\\n\",\n \"\\n\",\n \" # calculate expected free energy of actions\\n\",\n \" G = calculate_G_policies(A, B, C, qs_current, policies)\\n\",\n \"\\n\",\n \" # to get action posterior, we marginalize P(u|pi) with the probabilities of each policy Q(pi), given by \\\\sigma(-G)\\n\",\n \" Q_pi = softmax(-G)\\n\",\n \"\\n\",\n \" # compute the probability of each action\\n\",\n \" P_u = compute_prob_actions(actions, policies, Q_pi)\\n\",\n \"\\n\",\n \" # sample action from probability distribution over actions\\n\",\n \" chosen_action = utils.sample(P_u)\\n\",\n \"\\n\",\n \" # compute prior for next timestep of inference\\n\",\n \" prior = B[:,:,chosen_action].dot(qs_current) \\n\",\n \"\\n\",\n \" # step the generative process and get new observation\\n\",\n \" action_label = actions[chosen_action]\\n\",\n \" obs = env.step(action_label)\\n\",\n \" \\n\",\n \" return qs_current\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"HXiiTwznw5bG\"\n },\n \"source\": [\n \"Now run it to see if the agent is able to navigate to location `(2,2)`\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 60,\n \"metadata\": {\n \"id\": \"Pn1WIMem6S_v\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Starting state is (0, 0)\\n\",\n \"Re-initialized location to (0, 0)\\n\",\n \"..and sampled observation (0, 0)\\n\",\n \"Time 0: Agent observes itself in location: (0, 0)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 1: Agent observes itself in location: (0, 0)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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Qa37x5M7KysrQ5vL29oVarERMTI1puy5YtiI+PxwcffIAXL17AwsJCVPiZmZna0xjzPkbGxsZFZtV8oG/16tWio/4bN27gzJkz8Pb2LvKoWBcvXrwAIH6FKQgCNm7cCACi38fi8uZdDij5v4MumjdvDktLS2zYsEH0foNKpcK4ceOgUCjK/On3vxIe6VeghIQE7WlxgiDg8ePH2LZtG/744w+MHz9eu9zUqVMxePBgfPbZZ+jXrx9q1aqF/fv349q1a5g4cWKhp9a9KzQ0FOfOnUNQUBCCgoLQoEEDJCYm4tixYwgICBAdYedVrVo1DBw4EMuXL0dISAg8PT3x6tUrREdHo0aNGvjss88K3aeXlxfi4uIwbdo0ODo64v79+9r7COR/02/v3r1QqVRwcnLC8ePHcezYMQwfPlx7KYjg4GAcOnQI48aNQ79+/dC4cWOcPXsWhw4dgq+vr/aTtT4+Ppg1axa+/fZbPHjwANWqVcO2bdtETz7A2zliY2NjHDlyBA0aNICvry/Mzc2LfSz79OmDXbt2Yc6cOfjll1/QvHlzXL9+HTt37kTLli210xwdO3aEh4cH5syZg19//RWOjo64cuUKYmNjERISglq1asHLywurV6/G2LFj4eHhgbS0NGzfvl37qiTvY2RhYYHz589j27Zt8PDwyJfro48+wsCBA7FhwwYMGTIEPj4+SEtLw4YNG/D++++Xy3WUvLy8sGHDBgQHB+Pzzz9HTk4O4uPjcf36dRgbG+fLe+HCBURFRaFVq1b5Xn3kXQ4AIiMj0aZNm1JdPqQwVatWxdSpUzF+/Hj4+/vj888/x3vvvYeYmBg8fPgQ8+fPl87pmDrgI1GBZs+erf27iYkJzM3N4ejoiO+++070S+/s7IwtW7Zg8eLFWLt2LXJzc2Fra4s5c+aIPpJfHGtra2zbtg2RkZHYtm0bfv/9d1hZWUGhUBR7AakxY8agVq1a2LFjB8LDw2FiYoJPPvkE8+bNK3Q+H3h79k7NmjVx9OhR7N69G/Xr10evXr3QuXNn9OvXD2fPnkWzZs20y69evRqzZs3Cvn37UK9ePSgUCnzxxRfa22vVqoXo6GgsXLgQcXFxePnyJaysrDBp0iTRchYWFli9ejUWLFiAyMhI1K5dG3379sWHH34oekKtUaMGxo8fj3//+9+YNWsWrK2ttZ+KLkq1atWwbt06LF26FPHx8dizZw/q16+P4OBgjBo1SjvlY2xsjGXLlmHp0qXYu3cv9uzZA2tra0ybNg39+vUDAHz55Zd48+YN4uLicOzYMdStWxft2rXD0KFD0b17d5w9exadO3cG8PaJe8GCBZg5cyZmzpxZ4Pnl//znP2Fra4utW7dizpw5MDc3R+fOnTFmzBjtVEdZeHl5YdasWYiKitJu38HBAdHR0fj6669FF6UbPnw4bt++jX/961/w9/cvtPQ1vwtr1qzBTz/9VK6lDwBdu3aFubk5li9fjmXLlsHY2BgfffQRli9fXubLnfzVGAkV+VY8EREZFM7pExFJCEufiEhCWPpERBLC0icikhCWPhGRhLD0iYgk5E9xnv7z51lQq/V3ZmmdOjI8e1b6j7H/1XIAhpPFUHIAzGLIOQDDyaLvHMbGRqhdu/BvxftTlL5aLei19DX7NASGkgMwnCyGkgNgloIYSg7AcLIYSg6A0ztERJLC0icikpASl/7PP/8MBweHAr/0Oq+srCzMmDED7u7ucHZ2xj/+8Q/cu3evtDmJiKgclKj07969i+DgYJ0u9Tt+/HgcOHAAoaGhCA8Px5MnTzBo0CBkZmaWOiwREZWNTqWfm5uLTZs2oU+fPtpv5CnKxYsXcfz4cYSHh6N3797w9fXFunXrkJmZiS1btpQ5NBERlY5OpX/p0iXMnz8fQ4cORWhoaLHLnz59GqampnB3d9eOWVhYwMXFBSdOnCh9WiIiKhOdSt/Ozg4JCQkYPXq0Tt9Ak5SUBBsbm3zLWltbF/hVeEREpB86naf/wQcflGijKpUKMpks37ipqWmpvruzTp3829KFOjsbxtWqlWpdS0szve2rPHNUJEPJYig5AGYpiKHkAAwni6HkACrow1lFfS9LUd+3Wphnz1Sl+nCDpaUZTvcs/Kv+ypP77h1ISyvfN6ktLc3KfZulZShZDCUHwCyGnAMwnCz6zmFsbFTkgXKFnKcvk8nyfTcq8PY0zoJeARARkX5USOnb2toiNTU13xF/SkoKbG1tK2KXRESkgwopfQ8PD7x8+RJnzpzRjqWnp+PixYto165dReySiIh0UC6ln56ejqtXr2rfpHVxcYGrqysmTJiAmJgYHD58GF988QXMzMzQr1+/8tglERGVQrmUfmJiIgICAnDjxg3t2JIlS9CxY0fMnTsXkydPRv369bFu3TqYm5uXxy6JiKgUjISiTrUxEDx7p/IZShZDyQEwiyHnAAwniyTO3iEiIsPE0icikhCWPhGRhLD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEJY+kREEsLSJyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikhCWPhGRhLD0iYgkROfS37dvH7p37w4nJyf4+fkhNja2yOXT09OhUCjg4eEBV1dXBAcH4969e2WMS0REZaFT6cfFxSE0NBQeHh5YunQpXF1dERYWhgMHDhS4vCAICAkJwYkTJxAaGoq5c+ciLS0NgwYNQkZGRrneASIi0l0VXRaKiIiAn58fFAoFAMDT0xMZGRlYtGgRunbtmm/5e/fu4fLlywgPD0evXr0AAHZ2dvDx8cHRo0fRu3fv8rsHRESks2KP9FNTU6FUKuHr6ysa79KlC5KSkpCamppvndevXwMATE1NtWPm5uYAgBcvXpQlLxERlUGxpZ+UlAQAsLW1FY3b2NgAAJKTk/Ot07RpU7Rp0wZLly7F3bt3kZ6ejlmzZqFmzZrw8fEpj9xERFQKxU7vZGZmAgBkMploXHMUr1KpClxv+vTpGD58OLp16wYAqFatGpYuXQorK6syBSYiotIrtvQFQSjydmPj/C8W7t69i8DAQFhbW2PKlCmoXr06tm3bhjFjxmDNmjVo3bp1iULWqSMrfiEDYGlp9qfYZmkZShZDyQEwS0EMJQdgOFkMJQegQ+mbmb0Nm5WVJRrXHOFrbs9r3bp1AICoqCjtXL67uzv69++P77//Hjt37ixRyGfPVFCri37yKYi+H+i0tMxy3Z6lpVm5b7O0DCWLoeQAmMWQcwCGk0XfOYyNjYo8UC52Tl8zl69UKkXjKSkpotvzevjwIezs7LSFDwBGRkZo1aoV7ty5o1tyIiIqd8WWvo2NDRo1apTvnPxDhw6hcePGaNCgQb51bG1t8euvv+Lly5ei8WvXrqFhw4ZljExERKWl03n6ISEhUCgUMDc3R/v27XHkyBHEx8cjIiICwNtP3yqVSjRp0gQymQxffPEF9uzZg6FDh2LEiBGoXr06du/ejfPnz2vXISIi/dOp9P39/ZGdnY2oqCjExMTAysoK4eHh2jNzEhMToVAosH79erRp0waNGjXCli1bMH/+fCgUChgZGUEul2Pt2rVo165dhd4hIiIqnE6lDwCBgYEIDAws8DZ/f3/4+/uLxuzs7LB8+fKypSMionLFq2wSEUkIS5+ISEJY+kREEsLSJyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikhCWPhGRhLD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEJY+kREEsLSJyKSEJ1Lf9++fejevTucnJzg5+eH2NjYIpdXq9VYvnw5OnXqBCcnJ3z66afYv39/WfMSEVEZVNFlobi4OISGhmLw4MHw8PBAQkICwsLCUL16dXTt2rXAdb7//ntER0djwoQJaNq0Kfbv34+JEydCJpPB29u7XO8EERHpRqfSj4iIgJ+fHxQKBQDA09MTGRkZWLRoUYGlr1QqsWnTJnz77bfo06cPAMDNzQ337t3DyZMnWfpERJWk2NJPTU2FUqnEhAkTRONdunRBfHw8UlNTYWVlJbotISEB1atXR69evUTjGzduLHtiIiIqtWLn9JOSkgAAtra2onEbGxsAQHJycr51bt++DVtbW5w5cwY9evRAs2bN4Ovri7i4uPLITEREpVRs6WdmZgIAZDKZaNzU1BQAoFKp8q2Tnp6OR48eYcqUKRgwYADWrFkDBwcHjB8/HmfPni2P3EREVArFTu8IglDk7cbG+Z83cnJykJ6ejhUrVqBDhw4AgLZt2yIpKQlLlixB27ZtSxSyTh1Z8QsZAEtLsz/FNkvLULIYSg6AWQpiKDkAw8liKDkAHUrfzOxt2KysLNG45ghfc3tepqamMDExgbu7u3bM2NgY7dq1w/bt20sc8tkzFdTqop98CqLvBzotLbNct2dpaVbu2ywtQ8liKDkAZjHkHIDhZNF3DmNjoyIPlIud3tHM5SuVStF4SkqK6Pa8bGxsoFarkZubKxrPycmBkZFR8amJiKhCFFv6NjY2aNSoEQ4cOCAaP3ToEBo3bowGDRrkW8fT0xOCICA+Pl47lpubi5MnT6JVq1blEJuIiEpDp/P0Q0JCoFAoYG5ujvbt2+PIkSOIj49HREQEgLdv3CqVSjRp0gQymQxubm7w9vbGrFmz8Pvvv6Nx48bYvHkzHjx4gAULFlToHSIiosLpVPr+/v7Izs5GVFQUYmJiYGVlhfDwcHTr1g0AkJiYCIVCgfXr16NNmzYAgMjISCxatAirVq1CRkYGmjVrhqioKDRv3rzi7g0RERXJSCju9BwDUJY3ck/3/KwCEuXnvnsH38iVUA6AWQw5B2A4Wf50b+QSEdFfB0ufiEhCWPpERBLC0icikhCWPhGRhLD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEJY+kREEsLSJyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikhCWPhGRhOhc+vv27UP37t3h5OQEPz8/xMbG6ryTR48eoVWrVli2bFlpMhIRUTnRqfTj4uIQGhoKDw8PLF26FK6urggLC8OBAweKXVcQBEyZMgUqlarMYYmIqGyq6LJQREQE/Pz8oFAoAACenp7IyMjAokWL0LVr1yLX3bx5M5KSksqelIiIyqzYI/3U1FQolUr4+vqKxrt06YKkpCSkpqYWue78+fMxc+bMsiclIqIyK7b0NUfptra2onEbGxsAQHJycoHrqdVqTJ48GX5+fvDy8iprTiIiKgfFTu9kZmYCAGQymWjc1NQUAAqdq//hhx9w//59rFixoqwZUaeOrPiFDIClpdmfYpulZShZDCUHwCwFMZQcgOFkMZQcgA6lLwhCkbcbG+d/sXD37l0sXLgQkZGRMDMr+5199kwFtbroHAXR9wOdlpZZrtuztDQr922WlqFkMZQcALMYcg7AcLLoO4exsVGRB8rFTu9oSjsrK0s0rjnCf7fU37x5A4VCga5du8Ld3R25ubnIzc0F8HbKR/N3IiLSv2JLXzOXr1QqReMpKSmi2zUePXqEa9euITY2Fg4ODto/ALB48WLt34mISP+Knd6xsbFBo0aNcODAAXTu3Fk7fujQITRu3BgNGjQQLV+3bl1s374933Y+//xz9OvXD5999lk5xCYiotLQ6Tz9kJAQKBQKmJubo3379jhy5Aji4+MREREBAEhPT4dSqUSTJk0gk8ng6OhY4Hbq1q1b6G1ERFTxdPpErr+/P2bMmIFTp04hJCQEFy5cQHh4OLp16wYASExMREBAAG7cuFGhYYmIqGx0OtIHgMDAQAQGBhZ4m7+/P/z9/Ytc//bt2yVLRkRE5Y5X2SQikhCWPhGRhLD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEJY+kREEsLSJyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikhCWPhGRhLD0iYgkhKVPRCQhOpf+vn370L17dzg5OcHPzw+xsbFFLp+WloapU6eiQ4cOcHZ2hr+/P+Lj48ual4iIyqCKLgvFxcUhNDQUgwcPhoeHBxISEhAWFobq1auja9eu+ZbPzs7G8OHDkZmZiTFjxqBu3bo4ePAgxo0bhzdv3uDvf/97ud8RIiIqnk6lHxERAT8/PygUCgCAp6cnMjIysGjRogJL/8SJE7h16xZiYmLg5OQEAHB3d8fDhw+xevVqlj4RUSUpdnonNTUVSqUSvr6+ovEuXbogKSkJqamp+dYxNTVFQEAAHB0dReMffvghlEplGSMTEVFpFXukn5SUBACwtbUVjdvY2AAAkpOTYWVlJbrNzc0Nbm5uorGcnBwcP34cH330UZkCExFR6RV7pJ+ZmQkAkMlkonFTU1MAgEql0mlH8+bNw7179zBixIiSZiQionJS7JG+IAhF3m5sXPTzhiAImDdvHn744QcMGzYMPj4+JUsIoE4dWfELGQBLS7M/xTZLy1CyGEoOgFkKYig5AMPJYig5AB1K38zsbdisrCzRuOYIX3N7QbKzszF58mTs378fw4YNw6RJk0oV8tkzFdTqop98CqLvBzotLbNct2dpaVbu2ywtQ8liKDkAZjHkHIDhZNF3DmNjoyIPlIstfc1cvlKphL29vXY8JSVFdPu7VCoVgoODcfnyZUyZMgWDBw8uUXAiIip/xc7p29jYoFGjRjhw4IBo/NChQ2jcuDEaNGiQb503b95g1KhRuHbtGiIiIlj4REQGQqfz9ENCQqBQKGBubo727dvjyJEjiI+PR0REBAAgPT0dSqUSTZo0gUwmw9atW3H+/HkEBASgfv36uHr1qnZbRkZGaNGiRYXcGSIiKppOpe/v74/s7GxERUUhJiYGVlZWCA8PR7du3QAAiYmJUCgUWL9+Pdq0aYODBw8CAKKjoxEdHS3alomJCW7evFnOd4OIiHShU+kDQGBgIAIDAwu8zd/fH/7+/tqf169fX/ZkRERU7niVTSIiCWHpExFJCEufiEhCWPpERBLC0icikhCWPhGRhLD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEJY+kREEsLSJyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikhCdS3/fvn3o3r07nJyc4Ofnh9jY2CKXz8rKwowZM+Du7g5nZ2f84x//wL1798oYl4iIykKn0o+Li0NoaCg8PDywdOlSuLq6IiwsDAcOHCh0nfHjx+PAgQMIDQ1FeHg4njx5gkGDBiEzM7PcwhMRUclU0WWhiIgI+Pn5QaFQAAA8PT2RkZGBRYsWoWvXrvmWv3jxIo4fP47Vq1fDy8sLANC6dWt06tQJW7ZswYgRI8rxLhARka6KPdJPTU2FUqmEr6+vaLxLly5ISkpCampqvnVOnz4NU1NTuLu7a8csLCzg4uKCEydOlENsIiIqjWKP9JOSkgAAtra2onEbGxsAQHJyMqysrPKtY2NjAxMTE9G4tbU14uPjSxzS2NioxOtUhorIaUj33VCyGEoOgFkKYig5AMPJos8cxe2r2NLXzMHLZDLRuKmpKQBApVLlW0elUuVbXrNOQcsXp3Zt0xKvo+G+e0ep1y2pOnXy32dD3GZpGUoWQ8kBMEtBDCUHYDhZDCUHoMP0jiAIRW/AOP8milqnoOWJiEg/im1gMzMzAG9PwcxLc8SuuT0vmUyWb3nNNgp6BUBERPpRbOlr5vKVSqVoPCUlRXT7u+ukpqbmO+JPSUkpcHkiItKPYkvfxsYGjRo1yndO/qFDh9C4cWM0aNAg3zoeHh54+fIlzpw5ox1LT0/HxYsX0a5du3KITUREpaHTefohISFQKBQwNzdH+/btceTIEcTHxyMiIgLA20JXKpVo0qQJZDIZXFxc4OrqigkTJiA0NBS1atXC4sWLYWZmhn79+lXoHSIiosIZCcW9U/tfW7duRVRUFB49egQrKyuMGDECvXr1AgDs3LkTCoUC69evR5s2bQAAGRkZmDNnDhISEqBWq9GqVStMnjwZH374YYXdGSIiKprOpU9ERH9+PH+SiEhCWPpERBLC0s+jpJePrmg///wzHBwc8Pjx40rZv1qtxpYtW/Dpp5/C2dkZPj4+mD17dqk+VV1WgiBg3bp16NKlC5ycnNCjRw/s3btX7zneNXr0aHTu3LlS9p2bmwsnJyfY29uL/jg7O+s9y4ULF9CvXz+0aNECHh4emDlzZoGf1alI586dy/dY5P2za9cuvebZsmUL/Pz80LJlS3z66afYs2ePXvdfGJ3O3pECzeWjBw8eDA8PDyQkJCAsLAzVq1cv8EqiFe3u3bsIDg5Gbm6u3vetsWbNGixcuBDDhg2Dm5sbkpOTERkZiTt37uDf//63XrOsXLkSkZGR+PLLL9GyZUucOHECoaGhMDExQbdu3fSaRWP37t04fPgwrK2tK2X/ycnJeP36NcLDw9G4cWPtuL4/9X716lUMGTIEHTt2xPLly5GSkoJ//etfSE9P157hpw8ODg6Ijo4WjQmCgH/+85/4/fff4e3trbcs0dHRmD59OoYOHQpPT08cP34cX331FapWrQo/Pz+95SiQQIIgCIKPj48wbtw40djYsWOFrl276jVHTk6OsHHjRsHZ2VlwdXUV5HK58OjRI71mEARBUKvVgouLizB9+nTR+P79+wW5XC7cvHlTb1mys7MFFxcX4dtvvxWNDxgwQOjXr5/ecuT1+PFjwcXFRfDy8hJ8fHwqJcOePXuEpk2bCr///nul7F8jKChICAoKEtRqtXZs48aNQqdOnSo927p164SmTZsKV69e1et+AwIChIEDB4rG+vfvLwwYMECvOQrC6R2U7vLRFeXSpUuYP38+hg4ditDQUL3t911ZWVno0aMH/v73v4vGNafcvvsJ7YpkYmKCDRs25PsehqpVq+L169d6y5HX1KlT4e7uDjc3t0rZP/B2+s/a2ho1atSotAyaD13269cPRkb/u7pjUFAQEhISKjVbWloaFi1apJ120qfXr19rL0qpUatWLbx48UKvOQrC0odul4/WFzs7OyQkJGD06NH5Lk2tTzKZDFOnTkWrVq1E4wkJCQCAJk2a6C2LsbEx7O3tUa9ePQiCgKdPn2LVqlU4c+YMAgIC9JZDIyYmBjdu3MDXX3+t933ndfv2bVSrVg3Dhg2Ds7MzXFxcMG3aNL2+5/LLL79AEASYm5tj3LhxaNmyJVq1aoVvvvkGr1690luOgixevBjGxsYYN26c3vc9aNAgnDx5EvHx8VCpVDhw4AASExPRs2dPvWd5F+f0UbrLR1eUDz74QG/7Kqlr165h1apV8PHxgZ2dXaVkOHToEMaMGQMAaN++PXr06KHX/T948ACzZ8/G7NmzYWFhodd9v+vWrVtQqVTo06cPRo4cievXr2Px4sVITk7G+vXrRUfeFSU9PR0AMHnyZHTu3BnLly/H7du3sXDhQrx+/Rpz5syp8AwFefbsGWJjYzF06FC8//77et9/9+7dcfbsWdETTu/evTF8+HC9Z3kXSx+lu3y01Fy6dAkjR45Eo0aNMGvWrErL0axZM2zcuBG3b9/GokWLMGLECPzwww96KThBEDBlyhR4e3ujS5cuFb6/4kRERMDc3Bz29vYAABcXF9SpUwdfffUVzpw5I/rmuoqSk5MDAPjkk0/wzTffAADc3NwgCALCw8MREhKS70uW9CEmJgZqtRqDBg3S+74BYNSoUbhy5QoUCgWaNWuGa9euYdmyZdpX0JWJpY/SXT5aSuLi4jB58mQ0btwYa9asQe3atSsti5WVFaysrODi4gKZTIawsDBcuXIFn3zySYXve9OmTbh9+zb27t2rPatKc8CQm5sLExMTvTz5aLi6uuYba9++PYC3rwL0UfqaV8Oa78LW8PDwwJw5c3D79u1KKf2DBw/C09OzUl6NXb58GadOncLs2bPh7+8P4O2/1fvvv49p06ahb9++kMvles+lwUNYlO7y0VKxdu1aTJgwAS1btsSmTZtQt25dvWd48eIFYmNj8eTJE9F4s2bNAAC//fabXnIcPHgQz58/h4eHBxwcHODg4IDY2FgolUo4ODjo9TzwZ8+eISYmJt9JBpp5dH09MWtOFc3OzhaNa14B6PNJUOPJkye4efNmpZ0a+fDhQwDIdyDSunVrAMCdO3f0nikvlj5Kd/loKYiJicGcOXPg5+eHNWvWVNorHrVajcmTJ+c7B/v06dMAoLejphkzZmD79u2iPx06dED9+vW1f9cXIyMjTJs2DRs3bhSNx8XFwcTEJN8b8BXFzs4ODRs2RFxcnGj82LFjqFKlSqV8UOzatWsAoLfH4F2ag8RLly6Jxq9evQoAaNiwob4jiXB657+Ku3y01Dx79gzfffcdGjZsiKCgINy8eVN0u7W1td5eOltYWKB///5YtWoVqlevDkdHR1y6dAkrV65Enz599Hbl1oL2U6tWLVSrVg2Ojo56yaBhYWGBoKAgbNiwATKZDK1bt8alS5ewYsUKBAUFac88q2hGRkYIDQ3VXkbd398f169fx/LlyzFgwIBKmV755ZdfUKNGjUorVwcHB/j4+OC7775DZmYmPv74Y1y/fh1Lly6Fl5eX3k8ffRdL/7/8/f2RnZ2NqKgoxMTEwMrKCuHh4ZX2ac/KdvLkSfzxxx948OABgoKC8t0+d+5cvZ5+plAo8Le//Q3bt2/H4sWLUb9+fYwZMwbDhg3TWwZDExYWhnr16mHHjh1YtWoV6tWrhzFjxuj9DJFu3bqhWrVqWLp0KYKDg1GnTh2EhIQgODhYrzk0nj59Wiln7OQVERGBJUuWYN26dXj27BkaNmyIoUOH5vusSWXgpZWJiCSEc/pERBLC0icikhCWPhGRhLD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQS8v/HpilyijIppQAAAABJRU5ErkJggg==\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 2: Agent observes itself in location: (0, 0)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 3: Agent observes itself in location: (0, 1)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 4: Agent observes itself in location: (0, 2)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 5: Agent observes itself in location: (1, 2)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 6: Agent observes itself in location: (2, 2)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 7: Agent observes itself in location: (2, 2)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 8: Agent observes itself in location: (2, 2)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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AQLVq0qHBfzRV8RQ/emt/TmjwT+zvgnL6R3bx5EydOnMBzzz0HS0tLtG3bFs7Ozti9e7fOvGNpaSnmzZuH6dOn68zRVqZp06bw9fXFkSNH8Ouvv+rcFhMTg4iICJ2n/eU9ePAAEyZMwAcffKAzrimVqq4W79y5g3bt2ukU/rVr13DgwAHtscvbvn27ztcJCQkwMzPTrmbq378/Ll26pDdFtW7dOgBAv379AEA7dVL+vqpUKu1rAxqaq7ea/uIOGDAAKpUKW7Zs0Rn//PPPUVxcrM3h5+cHtVqNpKQkne22bt2K1NRUPPnkk7hz5w6sra11Cr+oqEi7jLH898jc3LzKrJo39K1fv17nqv/cuXPIyMiAn59flVfF1XHnzh0Aus8whRBITEwEAJ2fR0N5y28HNEyBOjs7w8bGBps3b9Z5vUGlUmHmzJlQKBSVrj579tln0bZtW+zevVvnzWP3799HcnIyWrdurXOR8k/AK/0GlJaWpl0WJ4TA9evXsX37dvz111+YNWuWdrv58+fj5ZdfxsiRIzFmzBi0atUK+/btw9mzZzFnzpxKl9Y9KjIyEt999x3CwsIQFhaGdu3aIT09HYcPH0ZISEilP7zNmzfH+PHjsXr1akRERMDHxwf37t3Dtm3b0LJlS4wcObLSc/r6+iIlJQULFiyAi4sL8vLytPcR0H/R76uvvoJKpYKrqyuOHDmCw4cPY8qUKdqPgggPD8eBAwcwc+ZMjBkzBp06dcKJEydw4MABBAQEaN9Z6+/vj/fffx/vvvsurly5gubNm2P79u06Dz7Awzlic3NzHDx4EO3atUNAQACsrKwMfi+Dg4Oxe/duxMTE4LfffoOzszMyMzOxa9cudO/eXTvNMWDAAHh7eyMmJga///47XFxc8OOPPyI5ORkRERFo1aoVfH19sX79esyYMQPe3t7Iz8/Hjh07tM9Kyn+PrK2tcfLkSWzfvh3e3t56uZ599lmMHz8emzdvxsSJE+Hv74/8/Hxs3rwZTzzxRL18jpKvry82b96M8PBwjBo1CqWlpUhNTUVmZibMzc318n7//feIj49Hr1699J59lN8OAFasWIE+ffrU6uNDKtOsWTPMnz8fs2bNQlBQEEaNGoXHHnsMSUlJuHr1KpYuXVrptFGTJk2wYMECTJ8+HaNGjcKoUaOgVquxc+dOZGVlaZdu/qM00qqhf7SKlmw+99xzom/fvuLVV18VGRkZevtkZmaK8PBw0atXL9GtWzfx4osvil27dulsY2jJphBCXL58WcyePVv06dNHuLi4iKFDh4qEhASdpWwVLdl88OCBSEhIEMOHDxfdu3cXvXr1Eq+++qr4+eefq7yvd+7cEfPmzRNeXl7C1dVVBAQEiJiYGHH69Gkhl8vFp59+KoT431LKn376SYwePVo4OzuLgQMH6i2JFEKI/Px88dZbbwlPT0/h7OwsAgMDxYYNG3Tug+Z+BAcHC2dnZ+Hj4yNWrlypXZJYfinn2rVrhbu7u3B1ddUuyXzUo0s2hRCiqKhIxMTECD8/P+Hk5CQGDhwo/vOf/4i//vpLZ9979+6JZcuWiX79+glnZ2cxdOhQkZiYKB48eKC9PSYmRvj6+goXFxcxcOBA8dZbb4lLly6JLl26iHfffVd7rF27dgkvLy/h7Owsdu/eXeGSU7VaLRITE8Xw4cOFk5OT8PT0FHPnzhV5eXnabSpbqlrdJazbt28XQ4YMES4uLsLb21uEh4eLzMxM8dJLL4nhw4drt8vMzBSBgYHCyclJvP3225UeLy8vT4wcOVI4OTmJSZMmCSEqXrL56PLPin5WK9s2IyNDjB8/XnTv3l307NlThISE6Cz/rEpGRoYYN26c6Natm+jWrZsYM2aMOHLkSLX2/bsxE4J/GJ2ISCo4p09EJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikpC/xZuzbt8uhlptvJWlbdrIcOtW7d/G/k/LAZhOFlPJATCLKecATCeLsXOYm5uhdevK/yre36L01Wph1NLXnNMUmEoOwHSymEoOgFkqYio5ANPJYio5AE7vEBFJCkufiEhCalz6v/zyC5ycnCr8o9flFRcXY9GiRfDy8kKPHj3w6quv4vLly7XNSURE9aBGpX/p0iWEh4dX66N+Z82ahf379yMyMhKxsbG4ceMGJkyYgKKiolqHJSKiuqlW6ZeVlWHLli0IDg7W+czpypw6dQpHjhxBbGwsXnrpJQQEBGDjxo0oKirC1q1b6xyaiIhqp1qlf/r0aSxduhSTJk1CZGSkwe2PHz8OCwsLeHl5acesra3h5uaGo0eP1j4tERHVSbVK38HBAWlpaXj99dcr/Qs05WVlZcHOzk5v244dO1b4p/CIiMg4qrVO/8knn6zRQVUqFWQymd64hYVFrf52Z5s2+sdqaDY2lkY/Z0VMJQdgOllMJQfALBUxlRxA/WZRl5TA/L9/U9cYOepyvqo0yJuzqvq7LFX9vdXK3LqlMuqbG2xsLJGf3/gvOJtKDsB0sphKDoBZTDkHUP9ZbGwscfyFyv90aH3z2rOzVvnNzc2qvFBukHX6MplM72+jAg+XcVb0DICIiIyjQUrf3t4eubm5elf8OTk5sLe3b4hTEhFRNTRI6Xt7e+Pu3bvIyMjQjhUUFODUqVPw9PRsiFMSEVE11EvpFxQU4MyZM9oXad3c3ODu7o7Zs2cjKSkJ33zzDV555RVYWlpizJgx9XFKIiKqhXop/fT0dISEhODcuXPasY8//hgDBgzAkiVLEB0djaeffhobN26ElZVVfZySiIhqwUxUtdTGRHD1TuMzlSymkgNgFlPOAXD1TqW31yUUERH9vbD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEJY+kREEsLSJyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikhCWPhGRhLD0iYgkhKVPRCQhLH0iIgmpdunv3bsXw4YNg6urKwIDA5GcnFzl9gUFBVAoFPD29oa7uzvCw8Nx+fLlOsYlIqK6qFbpp6SkIDIyEt7e3li1ahXc3d0RFRWF/fv3V7i9EAIRERE4evQoIiMjsWTJEuTn52PChAkoLCys1ztARETV17Q6G8XFxSEwMBAKhQIA4OPjg8LCQixfvhxDhgzR2/7y5cv44YcfEBsbixdffBEA4ODgAH9/fxw6dAgvvfRS/d0DIiKqNoNX+rm5uVAqlQgICNAZHzx4MLKyspCbm6u3z/379wEAFhYW2jErKysAwJ07d+qSl4iI6sBg6WdlZQEA7O3tdcbt7OwAANnZ2Xr7dOnSBX369MGqVatw6dIlFBQU4P3338fjjz8Of3//+shNRES1YHB6p6ioCAAgk8l0xjVX8SqVqsL9Fi5ciClTpmDo0KEAgObNm2PVqlWwtbWtU2AiIqo9g6UvhKjydnNz/ScLly5dQmhoKDp27Ih58+ahRYsW2L59O6ZPn44NGzagd+/eNQrZpo3M8Eb1zMbG0ujnrIip5ABMJ4up5ACYpSKmkgMwrSy10RD5DZa+peXDkxYXF+uMa67wNbeXt3HjRgBAfHy8di7fy8sLY8eOxQcffIBdu3bVKOStWyqo1VU/+NQnGxtL5OcXGe18pp4DMJ0sppIDYBZTzgHUf5bGeACpTX5zc7MqL5QNzulr5vKVSqXOeE5Ojs7t5V29ehUODg7awgcAMzMz9OrVCxcvXqxeciIiqncGS9/Ozg4dOnTQW5N/4MABdOrUCe3atdPbx97eHr///jvu3r2rM3727Fm0b9++jpGJiKi2qrVOPyIiAgqFAlZWVujXrx8OHjyI1NRUxMXFAXj47lulUonOnTtDJpPhlVdewZdffolJkyZh6tSpaNGiBfbs2YOTJ09q9yEiIuOrVukHBQWhpKQE8fHxSEpKgq2tLWJjY7Urc9LT06FQKLBp0yb06dMHHTp0wNatW7F06VIoFAqYmZlBLpcjISEBnp6eDXqHiIioctUqfQAIDQ1FaGhohbcFBQUhKChIZ8zBwQGrV6+uWzoiIqpX/JRNIiIJYekTEUkIS5+ISEJY+kREEsLSJyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikhCWPhGRhLD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEJY+kREElLt0t+7dy+GDRsGV1dXBAYGIjk5ucrt1Wo1Vq9ejYEDB8LV1RXPP/889u3bV9e8RERUB02rs1FKSgoiIyPx8ssvw9vbG2lpaYiKikKLFi0wZMiQCvf54IMPsG3bNsyePRtdunTBvn37MGfOHMhkMvj5+dXrnSAiouqpVunHxcUhMDAQCoUCAODj44PCwkIsX768wtJXKpXYsmUL3n33XQQHBwMAPDw8cPnyZRw7doylT0TUSAyWfm5uLpRKJWbPnq0zPnjwYKSmpiI3Nxe2trY6t6WlpaFFixZ48cUXdcYTExPrnpiIiGrN4Jx+VlYWAMDe3l5n3M7ODgCQnZ2tt8+FCxdgb2+PjIwMjBgxAl27dkVAQABSUlLqIzMREdWSwdIvKioCAMhkMp1xCwsLAIBKpdLbp6CgANeuXcO8efMwbtw4bNiwAU5OTpg1axZOnDhRH7mJiKgWDE7vCCGqvN3cXP9xo7S0FAUFBVizZg369+8PAOjbty+ysrLw8ccfo2/fvjUK2aaNzPBG9czGxtLo56yIqeQATCeLqeQAmKUippIDMK0stdEQ+Q2WvqXlw5MWFxfrjGuu8DW3l2dhYYEmTZrAy8tLO2Zubg5PT0/s2LGjxiFv3VJBra76wac+2dhYIj+/yGjnM/UcgOlkMZUcALOYcg6g/rM0xgNIbfKbm5tVeaFscHpHM5evVCp1xnNycnRuL8/Ozg5qtRplZWU646WlpTAzMzOcmoiIGoTB0rezs0OHDh2wf/9+nfEDBw6gU6dOaNeund4+Pj4+EEIgNTVVO1ZWVoZjx46hV69e9RCbiIhqo1rr9CMiIqBQKGBlZYV+/frh4MGDSE1NRVxcHICHL9wqlUp07twZMpkMHh4e8PPzw/vvv48///wTnTp1wueff44rV65g2bJlDXqHiIioctUq/aCgIJSUlCA+Ph5JSUmwtbVFbGwshg4dCgBIT0+HQqHApk2b0KdPHwDAihUrsHz5cqxbtw6FhYXo2rUr4uPj4ezs3HD3hoiIqmQmDC3PMQF8IbfxmUoWU8kBMIsp5wAa5oXc4y+MrLfjGeK1Z2fjvJBLRET/HCx9IiIJYekTEUkIS5+ISEJY+kREEsLSJyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikhCWPhGRhLD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEJY+kREElLt0t+7dy+GDRsGV1dXBAYGIjk5udonuXbtGnr16oVPPvmkNhmJiKieVKv0U1JSEBkZCW9vb6xatQru7u6IiorC/v37De4rhMC8efOgUqnqHJaIiOqmaXU2iouLQ2BgIBQKBQDAx8cHhYWFWL58OYYMGVLlvp9//jmysrLqnpSIiOrM4JV+bm4ulEolAgICdMYHDx6MrKws5ObmVrnv0qVL8d5779U9KRER1ZnB0tdcpdvb2+uM29nZAQCys7Mr3E+tViM6OhqBgYHw9fWta04iIqoHBqd3ioqKAAAymUxn3MLCAgAqnav/7LPPkJeXhzVr1tQ1I9q0kRneqJ7Z2Fga/ZwVMZUcgOlkMZUcALNUxFRyAKaVpTYaIr/B0hdCVHm7ubn+k4VLly7ho48+wooVK2BpWffQt26poFZXnaM+2dhYIj+/yGjnM/UcgOlkMZUcALOYcg6g/rM0xgNIbfKbm5tVeaFscHpHU9rFxcU645or/EdL/cGDB1AoFBgyZAi8vLxQVlaGsrIyAA+nfDT/TURExmew9DVz+UqlUmc8JydH53aNa9eu4ezZs0hOToaTk5P2HwCsXLlS+99ERGR8Bqd37Ozs0KFDB+zfvx+DBg3Sjh84cACdOnVCu3btdLZv27YtduzYoXecUaNGYcyYMRg5cmQ9xCYiotqo1jr9iIgIKBQKWFlZoV+/fjh48CBSU1MRFxcHACgoKIBSqUTnzp0hk8ng4uJS4XHatm1b6W1ERNTwqvWO3KCgICxatAjffvstIiIi8P333yM2NhZDhw4FAKSnpyMkJATnzp1r0LBERFQ31brSB4DQ0FCEhoZWeFtQUBCCgoKq3P/ChQs1S0ZERPWOn7JJRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEJY+kREEsLSJyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikhCWPhGRhLD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQqpd+nv37sWwYcPg6uqKwMBAJCcnV7l9fn4+5s+fj/79+6NHjx4ICgpCampqXfMSEVEdNK3ORikpKYiMjMTLL78Mb29vpKWlISoqCi1atMCQIUP0ti8pKcGUKVNQVFSE6dOno23btvj6668xc+ZMPHjwAMOHD6/3O0JERIZVq/Tj4uIQGBgIhUIBAPDx8UFhYSGWL19eYekfPXoUv/76K5KSkuDq6goA8PLywtWrV7F+/XqWPhFRIzE4vZObmwulUomAgACd8cGDByMrKwu5ubl6+1hYWCAkJAQuLi4648888wyUSmUdIxMRUW0ZvNLPysoCANjb2+uM29nZAQCys7Nha2urc5uHhwc8PDx0xkpLS3HkyBE8++yzdQpMRES1Z/BKv6ioCAAgk8l0xi0sLAAAKpWqWif68MMPcfnyZUydOrWmGYmIqJ4YvNIXQlR5u7l51Y8bQgh8+OGH+OyzzzB58mT4+/vXLCGANm1khjeqZzY2lkY/Z0VMJQdgOllMJQfALBUxlRyAaWWpjYbIb7D0LS0fnrS4uFhnXHOFr7m9IiUlJYiOjsa+ffswefJkzJ07t1Yhb91SQa2u+sGnPtnYWCI/v8ho5zP1HIDpZDGVHACzmHIOoP6zNMYDSG3ym5ubVXmhbLD0NXP5SqUSjo6O2vGcnByd2x+lUqkQHh6OH374AfPmzcPLL79co+BERFT/DM7p29nZoUOHDti/f7/O+IEDB9CpUye0a9dOb58HDx7gtddew9mzZxEXF8fCJyIyEdVapx8REQGFQgErKyv069cPBw8eRGpqKuLi4gAABQUFUCqV6Ny5M2QyGb744gucPHkSISEhePrpp3HmzBntsczMzNCtW7cGuTNERFS1apV+UFAQSkpKEB8fj6SkJNja2iI2NhZDhw4FAKSnp0OhUGDTpk3o06cPvv76awDAtm3bsG3bNp1jNWnSBOfPn6/nu0FERNVRrdIHgNDQUISGhlZ4W1BQEIKCgrRfb9q0qe7JiIio3vFTNomIJISlT0QkISx9IiIJYekTEUkIS5+ISEJY+kREEsLSJyKSEJY+EZGEsPSJiCSEpU9EJCEsfSIiCWHpExFJCEufiEhCWPpERBLC0icikhCWPhGRhLD0iYgkhKVPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkISx9IiIJYekTEUkIS5+ISEKqXfp79+7FsGHD4OrqisDAQCQnJ1e5fXFxMRYtWgQvLy/06NEDr776Ki5fvlzHuEREVBfVKv2UlBRERkbC29sbq1atgru7O6KiorB///5K95k1axb279+PyMhIxMbG4saNG5gwYQKKiorqLTwREdVM0+psFBcXh8DAQCgUCgCAj48PCgsLsXz5cgwZMkRv+1OnTuHIkSNYv349fH19AQC9e/fGwIEDsXXrVkydOrUe7wIREVWXwSv93NxcKJVKBAQE6IwPHjwYWVlZyM3N1dvn+PHjsLCwgJeXl3bM2toabm5uOHr0aD3EJiKi2jB4pZ+VlQUAsLe31xm3s7MDAGRnZ8PW1lZvHzs7OzRp0kRnvGPHjkhNTa1xSHNzsxrvU1eNcc6KmEoOwHSymEoOgFkqYio5ANPKUhu1yW9oH4Olr5mDl8lkOuMWFhYAAJVKpbePSqXS216zT0XbG9K6tUWN96mrNm308zcGU8kBmE4WU8kBMEtFTCUHUP9ZvPbsrNfjGdIQ30uD0ztCiKoPYK5/iKr2qWh7IiIyDoMNbGlpCeDhEszyNFfsmtvLk8lkettrjlHRMwAiIjIOg6WvmctXKpU64zk5OTq3P7pPbm6u3hV/Tk5OhdsTEZFxGCx9Ozs7dOjQQW9N/oEDB9CpUye0a9dObx9vb2/cvXsXGRkZ2rGCggKcOnUKnp6e9RCbiIhqo1rr9CMiIqBQKGBlZYV+/frh4MGDSE1NRVxcHICHha5UKtG5c2fIZDK4ubnB3d0ds2fPRmRkJFq1aoWVK1fC0tISY8aMadA7RERElTMThl6p/a8vvvgC8fHxuHbtGmxtbTF16lS8+OKLAIBdu3ZBoVBg06ZN6NOnDwCgsLAQMTExSEtLg1qtRq9evRAdHY1nnnmmwe4MERFVrdqlT0REf39cP0lEJCEsfSIiCWHpl1PTj49uaL/88gucnJxw/fr1Rjm/Wq3G1q1b8fzzz6NHjx7w9/fH4sWLa/Wu6roSQmDjxo0YPHgwXF1dMWLECHz11VdGz/Go119/HYMGDWqUc5eVlcHV1RWOjo46/3r06GH0LN9//z3GjBmDbt26wdvbG++9916F79VpSN99953e96L8v927dxs1z9atWxEYGIju3bvj+eefx5dffmnU81emWqt3pEDz8dEvv/wyvL29kZaWhqioKLRo0aLCTxJtaJcuXUJ4eDjKysqMfm6NDRs24KOPPsLkyZPh4eGB7OxsrFixAhcvXsSnn35q1Cxr167FihUr8MYbb6B79+44evQoIiMj0aRJEwwdOtSoWTT27NmDb775Bh07dmyU82dnZ+P+/fuIjY1Fp06dtOPGftf7mTNnMHHiRAwYMACrV69GTk4O/vOf/6CgoEC7ws8YnJycsG3bNp0xIQTeeust/Pnnn/Dz8zNalm3btmHhwoWYNGkSfHx8cOTIEbz55pto1qwZAgMDjZajQoKEEEL4+/uLmTNn6ozNmDFDDBkyxKg5SktLRWJioujRo4dwd3cXcrlcXLt2zagZhBBCrVYLNzc3sXDhQp3xffv2CblcLs6fP2+0LCUlJcLNzU28++67OuPjxo0TY8aMMVqO8q5fvy7c3NyEr6+v8Pf3b5QMX375pejSpYv4888/G+X8GmFhYSIsLEyo1WrtWGJiohg4cGCjZ9u4caPo0qWLOHPmjFHPGxISIsaPH68zNnbsWDFu3Dij5qgIp3dQu4+PbiinT5/G0qVLMWnSJERGRhrtvI8qLi7GiBEjMHz4cJ1xzZLbR9+h3ZCaNGmCzZs36/0dhmbNmuH+/ftGy1He/Pnz4eXlBQ8Pj0Y5P/Bw+q9jx45o2bJlo2XQvOlyzJgxMDP736c7hoWFIS0trVGz5efnY/ny5dppJ2O6f/++9kMpNVq1aoU7d+4YNUdFWPqo3sdHG4uDgwPS0tLw+uuv6300tTHJZDLMnz8fvXr10hlPS0sDAHTu3NloWczNzeHo6IinnnoKQgjcvHkT69atQ0ZGBkJCQoyWQyMpKQnnzp3D22+/bfRzl3fhwgU0b94ckydPRo8ePeDm5oYFCxYY9TWX3377DUIIWFlZYebMmejevTt69eqFd955B/fu3TNajoqsXLkS5ubmmDlzptHPPWHCBBw7dgypqalQqVTYv38/0tPT8cILLxg9y6M4p4/afXx0Q3nyySeNdq6aOnv2LNatWwd/f384ODg0SoYDBw5g+vTpAIB+/fphxIgRRj3/lStXsHjxYixevBjW1tZGPfejfv31V6hUKgQHB2PatGnIzMzEypUrkZ2djU2bNulceTeUgoICAEB0dDQGDRqE1atX48KFC/joo49w//59xMTENHiGity6dQvJycmYNGkSnnjiCaOff9iwYThx4oTOA85LL72EKVOmGD3Lo1j6qN3HR0vN6dOnMW3aNHTo0AHvv/9+o+Xo2rUrEhMTceHCBSxfvhxTp07FZ599ZpSCE0Jg3rx58PPzw+DBgxv8fIbExcXBysoKjo6OAAA3Nze0adMGb775JjIyMnT+cl1DKS0tBQD07NkT77zzDgDAw8MDQgjExsYiIiJC748sGUNSUhLUajUmTJhg9HMDwGuvvYYff/wRCoUCXbt2xdmzZ/HJJ59on0E3JpY+avfx0VKSkpKC6OhodOrUCRs2bEDr1q0bLYutrS1sbW3h5uYGmUyGqKgo/Pjjj+jZs2eDn3vLli24cOECvvrqK+2qKs0FQ1lZGZo0aWKUBx8Nd3d3vbF+/foBePgswBilr3k2rPlb2Bre3t6IiYnBhQsXGqX0v/76a/j4+DTKs7EffvgB3377LRYvXoygoCAAD/9fPfHEE1iwYAFGjx4NuVxu9FwavIRF7T4+WioSEhIwe/ZsdO/eHVu2bEHbtm2NnuHOnTtITk7GjRs3dMa7du0KAPjjjz+MkuPrr7/G7du34e3tDScnJzg5OSE5ORlKpRJOTk5GXQd+69YtJCUl6S0y0MyjG+uBWbNUtKSkRGdc8wzAmA+CGjdu3MD58+cbbWnk1atXAUDvQqR3794AgIsXLxo9U3ksfdTu46OlICkpCTExMQgMDMSGDRsa7RmPWq1GdHS03hrs48ePA4DRrpoWLVqEHTt26Pzr378/nn76ae1/G4uZmRkWLFiAxMREnfGUlBQ0adJE7wX4huLg4ID27dsjJSVFZ/zw4cNo2rRpo7xR7OzZswBgtO/BozQXiadPn9YZP3PmDACgffv2xo6kg9M7/2Xo46Ol5tatW/j3v/+N9u3bIywsDOfPn9e5vWPHjkZ76mxtbY2xY8di3bp1aNGiBVxcXHD69GmsXbsWwcHBRvvk1orO06pVKzRv3hwuLi5GyaBhbW2NsLAwbN68GTKZDL1798bp06exZs0ahIWFaVeeNTQzMzNERkZqP0Y9KCgImZmZWL16NcaNG9co0yu//fYbWrZs2Wjl6uTkBH9/f/z73/9GUVERnnvuOWRmZmLVqlXw9fU1+vLRR7H0/ysoKAglJSWIj49HUlISbG1tERsb22jv9mxsx44dw19//YUrV64gLCxM7/YlS5YYdfmZQqHAv/71L+zYsQMrV67E008/jenTp2Py5MlGy2BqoqKi8NRTT2Hnzp1Yt24dnnrqKUyfPt3oK0SGDh2K5s2bY9WqVQgPD0ebNm0QERGB8PBwo+bQuHnzZqOs2CkvLi4OH3/8MTZu3Ihbt26hffv2mDRpkt57TRoDP1qZiEhCOKdPRCQhLH0iIglh6RMRSQhLn4hIQlj6REQSwtInIpIQlj4RkYSw9ImIJISlT0QkIf8fS1bO+hr7+30AAAAASUVORK5CYII=\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Time 9: Agent observes itself in location: (2, 2)\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"D = utils.onehot(grid_locations.index((0,0)), n_states) # let's have the agent believe it starts in location (0,0) (upper left corner) \\n\",\n \"env = GridWorldEnv(starting_state = (0,0))\\n\",\n \"qs_final = active_inference_with_planning(A, B, C, D, n_actions, env, policy_len = 3, T = 10)\"\n ]\n }\n ],\n \"metadata\": {\n \"colab\": {\n \"collapsed_sections\": [\n \"yJ9312In3r0Y\",\n \"kZmnZPB74Sc1\",\n \"61gmngb9449T\",\n \"v_ACEjni5fXJ\",\n \"_JMDEO2H6wMj\",\n \"ttPFk03l8PDa\",\n \"rh2fsJo_My-7\",\n \"E519ke5jNOIX\",\n \"Hi0XgIjzPrYX\",\n \"hBrU3E67QCYB\",\n \"gu73H44qQXwg\",\n \"rKkZTJHtRUhl\",\n \"_FXn27owS96w\",\n \"6HAHCc7bT5eC\",\n \"jofLVCH7quQp\",\n \"_Bpows4RsRLd\",\n \"JLPPVtrysl41\"\n ],\n \"name\": \"Active Inference with pymdp: Tutorial 1\",\n \"provenance\": []\n },\n \"kernelspec\": {\n \"display_name\": \"Python 3.8.8 ('base')\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.8.8\"\n },\n \"vscode\": {\n \"interpreter\": {\n \"hash\": \"70b7ceca5df5387258d861d4588082cea9500e731be001548c95afd8cd8c3af8\"\n }\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": "docs/notebooks/cue_chaining_demo.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Active Inference Demo: Epistemic Chaining\\n\",\n \"\\n\",\n \"[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/infer-actively/pymdp/blob/main/docs/notebooks/cue_chaining_demo.ipynb)\\n\",\n \"\\n\",\n \"*Author: Conor Heins*\\n\",\n \"\\n\",\n \"This demo notebook builds a generative model from scratch, constructs an `Agent` instance using the constructed generative model, and then runs an active inference simulation in a simple environment.\\n\",\n \"\\n\",\n \"The environment used here is similar in spirit to the [T-Maze demo](https://pymdp-rtd.readthedocs.io/en/latest/notebooks/tmaze_demo.html), but the task structure is more complex. Here, we analogize the agent to a rat tasked with solving a spatial puzzle. The rat must sequentially visit a sequence of two cues located at different locations in a 2-D grid world, in order to ultimately reveal the locations of two (opposite) reward outcomes: one location will give the rat a reward (\\\"Cheese\\\") and the other location will give the rat a punishment (\\\"Shock\\\").\\n\",\n \"\\n\",\n \"Using active inference to solve a POMDP representation of this task, the rat can successfully forage the correct cues in sequence, in order to ultimately discover the location of the \\\"Cheese\\\", and avoid the \\\"Shock\\\".\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"*Note*: When running this notebook in Google Colab, you may have to run `!pip install inferactively-pymdp` at the top of the notebook, before you can `import pymdp`. That cell is left commented out below, in case you are running this notebook from Google Colab.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# ! pip install inferactively-pymdp\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Imports\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import numpy as np\\n\",\n \"\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp import utils\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Grid World Parameters\\n\",\n \"Let's begin by initializing several variables related to the physical environment inhabited by the agent. These variables will encode things like the dimensions of the grid, the possible locations of the different cues, and the possible locations of the reward or punishment.\\n\",\n \"\\n\",\n \"Having these variables defined will also come in handy when setting up the generative model of our agent and when creating the environment class.\\n\",\n \"\\n\",\n \"We will create a grid world with dimensions $5 \\\\times 7$. Particular locations of the grid are indexed as (y, x) tuples, that select a particular row and column respectively of that location in the grid.\\n\",\n \"\\n\",\n \"By design of the task, one location in the grid world contain a cue: **Cue 1**. There will be four additional locations, that will serve as possible locations for a second cue: **Cue 2**. Crucially, only *one* of these four additional locations will actually contain **Cue 2** - the other 3 will be empty. When the agent visits **Cue 1** by moving to its location, one of four signals is presented, which each unambiguously signal which of the 4 possible locations **Cue 2** occupies -- we can refer to these Cue-2-location-signals with obvious names: `L1`, `L2`, `L3`, `L4`. Once **Cue 2**'s location has been revealed, by visiting that location the agent will then receive one of two possible signals, that indicate where the hidden reward is located (and conversely, where the hidden punishment lies). These two possible reward/punishment locations are indicated by two locations: \\\"TOP\\\" (meaning the \\\"Cheese\\\" reward is on the upper of the two locations) or \\\"BOTTOM\\\" (meaning the \\\"Cheese\\\" reward is on the lower of the two locations).\\n\",\n \"\\n\",\n \"In this way, the most efficient and risk-sensitive way to achieve reward in this task is to first visit **Cue 1**, in order to figure out the location of **Cue 2**, in order to figure out the location of the reward.\\n\",\n \"\\n\",\n \"*Tip*: When setting up `pymdp` generative models and task environments, we recommend creating additional variables, like lists of strings or dicts with string-valued keys, that help you relate the values of various aspects of the task to semantically-meaning labels. These come in handy when generating print statements during debugging or labels for plotting. For example, below we create a list called `reward_conditions` that stores the \\\"names\\\" of the two reward conditions: `\\\"TOP\\\"` and `\\\"BOTTOM\\\"`\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"grid_dims = [5, 7] # dimensions of the grid (number of rows, number of columns)\\n\",\n \"num_grid_points = np.prod(grid_dims) # total number of grid locations (rows X columns)\\n\",\n \"\\n\",\n \"# create a look-up table `loc_list` that maps linear indices to tuples of (y, x) coordinates \\n\",\n \"grid = np.arange(num_grid_points).reshape(grid_dims)\\n\",\n \"it = np.nditer(grid, flags=[\\\"multi_index\\\"])\\n\",\n \"\\n\",\n \"loc_list = []\\n\",\n \"while not it.finished:\\n\",\n \" loc_list.append(it.multi_index)\\n\",\n \" it.iternext()\\n\",\n \"\\n\",\n \"# (y, x) coordinate of the first cue's location, and then a list of the (y, x) coordinates of the possible locations of the second cue, and their labels (`L1`, `L2`, ...)\\n\",\n \"cue1_location = (2, 0)\\n\",\n \"\\n\",\n \"cue2_loc_names = ['L1', 'L2', 'L3', 'L4']\\n\",\n \"cue2_locations = [(0, 2), (1, 3), (3, 3), (4, 2)]\\n\",\n \"\\n\",\n \"# names of the reward conditions and their locations\\n\",\n \"reward_conditions = [\\\"TOP\\\", \\\"BOTTOM\\\"]\\n\",\n \"reward_locations = [(1, 5), (3, 5)]\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Visualize the grid world\\n\",\n \"\\n\",\n \"Let's quickly use the variables we just defined to visualize the grid world, including the **Cue 1** location, the possible **Cue 2** locations, and the possible reward locations (in gray, since we don't know which one has the \\\"Cheese\\\" and which one has the \\\"Shock\\\")\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": \"iVBORw0KGgoAAAANSUhEUgAAAkwAAAFpCAYAAABu7XfbAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAAAUYElEQVR4nO3df7DddX3n8dcboggSiAIqTRApQZwpY0VTxRJtq+JimlFsO1Nh5A/d3TjWCvbHdDSz1jjtQHdnp1NZa5cMwtpWtCqINhvrwvJD4opI+GERkCCQhSwSqQIBmYSQz/6RawwG8jk398e5597HYybDud/7ycl7PnPuvU++53vOrdZaAAB4dvsNewAAgJlOMAEAdAgmAIAOwQQA0CGYAAA6BBMAQMdAwVRVp1bV96vqrqr68FQPBQAwk1TvfZiqav8kdyY5Jcn9Sb6T5PTW2m1TPx4AwPANcobptUnuaq3d3VrbluTzSd4xtWMBAMwcgwTTwiT37fbx/WPHAADmhHmTdUdVtSLJirEPXzNZ9wsAMMUeaq0dsbcFgwTTpiRH7fbxorFjT9NaW51kdZJUlV9QBwCMio29BYME03eSHFdVx2RnKL0ryRmD/OtvOeOGQZYx5oqLl+y6be/Gb/f9O/u8LUOcZDR94qz5u257/I2Pr92JsX8TY/8mZvf925tuMLXWtlfVHyb5epL9k1zYWvvexMYDABgdA13D1Fpbm2TtFM8CADAjeadvAIAOwQQA0CGYAAA6BBMAQIdgAgDoEEwAAB2CCQCgQzABAHQIJgCADsEEANAhmAAAOgQTAECHYAIA6BBMAAAdggkAoEMwAQB0CCYAgA7BBADQIZgAADoEEwBAh2ACAOgQTAAAHfOGPQDMNtetPSe3XHt+3nfuxmf8/Lf/5T9n013r8uDG9dm2dUve87Fbc8hhR0/zlACMhzNMMM1u/eaF2bFjexYd94ZhjwLAgJxhgmn23o/fntpvv9x969dy961rhz0OAANwhgmmWe3nyw5g1PjODQDQIZgAADoEEwBAh2ACAOgQTAAAHYIJAKDD+zDBFNix/clsuOmyPY4vXHxyfvzD7+eJxx7K5vtuSpLce9vlOfDgw/PCl7wihx35immeFIBBCCaYAtu2bsnai87c4/jvfnBtrvvaOdl017pdx6764h8lSV536kdy2JErp21GAAYnmGCSnbRsZU5a9uzh83vHfW0apwFgMriGCQCgQzABAHQIJgCADsEEANAhmAAAOgQTAECHYAIA6BBMAAAdggkAoEMwAQB0CCYAgA7BBADQIZgAADoEEwBAh2ACAOgQTAAAHYIJAKBDMAEAdAgmAIAOwQQA0CGYAAA6usFUVRdW1eaqunU6BgIAmGkGOcP0P5KcOsVzAADMWPN6C1pr36iql03DLADMMUtfviZLV63a7ciaYY0ysn5x/9bduXxYo8xq1VrrL9oZTGtaaycMdKdV/TsFYM5b9bQf9kwGe7pP1rfWluxtQfcM06CqakWSFZN1fwAAM8WkBVNrbXWS1YkzTADA7DJpwfRM3nLGDVN597POFRf//GygvRs/+zcxu+/f2edtGeIko+cTZ83fddtjb7xcszTZPAbHZ/fvfXszyNsKfC7Jt5IcX1X3V9W/n+BsAAAjZZBXyZ0+HYMAAMxU3ukbAKBDMAEAdAgmAIAOwQQA0CGYAAA6BBMAQIdgAgDoEEwAAB2CCQCgQzABAHQIJgCADsEEANAhmAAAOgQTAECHYAIA6BBMAAAdggkAoEMwAQB0CCYAgA7BBADQIZgAADoEEwBAh2ACAOiYN+wBAHZ33dpzcsu15+d9527c43M/efDO3HzNf899G67Jlh/fl4MOeXF++YS35aS3rcwBBy2Y/mGBOUMwASPj/37/qvy/e67LK5f+hxz+SyfkkYfuybf+51/kgXuuz+//8ZWp/Zw0B6aGYAJGxstf83t55RtWpKqSJIuOe0MOXrAwl/3dadn0g/+TRcctHfKEwGwlmICRceDzD9vj2BGLXpkkefzRB6Z7HGAOcf4aGGk/vPf6JMmCIxYPeRJgNhNMwMh6cttPs+6rf56Fi5fmxS89cdjjALOYYAJGUmstV1z8gTyx5Uc55YxPDXscYJYTTMBI+uZXP5offPefs/w/fi6HHn7MsMcBZjnBBIycG6/6ZNZfeV7e+u7VWXjsycMeB5gDBBMwUu74zj/l2stW5o2nnZuXv/p3hj0OMEd4WwFgxtmx/clsuOmyPY4fePDhufzi9+fo49+cl7zs1/LAPdfv+tzBCxZm/gsWTuOUwFwimIAZZ9vWLVl70Zl7HF+4eGl2PPVkNt5xRTbeccXTPve6Uz+Sk5atnK4RgTlGMAEzyknLVgofYMZxDRMAQIdgAgDoEEwAAB2CCQCgQzABAHQIJgCADsEEANAhmAAAOgQTAECHYAIA6BBMAAAdggkAoEMwAQB0CCYAgA7BBADQIZgAADoEEwBAh2ACAOgQTAAAHYIJAKBDMAEAdHSDqaqOqqqrquq2qvpeVZ09HYMBAMwU8wZYsz3Jn7TWbqyq+UnWV9XlrbXbpng2AIAZoVpr4/sLVV9J8snW2uV7WTO+OwVgTlq1atWwR5h17Ok+Wd9aW7K3BYOcYdqlql6W5MQk336Gz61IsmI89wcAMAoGDqaqOjjJJUk+1Fp79Bc/31pbnWT12FpnmACAWWOgYKqq52RnLH22tXbpoHf+g7vu2te55qRjFy/edfstZ9wwxElG0xUX//xsqv0bP/u37+zdRKwZ9gCzjsfg+Oz+9bs33WCqqkry6SS3t9b+eoJzAcAu6+5cLjgnyP5Nj0Heh+nkJGcmeVNV3Tz2Z9kUzwUAMGN0zzC11tYlqWmYBQBgRvJO3wAAHYIJAKBDMAEAdAgmAIAOwQQA0CGYAAA6BBMAQIdgAgDoEEwAAB2CCQCgQzABAHQIJgCADsEEANAhmAAAOgQTAECHYAIA6BBMAAAdggkAoEMwAQB0CCYAgA7BBADQIZgAADoEEwBAh2ACAOgQTAAAHYIJAKBDMAEAdAgmAIAOwQQA0CGYAAA6BBMAQIdgAgDoEEwAAB2CCQCgQzABAHQIJgCADsEEANAhmAAAOgQTAECHYAIA6BBMAAAdggkAoEMwAQB0CCYAgA7BBADQIZgAADoEEwBAh2ACAOgQTAAAHYIJAKBDMAEAdAgmAIAOwQQA0CGYAAA6BBMAQIdgAgDo6AZTVT2vqq6vqluq6ntV9fHpGAwAYKaYN8CarUne1Fp7rKqek2RdVX2ttXbdFM8GwCy39OVrsnTVqt2OrBnWKCPrF/dv3Z3LhzXKrFattcEXVx2UZF2S97fWvr2XdYPfKQBz1qqn/bBnMtjTfbK+tbZkbwsGuoapqvavqpuTbE5y+TPFUlWtqKobquqGfRoVAGCGGiiYWmtPtdZelWRRktdW1QnPsGZ1a21Jr9AAAEbNINcw7dJae7iqrkpyapJbe+vfcoaTTeNxxcU/b017N372b2J237+zz9syxElGzyfOmr/rtsfeeLlmabJ5DI7P7t/79maQV8kdUVULxm4fmOSUJHdMZDgAgFEyyBmmI5N8pqr2z87A+kJrzf8SAABzRjeYWmvfTXLiNMwCADAjeadvAIAOwQQA0CGYAAA6BBMAQIdgAgDoEEwAAB2CCQCgQzABAHQIJgCADsEEANAhmAAAOgQTAECHYAIA6BBMAAAdggkAoEMwAQB0CCYAgA7BBADQIZgAADoEEwBAh2ACAOgQTAAAHfOGPQDA7q5be05uufb8vO/cjXt87vFHH8yVnz8rmzd9N09s+VEOOGhBfumXX59fX/6xvOBFi4cwLTBXOMMEjIzt236aAw5akNcv+0857f1fzhvf+Vf5yeYNufSTy7P1pw8PezxgFnOGCRgZhx5+TN767vOfduxFR70qf/+XJ+a+Dddk8a++Y0iTAbOdM0zASDvw+S9Mkjy1/ckhTwLMZs4wASOn7diRHe2pPP7IA/nWmr/I/Be+NMf8yr8b9ljALCaYgJFz5Rf/KLd+88IkyaGHHZN3/sFX8tznzR/yVMBs5ik5YOT82il/mt//k6uz7D3/kAMPPiyXfeq0PP7o5mGPBcxiggkYOYe88Ki85OjX5LgTT8tpf/CVbH3ikXz32tXDHguYxQQTMNIOOPCQHHr4MXnk3+4d9ijALCaYgJH2xGMP5SebN+TQw44e9ijALOaib2DG2bH9yWy46bI9jj/y0N3Z8vCmLDz25Bw0/4g88m/35qar/zb7z3tuTvj1907/oMCcIZiAGWfb1i1Ze9GZexx/5we+mo3fvzIbbrwk27Y+loMXLMyixUvz2lM/nPkvWDiESYG5QjABM8pJy1bmpGUrn/XzLz3+t6ZxGoCdXMMEANAhmAAAOgQTAECHYAIA6BBMAAAdggkAoEMwAQB0CCYAgA7BBADQIZgAADoEEwBAh2ACAOgQTAAAHYIJAKBDMAEAdAgmAIAOwQQA0CGYAAA6BBMAQIdgAgDoEEwAAB0DB1NV7V9VN1XVmqkcCABgphnPGaazk9w+VYMAAMxUAwVTVS1K8ttJLpjacQAAZp5qrfUXVX0pyblJ5if509ba8s76/p0CMOetWrVq2CPMOvZ0n6xvrS3Z24LuGaaqWp5kc2ttfWfdiqq6oapuGOeQAAAz2iBPyZ2c5O1VdW+Szyd5U1X94y8uaq2tbq0t6RUaAMCoGegpuV2Lq34z43hK7i1nONk0Hldc/PPWtHfjt/v+nX3eliFOMpo+cdb8Xbc9/sbH1+6+W/pyL7yebOvu3OuPaH7B2Ndv9ym5edMzDgDsad2dywXnBNm/6TGuYGqtXZ3k6imZBABghvJO3wAAHYIJAKBDMAEAdAgmAIAOwQQA0CGYAAA6BBMAQIdgAgDoEEwAAB2CCQCgQzABAHQIJgCADsEEANAhmAAAOgQTAECHYAIA6BBMAAAdggkAoEMwAQB0CCYAgA7BBADQIZgAADoEE0yy69aek/M/cvRAa9dccHo+cdb83PKN86d4KgAmQjDBkGy8/X/ngXuuH/YYAAxAMMEQPPXUk7nm0j/L65f/+bBHAWAAggmG4OarP5V5zzkwv/K6M4c9CgADEEwwzR5/9MFc//X/kt/4nb9K7edLEGAU+G4N02zdVz6ao1/x5ixcvHTYowAwIMEE0+iBe76du26+LEtP+8thjwLAOMwb9gAwl1xz6YdzwsnvzQHPOyRbf/rwruPbn3wiW594JAcceOjwhgPgWQkmmEY/2bwhD268ITdf/bdPO77uKx/NN/95Vc76m4eHMxgAeyWYYBq9fcUX0nY89bRjl/y3ZXnVb7w/x77y7UOaCoAewQRTYMf2J7Phpsv2OL5w8ck5aP4RexxfcMSxWXSci8ABZirBBFNg29YtWXvRnu+x9LsfXPuMwQTAzCaYYJKdtGxlTlq2cuD1Z5+3ZQqnAWAyeFsBAIAOwQQA0CGYAAA6BBMAQIdgAgDoEEwAAB2CCQCgQzABAHQIJgCADsEEANAhmAAAOgQTAECHYAIA6BBMAAAdggkAoEMwAQB0CCYAgA7BBADQIZgAADoEEwBAh2ACAOiYN8iiqro3yZYkTyXZ3lpbMpVDAQDMJAMF05jfaq09NGWTAADMUJ6SAwDoqNZaf1HVPUl+kqQlOb+1trqzvn+nAAAzw/re5UaDPiW3tLW2qapelOTyqrqjtfaN3RdU1YokK8Y+3Jrk1nGPS5IcnsRTn/vO/k2M/dt39m5i7N/E2L+JOb63YKAzTE/7C1WrkjzWWvuve1lzgwvD9429mxj7NzH2b9/Zu4mxfxNj/yZmkP3rXsNUVc+vqvk/u53krXH2CACYQwZ5Su7FSb5cVT9bf3Fr7V+mdCoAgBmkG0yttbuT/Oo473evF4WzV/ZuYuzfxNi/fWfvJsb+TYz9m5ju/o37GiYAgLnG+zABAHRMajBV1alV9f2ququqPjyZ9z3bVdWFVbW5qlxQvw+q6qiquqqqbquq71XV2cOeaVRU1fOq6vqqumVs7z4+7JlGUVXtX1U3VdWaYc8yaqrq3qr616q6uapuGPY8o6SqFlTVl6rqjqq6vapeP+yZRkVVHT/2mPvZn0er6kPPun6ynpKrqv2T3JnklCT3J/lOktNba7dNyj8wy1XVG5M8luTvW2snDHueUVNVRyY5srV249irOtcnOc3jr692vqLj+a21x6rqOUnWJTm7tXbdkEcbKVX1x0mWJDmktbZ82POMkrHfV7rEr98av6r6TJJrW2sXVNVzkxzUWnt4yGONnLGG2ZTkda21jc+0ZjLPML02yV2ttbtba9uSfD7JOybx/me1sTcC/fGw5xhVrbUHWms3jt3ekuT2JAuHO9VoaDs9Nvbhc8b+uLhxHKpqUZLfTnLBsGdh7qiqQ5O8Mcmnk6S1tk0s7bM3J/nBs8VSMrnBtDDJfbt9fH/8wGIIquplSU5M8u0hjzIyxp5OujnJ5iSXt9bs3fj8TZI/S7JjyHOMqpbkf1XV+rHfGsFgjknyoyQXjT0dfMHY+yUyfu9K8rm9LXDRN7NKVR2c5JIkH2qtPTrseUZFa+2p1tqrkixK8tqq8rTwgKpqeZLNrbX1w55lhC1trb06yduSfGDsEgX65iV5dZK/a62dmOTxJK4fHqexpzLfnuSLe1s3mcG0KclRu328aOwYTIux628uSfLZ1tqlw55nFI2dzr8qyalDHmWUnJzk7WPX4Xw+yZuq6h+HO9Joaa1tGvvv5iRfzs5LPOi7P8n9u50R/lJ2BhTj87YkN7bWHtzboskMpu8kOa6qjhmrtXcl+eok3j88q7ELlz+d5PbW2l8Pe55RUlVHVNWCsdsHZucLN+4Y6lAjpLX2kdbaotbay7Lz+96VrbV3D3mskeHXb+271toPk9xXVT/7xbFvTuKFLuN3ejpPxyWD/WqUgbTWtlfVHyb5epL9k1zYWvveZN3/bFdVn0vym0kOr6r7k3ystfbp4U41Uk5OcmaSfx27FidJVrbW1g5vpJFxZJLPjL1KZL8kX2iteWk808Wv35qYDyb57NiJiruTvGfI84yUsUg/Jcn7umu90zcAwN656BsAoEMwAQB0CCYAgA7BBADQIZgAADoEEwBAh2ACAOgQTAAAHf8fFFWI3dH8SaAAAAAASUVORK5CYII=\",\n 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"import matplotlib.pyplot as plt\\n\",\n \"import matplotlib.patches as patches\\n\",\n \"import matplotlib.cm as cm\\n\",\n \"\\n\",\n \"fig, ax = plt.subplots(figsize=(10, 6)) \\n\",\n \"\\n\",\n \"# create the grid visualization\\n\",\n \"X, Y = np.meshgrid(np.arange(grid_dims[1]+1), np.arange(grid_dims[0]+1))\\n\",\n \"h = ax.pcolormesh(X, Y, np.ones(grid_dims), edgecolors='k', vmin = 0, vmax = 30, linewidth=3, cmap = 'coolwarm')\\n\",\n \"ax.invert_yaxis()\\n\",\n \"\\n\",\n \"# Put gray boxes around the possible reward locations\\n\",\n \"reward_top = ax.add_patch(patches.Rectangle((reward_locations[0][1],reward_locations[0][0]),1.0,1.0,linewidth=5,edgecolor=[0.5, 0.5, 0.5],facecolor=[0.5, 0.5, 0.5]))\\n\",\n \"reward_bottom = ax.add_patch(patches.Rectangle((reward_locations[1][1],reward_locations[1][0]),1.0,1.0,linewidth=5,edgecolor=[0.5, 0.5, 0.5],facecolor=[0.5, 0.5, 0.5]))\\n\",\n \"\\n\",\n \"text_offsets = [0.4, 0.6]\\n\",\n \"\\n\",\n \"cue_grid = np.ones(grid_dims)\\n\",\n \"cue_grid[cue1_location[0],cue1_location[1]] = 15.0\\n\",\n \"for ii, loc_ii in enumerate(cue2_locations):\\n\",\n \" row_coord, column_coord = loc_ii\\n\",\n \" cue_grid[row_coord, column_coord] = 5.0\\n\",\n \" ax.text(column_coord+text_offsets[0], row_coord+text_offsets[1], cue2_loc_names[ii], fontsize = 15, color='k')\\n\",\n \"h.set_array(cue_grid.ravel())\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Generative model\\n\",\n \"\\n\",\n \"The hidden states $\\\\mathbf{s}$ of the generative model are factorized into three hidden states factors:\\n\",\n \"\\n\",\n \"1. a **Location** hidden state factor with as many levels as there are grid locations. This encodes the agent's location in the grid world.\\n\",\n \"2. a **Cue 2 Location** hidden state factor with 4 levels -- this encodes in which of the four possible locations **Cue 2** is located.\\n\",\n \"3. a **Reward Condition** hidden state factor with 2 levels -- this encodes which of the two reward locations (\\\"TOP\\\" or \\\"BOTTOM\\\") the \\\"Cheese\\\" is to be found in. When the **Reward Condition** level is \\\"TOP\\\", then the \\\"Cheese\\\" reward is the upper of the two locations, and the \\\"Shock\\\" punishment is on the lower of the two locations. The locations are switched in the \\\"BOTTOM\\\" level of the **Reward Condition** factor.\\n\",\n \"\\n\",\n \"The observations $\\\\mathbf{o}$ of the generative model are factorized into four different observation modalities:\\n\",\n \"\\n\",\n \"1. a **Location** observation modality with as many levels as there are grid locations, representing the agent's observation of its location in the grid world.\\n\",\n \"2. a **Cue 1** observation modality with 5 levels -- this is an observation, only obtained at the **Cue 1** location, that signals in which of the 4 possible locations **Cue 2** is located. When not at the **Cue 1** location, the agent sees `Null` or a meaningless observation.\\n\",\n \"3. a **Cue 2** observation modality with 3 levels -- this is an observation, only obtained at the **Cue 2** location, that signals in which of the two reward locations (\\\"TOP\\\" or \\\"BOTTOM\\\") the \\\"Cheese\\\" is located. When not at the **Cue 2** location, the agent sees `Null` or a meaningless observation.\\n\",\n \"4. a **Reward** observation modality with 3 levels -- this is an observation that signals whether the agent is receiving \\\"Cheese\\\", \\\"Shock\\\" or nothing at all (\\\"Null\\\"). The agent only receives \\\"Cheese\\\" or \\\"Shock\\\" when occupying one of the two reward locations, and `Null` otherwise.\\n\",\n \"\\n\",\n \"\\n\",\n \"As is the usual convention in `pymdp`, let's create a list that contains the dimensionalities of the hidden state factors, named `num_states`, and a list that contains the dimensionalities of the observation modalities, named `num_obs`. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# list of dimensionalities of the hidden states -- useful for creating generative model later on\\n\",\n \"num_states = [num_grid_points, len(cue2_locations), len(reward_conditions)]\\n\",\n \"\\n\",\n \"# Names of the cue1 observation levels, the cue2 observation levels, and the reward observation levels\\n\",\n \"cue1_names = ['Null'] + cue2_loc_names # signals for the possible Cue 2 locations, that only are seen when agent is visiting Cue 1\\n\",\n \"cue2_names = ['Null', 'reward_on_top', 'reward_on_bottom']\\n\",\n \"reward_names = ['Null', 'Cheese', 'Shock']\\n\",\n \"\\n\",\n \"num_obs = [num_grid_points, len(cue1_names), len(cue2_names), len(reward_names)]\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### The observation model: **A** array\\n\",\n \"Now using `num_states` and `num_obs` we can initialize `A`, the observation model\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"A_m_shapes = [ [o_dim] + num_states for o_dim in num_obs] # list of shapes of modality-specific A[m] arrays\\n\",\n \"A = utils.obj_array_zeros(A_m_shapes) # initialize A array to an object array of all-zero subarrays\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's fill out the various modalities of the `A` array, encoding the agents beliefs about how hidden states probabilistically cause observations within each modality.\\n\",\n \"\\n\",\n \"Starting with the `0`-th modality, the **Location** observation modality: `A[0]`\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# make the location observation only depend on the location state (proprioceptive observation modality)\\n\",\n \"A[0] = np.tile(np.expand_dims(np.eye(num_grid_points), (-2, -1)), (1, 1, num_states[1], num_states[2]))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can build the `1`-st modality, the **Cue 1** observation modality: `A[1]`\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# make the cue1 observation depend on the location (being at cue1_location) and the true location of cue2\\n\",\n \"A[1][0,:,:,:] = 1.0 # default makes Null the most likely observation everywhere\\n\",\n \"\\n\",\n \"# Make the Cue 1 signal depend on 1) being at the Cue 1 location and 2) the location of Cue 2\\n\",\n \"for i, cue_loc2_i in enumerate(cue2_locations):\\n\",\n \" A[1][0,loc_list.index(cue1_location),i,:] = 0.0\\n\",\n \" A[1][i+1,loc_list.index(cue1_location),i,:] = 1.0\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can build the `2`-nd modality, the **Cue 2** observation modality: `A[2]`\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# make the cue2 observation depend on the location (being at the correct cue2_location) and the reward condition\\n\",\n \"A[2][0,:,:,:] = 1.0 # default makes Null the most likely observation everywhere\\n\",\n \"\\n\",\n \"for i, cue_loc2_i in enumerate(cue2_locations):\\n\",\n \"\\n\",\n \" # if the cue2-location is the one you're currently at, then you get a signal about where the reward is\\n\",\n \" A[2][0,loc_list.index(cue_loc2_i),i,:] = 0.0 \\n\",\n \" A[2][1,loc_list.index(cue_loc2_i),i,0] = 1.0\\n\",\n \" A[2][2,loc_list.index(cue_loc2_i),i,1] = 1.0\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Finally, we build the 3rd modality, the **Reward** observation modality: `A[3]`\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# make the reward observation depend on the location (being at reward location) and the reward condition\\n\",\n \"A[3][0,:,:,:] = 1.0 # default makes Null the most likely observation everywhere\\n\",\n \"\\n\",\n \"rew_top_idx = loc_list.index(reward_locations[0]) # linear index of the location of the \\\"TOP\\\" reward location\\n\",\n \"rew_bott_idx = loc_list.index(reward_locations[1]) # linear index of the location of the \\\"BOTTOM\\\" reward location\\n\",\n \"\\n\",\n \"# fill out the contingencies when the agent is in the \\\"TOP\\\" reward location\\n\",\n \"A[3][0,rew_top_idx,:,:] = 0.0\\n\",\n \"A[3][1,rew_top_idx,:,0] = 1.0\\n\",\n \"A[3][2,rew_top_idx,:,1] = 1.0\\n\",\n \"\\n\",\n \"# fill out the contingencies when the agent is in the \\\"BOTTOM\\\" reward location\\n\",\n \"A[3][0,rew_bott_idx,:,:] = 0.0\\n\",\n \"A[3][1,rew_bott_idx,:,1] = 1.0\\n\",\n \"A[3][2,rew_bott_idx,:,0] = 1.0\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### The transition model: **B** array\\n\",\n \"To create the `B` array or transition model, we have to further specify `num_controls`, which like `num_states` / `num_obs` is a list, but this time of the dimensionalities of each *control factor*, which are the hidden state factors that are controllable by the agent. Uncontrollable hidden state factors can be encoded as control factors of dimension 1. Once `num_controls` is defined, we can then use it and `num_states` to specify the dimensionality of the `B` arrays. Recall that in `pymdp` hidden state factors are conditionally independent of eachother, meaning that each sub-array `B[f]` describes the dynamics of only a single hidden state factor, and its probabilistic dependence on both its own state (at the previous time) and the state of its corresponding control factor.\\n\",\n \"\\n\",\n \"In the current grid world task, we will have the agent have the ability to make movements in the 4 cardinal directions (UP, DOWN, LEFT, RIGHT) as well as the option to stay in the same place (STAY). This means we will associate a single 5-dimensional control state factor with the first hidden state factor. \\n\",\n \"\\n\",\n \"*Note*: Make sure the indices of the `num_controls` variables \\\"lines up\\\" with those of `num_states`.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# initialize `num_controls`\\n\",\n \"num_controls = [5, 1, 1]\\n\",\n \"\\n\",\n \"# initialize the shapes of each sub-array `B[f]`\\n\",\n \"B_f_shapes = [ [ns, ns, num_controls[f]] for f, ns in enumerate(num_states)]\\n\",\n \"\\n\",\n \"# create the `B` array and fill it out\\n\",\n \"B = utils.obj_array_zeros(B_f_shapes)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Fill out `B[0]` according to the expected consequences of each of the 5 actions. Note that we also create a list that stores the names of each action, for interpretability.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"actions = [\\\"UP\\\", \\\"DOWN\\\", \\\"LEFT\\\", \\\"RIGHT\\\", \\\"STAY\\\"]\\n\",\n \"\\n\",\n \"# fill out `B[0]` using the \\n\",\n \"for action_id, action_label in enumerate(actions):\\n\",\n \"\\n\",\n \" for curr_state, grid_location in enumerate(loc_list):\\n\",\n \"\\n\",\n \" y, x = grid_location\\n\",\n \"\\n\",\n \" if action_label == \\\"UP\\\":\\n\",\n \" next_y = y - 1 if y > 0 else y \\n\",\n \" next_x = x\\n\",\n \" elif action_label == \\\"DOWN\\\":\\n\",\n \" next_y = y + 1 if y < (grid_dims[0]-1) else y \\n\",\n \" next_x = x\\n\",\n \" elif action_label == \\\"LEFT\\\":\\n\",\n \" next_x = x - 1 if x > 0 else x \\n\",\n \" next_y = y\\n\",\n \" elif action_label == \\\"RIGHT\\\":\\n\",\n \" next_x = x + 1 if x < (grid_dims[1]-1) else x \\n\",\n \" next_y = y\\n\",\n \" elif action_label == \\\"STAY\\\":\\n\",\n \" next_x = x\\n\",\n \" next_y = y\\n\",\n \"\\n\",\n \" new_location = (next_y, next_x)\\n\",\n \" next_state = loc_list.index(new_location)\\n\",\n \" B[0][next_state, curr_state, action_id] = 1.0\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Fill out `B[1]` and `B[2]` as identity matrices, encoding the fact that those hidden states are uncontrollable\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"B[1][:,:,0] = np.eye(num_states[1])\\n\",\n \"B[2][:,:,0] = np.eye(num_states[2])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Prior preferences: the **C** vectors\\n\",\n \"\\n\",\n \"Now we specify the agent's prior over observations, also known as the \\\"prior preferences\\\" or \\\"goal vector.\\\" This is not technically a part of the same generative model used for inference of hidden states, but part of a special predictive generative model using for policy inference. \\n\",\n \"\\n\",\n \"Since the prior preferences are defined in `pymdp` as priors over observations, not states, so `C` will be an object array whose sub-arrays correspond to the priors over specific observation modalities, e.g `C[3]` encodes the prior preferences for different levels of the **Reward** observation modality.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"C = utils.obj_array_zeros(num_obs)\\n\",\n \"\\n\",\n \"C[3][1] = 2.0 # make the agent want to encounter the \\\"Cheese\\\" observation level\\n\",\n \"C[3][2] = -4.0 # make the agent not want to encounter the \\\"Shock\\\" observation level\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Prior over (initial) hidden states: the **D** vectors\\n\",\n \"\\n\",\n \"Now we specify the agent's prior over initial hidden states, the `D` array. Since it's defined over the multi-factor hidden states in this case, `D` will be an object array whose sub-arrays correspond to the priors over specific hidden state factors, e.g `D[0]` encodes the prior beliefs over the initial location of the agent in the grid world.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"D = utils.obj_array_uniform(num_states)\\n\",\n \"D[0] = utils.onehot(loc_list.index((0,0)), num_grid_points)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Generative process\\n\",\n \"\\n\",\n \"Now we need to write down the \\\"rules\\\" of the game, i.e. the environment that the agent will actually be interacting with. The most concise way to do this in `pymdp` is by adopting a similar format to what's used in frameworks like OpenAIGym -- namely, we create an `env` class that takes actions as inputs to a `self.step()` method, and returns observations for the agent as outputs. In Active inference we refer to this agent-independent, physical \\\"reality\\\" in which the agent operates as the *generative process*, to be distinguished from the agent's representation of that reality the *generative model* (the `A`, `B`, `C` and `D` that we just wrote down above).\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Writing a custom `env` \\n\",\n \"\\n\",\n \"Now we'll define an environment class called `GridWorldEnv`. The constructor for this class allows you to establish various parameters of the generative process, like where the agent starts in the grid-world at the beginning of the trial (`starting_loc`), the location of **Cue 1** (`cue1_loc`), the location of **Cue 2** (`cue2_loc`), and the reward condition (`reward_condition`).\\n\",\n \"\\n\",\n \"*Note*: Remember the distinction between the generative model and the generative process: one can build the environment class to be as arbitrarily different from the agent's generative model as desired. For example, for the `GridWorldEnv` example, you could construct the agent's `A` array such that the agent *believes* **Cue 1** is in Location `(1,0)`, but in fact the cue is located somewhere else like `(3,0)` (as would be set by the `cue1_loc` argument to the `GridWorldEnv` constructor). Similarly, one could write the internal `step` method of the `GridWorldEnv` class so that the way the `reward_condition` is signalled is opposite from what the agent expects -- so when the agent sees a particular signal at the **Cue 2** location, they *assume* (via the `A` array) it means that the \\\"Cheese\\\" is located on the `\\\"TOP\\\"` location, but in fact the rule is switched so that \\\"Shock\\\" is at the `\\\"TOP\\\"` location in reality, and \\\"Cheese\\\" is actually at the `\\\"BOTTOM\\\"` location.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"class GridWorldEnv():\\n\",\n \" \\n\",\n \" def __init__(self,starting_loc = (0,0), cue1_loc = (2, 0), cue2 = 'L1', reward_condition = 'TOP'):\\n\",\n \"\\n\",\n \" self.init_loc = starting_loc\\n\",\n \" self.current_location = self.init_loc\\n\",\n \"\\n\",\n \" self.cue1_loc = cue1_loc\\n\",\n \" self.cue2_name = cue2\\n\",\n \" self.cue2_loc_names = ['L1', 'L2', 'L3', 'L4']\\n\",\n \" self.cue2_loc = cue2_locations[self.cue2_loc_names.index(self.cue2_name)]\\n\",\n \"\\n\",\n \" self.reward_condition = reward_condition\\n\",\n \" print(f'Starting location is {self.init_loc}, Reward condition is {self.reward_condition}, cue is located in {self.cue2_name}')\\n\",\n \" \\n\",\n \" def step(self,action_label):\\n\",\n \"\\n\",\n \" (Y, X) = self.current_location\\n\",\n \"\\n\",\n \" if action_label == \\\"UP\\\": \\n\",\n \" \\n\",\n \" Y_new = Y - 1 if Y > 0 else Y\\n\",\n \" X_new = X\\n\",\n \"\\n\",\n \" elif action_label == \\\"DOWN\\\": \\n\",\n \"\\n\",\n \" Y_new = Y + 1 if Y < (grid_dims[0]-1) else Y\\n\",\n \" X_new = X\\n\",\n \"\\n\",\n \" elif action_label == \\\"LEFT\\\": \\n\",\n \" Y_new = Y\\n\",\n \" X_new = X - 1 if X > 0 else X\\n\",\n \"\\n\",\n \" elif action_label == \\\"RIGHT\\\": \\n\",\n \" Y_new = Y\\n\",\n \" X_new = X +1 if X < (grid_dims[1]-1) else X\\n\",\n \"\\n\",\n \" elif action_label == \\\"STAY\\\":\\n\",\n \" Y_new, X_new = Y, X \\n\",\n \" \\n\",\n \" self.current_location = (Y_new, X_new) # store the new grid location\\n\",\n \"\\n\",\n \" loc_obs = self.current_location # agent always directly observes the grid location they're in \\n\",\n \"\\n\",\n \" if self.current_location == self.cue1_loc:\\n\",\n \" cue1_obs = self.cue2_name\\n\",\n \" else:\\n\",\n \" cue1_obs = 'Null'\\n\",\n \"\\n\",\n \" if self.current_location == self.cue2_loc:\\n\",\n \" cue2_obs = cue2_names[reward_conditions.index(self.reward_condition)+1]\\n\",\n \" else:\\n\",\n \" cue2_obs = 'Null'\\n\",\n \" \\n\",\n \" # @NOTE: here we use the same variable `reward_locations` to create both the agent's generative model (the `A` matrix) as well as the generative process. \\n\",\n \" # This is just for simplicity, but it's not necessary - you could have the agent believe that the Cheese/Shock are actually stored in arbitrary, incorrect locations.\\n\",\n \"\\n\",\n \" if self.current_location == reward_locations[0]:\\n\",\n \" if self.reward_condition == 'TOP':\\n\",\n \" reward_obs = 'Cheese'\\n\",\n \" else:\\n\",\n \" reward_obs = 'Shock'\\n\",\n \" elif self.current_location == reward_locations[1]:\\n\",\n \" if self.reward_condition == 'BOTTOM':\\n\",\n \" reward_obs = 'Cheese'\\n\",\n \" else:\\n\",\n \" reward_obs = 'Shock'\\n\",\n \" else:\\n\",\n \" reward_obs = 'Null'\\n\",\n \"\\n\",\n \" return loc_obs, cue1_obs, cue2_obs, reward_obs\\n\",\n \"\\n\",\n \" def reset(self):\\n\",\n \" self.current_location = self.init_loc\\n\",\n \" print(f'Re-initialized location to {self.init_loc}')\\n\",\n \" loc_obs = self.current_location\\n\",\n \" cue1_obs = 'Null'\\n\",\n \" cue2_obs = 'Null'\\n\",\n \" reward_obs = 'Null'\\n\",\n \"\\n\",\n \" return loc_obs, cue1_obs, cue2_obs, reward_obs\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Active Inference\\n\",\n \"\\n\",\n \"Now that we have a generative model and generative process set up, we can quickly run active inference in `pymdp`. In order to do this, all we need to do is to create an `Agent` using the `Agent()` constructor and create a generative process / environment using our custom `GridWorldEnv` class. Then we just exchange observations and actions between the two in a loop over time, where the agent updates its beliefs and actions using the `Agent` methods like `infer_states()` and `infer_policies()`.\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Initialize an `Agent` and an instance of `GridWorldEnv`\\n\",\n \"We can quickly construct an instance of `Agent` using our generative model arrays as inputs: `A`, `B`, `C`, and `D`. Since we are dealing with a spatially-extended navigation example, we will also use a `policy_len` parameter that lets the agent plan its movements forward in time. This sort of temporally deep planning is needed because of A) the local nature of the agent's action repetoire (only being able to move UP, LEFT, RIGHT, and DOWN), and B) the physical distance between the cues and reward locations in the grid world.\\n\",\n \"\\n\",\n \"We can also initialize the `GridWorldEnv` class using a desired starting location, a Cue 1 location, Cue 2 location, and reward condition. We can get the first (multi-modality) observation of the simulation by using `env.reset()`\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 17,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Starting location is (0, 0), Reward condition is BOTTOM, cue is located in L4\\n\",\n \"Re-initialized location to (0, 0)\\n\"\n ]\n }\n ],\n \"source\": [\n \"my_agent = Agent(A = A, B = B, C = C, D = D, policy_len = 4)\\n\",\n \"\\n\",\n \"my_env = GridWorldEnv(starting_loc = (0,0), cue1_loc = (2, 0), cue2 = 'L4', reward_condition = 'BOTTOM')\\n\",\n \"\\n\",\n \"loc_obs, cue1_obs, cue2_obs, reward_obs = my_env.reset()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Run an active inference loop over time\\n\",\n \"...saving the history of the rat's locations as you do so. Include some print statements if you want to see the output of the agent's choices as they unfold.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 18,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action at time 0: DOWN\\n\",\n \"Grid location at time 0: (1, 0)\\n\",\n \"Reward at time 0: Null\\n\",\n \"Action at time 1: DOWN\\n\",\n \"Grid location at time 1: (2, 0)\\n\",\n \"Reward at time 1: Null\\n\",\n \"Action at time 2: DOWN\\n\",\n \"Grid location at time 2: (3, 0)\\n\",\n \"Reward at time 2: Null\\n\",\n \"Action at time 3: RIGHT\\n\",\n \"Grid location at time 3: (3, 1)\\n\",\n \"Reward at time 3: Null\\n\",\n \"Action at time 4: DOWN\\n\",\n \"Grid location at time 4: (4, 1)\\n\",\n \"Reward at time 4: Null\\n\",\n \"Action at time 5: RIGHT\\n\",\n \"Grid location at time 5: (4, 2)\\n\",\n \"Reward at time 5: Null\\n\",\n \"Action at time 6: RIGHT\\n\",\n \"Grid location at time 6: (4, 3)\\n\",\n \"Reward at time 6: Null\\n\",\n \"Action at time 7: RIGHT\\n\",\n \"Grid location at time 7: (4, 4)\\n\",\n \"Reward at time 7: Null\\n\",\n \"Action at time 8: RIGHT\\n\",\n \"Grid location at time 8: (4, 5)\\n\",\n \"Reward at time 8: Null\\n\",\n \"Action at time 9: UP\\n\",\n \"Grid location at time 9: (3, 5)\\n\",\n \"Reward at time 9: Cheese\\n\"\n ]\n }\n ],\n \"source\": [\n \"history_of_locs = [loc_obs]\\n\",\n \"obs = [loc_list.index(loc_obs), cue1_names.index(cue1_obs), cue2_names.index(cue2_obs), reward_names.index(reward_obs)]\\n\",\n \"\\n\",\n \"T = 10 # number of total timesteps\\n\",\n \"\\n\",\n \"for t in range(T):\\n\",\n \"\\n\",\n \" qs = my_agent.infer_states(obs)\\n\",\n \" \\n\",\n \" my_agent.infer_policies()\\n\",\n \" chosen_action_id = my_agent.sample_action()\\n\",\n \"\\n\",\n \" movement_id = int(chosen_action_id[0])\\n\",\n \"\\n\",\n \" choice_action = actions[movement_id]\\n\",\n \"\\n\",\n \" print(f'Action at time {t}: {choice_action}')\\n\",\n \"\\n\",\n \" loc_obs, cue1_obs, cue2_obs, reward_obs = my_env.step(choice_action)\\n\",\n \"\\n\",\n \" obs = [loc_list.index(loc_obs), cue1_names.index(cue1_obs), cue2_names.index(cue2_obs), reward_names.index(reward_obs)]\\n\",\n \"\\n\",\n \" history_of_locs.append(loc_obs)\\n\",\n \"\\n\",\n \" print(f'Grid location at time {t}: {loc_obs}')\\n\",\n \"\\n\",\n \" print(f'Reward at time {t}: {reward_obs}')\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Visualization\\n\",\n \"\\n\",\n \"Now let's do a quick visualization of the rat's movements over a single trial. We'll indicate the grid location and time of its movements using a hot colormap (so hotter colors means later in the trial), and indicate the Cue 1 and Cue 2 locations with purple outlined boxes. Each of the possible Cue 2 locations will be highlighted in a light blue.\\n\",\n \"\\n\",\n \"Try changing the initial settings of the generative process (the locations of Cue1, Cue 2, the reward condition, etc.) to see how and the extent to which the active inference agent can adapt its behavior to the changing environmental contingencies.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 19,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"Text(0.5, 1.0, 'Cue 1 located at (4, 2), Cue 2 located at (4, 2), Cheese on BOTTOM')\"\n ]\n },\n \"execution_count\": 19,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"all_locations = np.vstack(history_of_locs).astype(float) # create a matrix containing the agent's Y/X locations over time (each coordinate in one row of the matrix)\\n\",\n \"\\n\",\n \"fig, ax = plt.subplots(figsize=(10, 6)) \\n\",\n \"\\n\",\n \"# create the grid visualization\\n\",\n \"X, Y = np.meshgrid(np.arange(grid_dims[1]+1), np.arange(grid_dims[0]+1))\\n\",\n \"h = ax.pcolormesh(X, Y, np.ones(grid_dims), edgecolors='k', vmin = 0, vmax = 30, linewidth=3, cmap = 'coolwarm')\\n\",\n \"ax.invert_yaxis()\\n\",\n \"\\n\",\n \"# get generative process global parameters (the locations of the Cues, the reward condition, etc.)\\n\",\n \"cue1_loc, cue2_loc, reward_condition = my_env.cue1_loc, my_env.cue2_loc, my_env.reward_condition\\n\",\n \"reward_top = ax.add_patch(patches.Rectangle((reward_locations[0][1],reward_locations[0][0]),1.0,1.0,linewidth=5,edgecolor=[0.5, 0.5, 0.5],facecolor='none'))\\n\",\n \"reward_bottom = ax.add_patch(patches.Rectangle((reward_locations[1][1],reward_locations[1][0]),1.0,1.0,linewidth=5,edgecolor=[0.5, 0.5, 0.5],facecolor='none'))\\n\",\n \"reward_loc = reward_locations[0] if reward_condition == \\\"TOP\\\" else reward_locations[1]\\n\",\n \"\\n\",\n \"if reward_condition == \\\"TOP\\\":\\n\",\n \" reward_top.set_edgecolor('g')\\n\",\n \" reward_top.set_facecolor('g')\\n\",\n \" reward_bottom.set_edgecolor([0.7, 0.2, 0.2])\\n\",\n \" reward_bottom.set_facecolor([0.7, 0.2, 0.2])\\n\",\n \"elif reward_condition == \\\"BOTTOM\\\":\\n\",\n \" reward_bottom.set_edgecolor('g')\\n\",\n \" reward_bottom.set_facecolor('g')\\n\",\n \" reward_top.set_edgecolor([0.7, 0.2, 0.2])\\n\",\n \" reward_top.set_facecolor([0.7, 0.2, 0.2])\\n\",\n \"reward_top.set_zorder(1)\\n\",\n \"reward_bottom.set_zorder(1)\\n\",\n \"\\n\",\n \"text_offsets = [0.4, 0.6]\\n\",\n \"cue_grid = np.ones(grid_dims)\\n\",\n \"cue_grid[cue1_loc[0],cue1_loc[1]] = 15.0\\n\",\n \"for ii, loc_ii in enumerate(cue2_locations):\\n\",\n \" row_coord, column_coord = loc_ii\\n\",\n \" cue_grid[row_coord, column_coord] = 5.0\\n\",\n \" ax.text(column_coord+text_offsets[0], row_coord+text_offsets[1], cue2_loc_names[ii], fontsize = 15, color='k')\\n\",\n \" \\n\",\n \"h.set_array(cue_grid.ravel())\\n\",\n \"\\n\",\n \"cue1_rect = ax.add_patch(patches.Rectangle((cue1_loc[1],cue1_loc[0]),1.0,1.0,linewidth=8,edgecolor=[0.5, 0.2, 0.7],facecolor='none'))\\n\",\n \"cue2_rect = ax.add_patch(patches.Rectangle((cue2_loc[1],cue2_loc[0]),1.0,1.0,linewidth=8,edgecolor=[0.5, 0.2, 0.7],facecolor='none'))\\n\",\n \"\\n\",\n \"ax.plot(all_locations[:,1]+0.5,all_locations[:,0]+0.5, 'r', zorder = 2)\\n\",\n \"\\n\",\n \"temporal_colormap = cm.hot(np.linspace(0,1,T+1))\\n\",\n \"dots = ax.scatter(all_locations[:,1]+0.5,all_locations[:,0]+0.5, 450, c = temporal_colormap, zorder=3)\\n\",\n \"\\n\",\n \"ax.set_title(f\\\"Cue 1 located at {cue2_loc}, Cue 2 located at {cue2_loc}, Cheese on {reward_condition}\\\", fontsize=16)\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Experimenting with different environmental structure\\n\",\n \"\\n\",\n \"Try changing around the locations of the rewards, the cues, the agent's beliefs, etc. For example, below we'll change the location of the rewards, both in the generative model and the generative process.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 20,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# names of the reward conditions and their locations\\n\",\n \"reward_conditions = [\\\"LEFT\\\", \\\"RIGHT\\\"]\\n\",\n \"reward_locations = [(2, 2), (2, 4)] # DIFFERENT REWARD LOCATIONS\\n\",\n \"\\n\",\n \"## reset `A[3]`, the reward observation model\\n\",\n \"\\n\",\n \"A[3] = np.zeros([num_obs[3]] + num_states)\\n\",\n \"# make the reward observation depend on the location (being at reward location) and the reward condition\\n\",\n \"A[3][0,:,:,:] = 1.0 # default makes Null the most likely observation everywhere\\n\",\n \"\\n\",\n \"rew_top_idx = loc_list.index(reward_locations[0]) # linear index of the location of the \\\"TOP\\\" reward location\\n\",\n \"rew_bott_idx = loc_list.index(reward_locations[1]) # linear index of the location of the \\\"BOTTOM\\\" reward location\\n\",\n \"\\n\",\n \"# fill out the contingencies when the agent is in the \\\"TOP\\\" reward location\\n\",\n \"A[3][0,rew_top_idx,:,:] = 0.0\\n\",\n \"A[3][1,rew_top_idx,:,0] = 1.0\\n\",\n \"A[3][2,rew_top_idx,:,1] = 1.0\\n\",\n \"\\n\",\n \"# fill out the contingencies when the agent is in the \\\"BOTTOM\\\" reward location\\n\",\n \"A[3][0,rew_bott_idx,:,:] = 0.0\\n\",\n \"A[3][1,rew_bott_idx,:,1] = 1.0\\n\",\n \"A[3][2,rew_bott_idx,:,0] = 1.0\\n\",\n \"\\n\",\n \"class GridWorldEnv():\\n\",\n \" \\n\",\n \" def __init__(self,starting_loc = (4,0), cue1_loc = (2, 0), cue2 = 'L1', reward_condition = 'LEFT'):\\n\",\n \"\\n\",\n \" self.init_loc = starting_loc\\n\",\n \" self.current_location = self.init_loc\\n\",\n \"\\n\",\n \" self.cue1_loc = cue1_loc\\n\",\n \" self.cue2_name = cue2\\n\",\n \" self.cue2_loc_names = ['L1', 'L2', 'L3', 'L4']\\n\",\n \" self.cue2_loc = cue2_locations[self.cue2_loc_names.index(self.cue2_name)]\\n\",\n \"\\n\",\n \" self.reward_condition = reward_condition\\n\",\n \" print(f'Starting location is {self.init_loc}, Reward condition is {self.reward_condition}, cue is located in {self.cue2_name}')\\n\",\n \" \\n\",\n \" def step(self,action_label):\\n\",\n \"\\n\",\n \" (Y, X) = self.current_location\\n\",\n \"\\n\",\n \" if action_label == \\\"UP\\\": \\n\",\n \" \\n\",\n \" Y_new = Y - 1 if Y > 0 else Y\\n\",\n \" X_new = X\\n\",\n \"\\n\",\n \" elif action_label == \\\"DOWN\\\": \\n\",\n \"\\n\",\n \" Y_new = Y + 1 if Y < (grid_dims[0]-1) else Y\\n\",\n \" X_new = X\\n\",\n \"\\n\",\n \" elif action_label == \\\"LEFT\\\": \\n\",\n \" Y_new = Y\\n\",\n \" X_new = X - 1 if X > 0 else X\\n\",\n \"\\n\",\n \" elif action_label == \\\"RIGHT\\\": \\n\",\n \" Y_new = Y\\n\",\n \" X_new = X +1 if X < (grid_dims[1]-1) else X\\n\",\n \"\\n\",\n \" elif action_label == \\\"STAY\\\":\\n\",\n \" Y_new, X_new = Y, X \\n\",\n \" \\n\",\n \" self.current_location = (Y_new, X_new) # store the new grid location\\n\",\n \"\\n\",\n \" loc_obs = self.current_location # agent always directly observes the grid location they're in \\n\",\n \"\\n\",\n \" if self.current_location == self.cue1_loc:\\n\",\n \" cue1_obs = self.cue2_name\\n\",\n \" else:\\n\",\n \" cue1_obs = 'Null'\\n\",\n \"\\n\",\n \" if self.current_location == self.cue2_loc:\\n\",\n \" cue2_obs = cue2_names[reward_conditions.index(self.reward_condition)+1]\\n\",\n \" else:\\n\",\n \" cue2_obs = 'Null'\\n\",\n \" \\n\",\n \" # @NOTE: here we use the same variable `reward_locations` to create both the agent's generative model (the `A` matrix) as well as the generative process. \\n\",\n \" # This is just for simplicity, but it's not necessary - you could have the agent believe that the Cheese/Shock are actually stored in arbitrary, incorrect locations.\\n\",\n \"\\n\",\n \" if self.current_location == reward_locations[0]:\\n\",\n \" if self.reward_condition == 'LEFT':\\n\",\n \" reward_obs = 'Cheese'\\n\",\n \" else:\\n\",\n \" reward_obs = 'Shock'\\n\",\n \" elif self.current_location == reward_locations[1]:\\n\",\n \" if self.reward_condition == 'RIGHT':\\n\",\n \" reward_obs = 'Cheese'\\n\",\n \" else:\\n\",\n \" reward_obs = 'Shock'\\n\",\n \" else:\\n\",\n \" reward_obs = 'Null'\\n\",\n \"\\n\",\n \" return loc_obs, cue1_obs, cue2_obs, reward_obs\\n\",\n \"\\n\",\n \" def reset(self):\\n\",\n \" self.current_location = self.init_loc\\n\",\n \" print(f'Re-initialized location to {self.init_loc}')\\n\",\n \" loc_obs = self.current_location\\n\",\n \" cue1_obs = 'Null'\\n\",\n \" cue2_obs = 'Null'\\n\",\n \" reward_obs = 'Null'\\n\",\n \"\\n\",\n \" return loc_obs, cue1_obs, cue2_obs, reward_obs\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 21,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Starting location is (0, 0), Reward condition is RIGHT, cue is located in L1\\n\",\n \"Re-initialized location to (0, 0)\\n\",\n \"Action at time 0: DOWN\\n\",\n \"Grid location at time 0: (1, 0)\\n\",\n \"Reward at time 0: Null\\n\",\n \"Action at time 1: DOWN\\n\",\n \"Grid location at time 1: (2, 0)\\n\",\n \"Reward at time 1: Null\\n\",\n \"Action at time 2: UP\\n\",\n \"Grid location at time 2: (1, 0)\\n\",\n \"Reward at time 2: Null\\n\",\n \"Action at time 3: RIGHT\\n\",\n \"Grid location at time 3: (1, 1)\\n\",\n \"Reward at time 3: Null\\n\",\n \"Action at time 4: UP\\n\",\n \"Grid location at time 4: (0, 1)\\n\",\n \"Reward at time 4: Null\\n\",\n \"Action at time 5: RIGHT\\n\",\n \"Grid location at time 5: (0, 2)\\n\",\n \"Reward at time 5: Null\\n\",\n \"Action at time 6: RIGHT\\n\",\n \"Grid location at time 6: (0, 3)\\n\",\n \"Reward at time 6: Null\\n\",\n \"Action at time 7: DOWN\\n\",\n \"Grid location at time 7: (1, 3)\\n\",\n \"Reward at time 7: Null\\n\",\n \"Action at time 8: DOWN\\n\",\n \"Grid location at time 8: (2, 3)\\n\",\n \"Reward at time 8: Null\\n\",\n \"Action at time 9: RIGHT\\n\",\n \"Grid location at time 9: (2, 4)\\n\",\n \"Reward at time 9: Cheese\\n\"\n ]\n }\n ],\n \"source\": [\n \"my_agent = Agent(A = A, B = B, C = C, D = D, policy_len = 4)\\n\",\n \"\\n\",\n \"my_env = GridWorldEnv(starting_loc = (0,0), cue1_loc = (2, 0), cue2 = 'L1', reward_condition = 'RIGHT')\\n\",\n \"\\n\",\n \"loc_obs, cue1_obs, cue2_obs, reward_obs = my_env.reset()\\n\",\n \"\\n\",\n \"history_of_locs = [loc_obs]\\n\",\n \"obs = [loc_list.index(loc_obs), cue1_names.index(cue1_obs), cue2_names.index(cue2_obs), reward_names.index(reward_obs)]\\n\",\n \"\\n\",\n \"T = 10 # number of total timesteps\\n\",\n \"\\n\",\n \"for t in range(T):\\n\",\n \"\\n\",\n \" qs = my_agent.infer_states(obs)\\n\",\n \" \\n\",\n \" my_agent.infer_policies()\\n\",\n \" chosen_action_id = my_agent.sample_action()\\n\",\n \"\\n\",\n \" movement_id = int(chosen_action_id[0])\\n\",\n \"\\n\",\n \" choice_action = actions[movement_id]\\n\",\n \"\\n\",\n \" print(f'Action at time {t}: {choice_action}')\\n\",\n \"\\n\",\n \" loc_obs, cue1_obs, cue2_obs, reward_obs = my_env.step(choice_action)\\n\",\n \"\\n\",\n \" obs = [loc_list.index(loc_obs), cue1_names.index(cue1_obs), cue2_names.index(cue2_obs), reward_names.index(reward_obs)]\\n\",\n \"\\n\",\n \" history_of_locs.append(loc_obs)\\n\",\n \"\\n\",\n \" print(f'Grid location at time {t}: {loc_obs}')\\n\",\n \"\\n\",\n \" print(f'Reward at time {t}: {reward_obs}')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 22,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"Text(0.5, 1.0, 'Cue 1 located at (0, 2), Cue 2 located at (0, 2), Cheese on RIGHT')\"\n ]\n },\n \"execution_count\": 22,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\n\",\n \"all_locations = np.vstack(history_of_locs).astype(float) # create a matrix containing the agent's Y/X locations over time (each coordinate in one row of the matrix)\\n\",\n \"\\n\",\n \"fig, ax = plt.subplots(figsize=(10, 6)) \\n\",\n \"\\n\",\n \"# create the grid visualization\\n\",\n \"X, Y = np.meshgrid(np.arange(grid_dims[1]+1), np.arange(grid_dims[0]+1))\\n\",\n \"h = ax.pcolormesh(X, Y, np.ones(grid_dims), edgecolors='k', vmin = 0, vmax = 30, linewidth=3, cmap = 'coolwarm')\\n\",\n \"ax.invert_yaxis()\\n\",\n \"\\n\",\n \"# get generative process global parameters (the locations of the Cues, the reward condition, etc.)\\n\",\n \"cue1_loc, cue2_loc, reward_condition = my_env.cue1_loc, my_env.cue2_loc, my_env.reward_condition\\n\",\n \"reward_top = ax.add_patch(patches.Rectangle((reward_locations[0][1],reward_locations[0][0]),1.0,1.0,linewidth=5,edgecolor=[0.5, 0.5, 0.5],facecolor='none'))\\n\",\n \"reward_bottom = ax.add_patch(patches.Rectangle((reward_locations[1][1],reward_locations[1][0]),1.0,1.0,linewidth=5,edgecolor=[0.5, 0.5, 0.5],facecolor='none'))\\n\",\n \"reward_loc = reward_locations[0] if reward_condition == \\\"LEFT\\\" else reward_locations[1]\\n\",\n \"\\n\",\n \"if reward_condition == \\\"LEFT\\\":\\n\",\n \" reward_top.set_edgecolor('g')\\n\",\n \" reward_top.set_facecolor('g')\\n\",\n \" reward_bottom.set_edgecolor([0.7, 0.2, 0.2])\\n\",\n \" reward_bottom.set_facecolor([0.7, 0.2, 0.2])\\n\",\n \"elif reward_condition == \\\"RIGHT\\\":\\n\",\n \" reward_bottom.set_edgecolor('g')\\n\",\n \" reward_bottom.set_facecolor('g')\\n\",\n \" reward_top.set_edgecolor([0.7, 0.2, 0.2])\\n\",\n \" reward_top.set_facecolor([0.7, 0.2, 0.2])\\n\",\n \"reward_top.set_zorder(1)\\n\",\n \"reward_bottom.set_zorder(1)\\n\",\n \"\\n\",\n \"text_offsets = [0.4, 0.6]\\n\",\n \"cue_grid = np.ones(grid_dims)\\n\",\n \"cue_grid[cue1_loc[0],cue1_loc[1]] = 15.0\\n\",\n \"for ii, loc_ii in enumerate(cue2_locations):\\n\",\n \" row_coord, column_coord = loc_ii\\n\",\n \" cue_grid[row_coord, column_coord] = 5.0\\n\",\n \" ax.text(column_coord+text_offsets[0], row_coord+text_offsets[1], cue2_loc_names[ii], fontsize = 15, color='k')\\n\",\n \" \\n\",\n \"h.set_array(cue_grid.ravel())\\n\",\n \"\\n\",\n \"cue1_rect = ax.add_patch(patches.Rectangle((cue1_loc[1],cue1_loc[0]),1.0,1.0,linewidth=8,edgecolor=[0.5, 0.2, 0.7],facecolor='none'))\\n\",\n \"cue2_rect = ax.add_patch(patches.Rectangle((cue2_loc[1],cue2_loc[0]),1.0,1.0,linewidth=8,edgecolor=[0.5, 0.2, 0.7],facecolor='none'))\\n\",\n \"\\n\",\n \"ax.plot(all_locations[:,1]+0.5,all_locations[:,0]+0.5, 'r', zorder = 2)\\n\",\n \"\\n\",\n \"temporal_colormap = cm.hot(np.linspace(0,1,T+1))\\n\",\n \"dots = ax.scatter(all_locations[:,1]+0.5,all_locations[:,0]+0.5, 450, c = temporal_colormap, zorder=3)\\n\",\n \"\\n\",\n \"ax.set_title(f\\\"Cue 1 located at {cue2_loc}, Cue 2 located at {cue2_loc}, Cheese on {reward_condition}\\\", fontsize=16)\"\n ]\n }\n ],\n \"metadata\": {\n \"interpreter\": {\n \"hash\": \"24ee14d9f6452059a99d44b6cbd71d1bb479b0539b0360a6a17428ecea9f0810\"\n },\n \"kernelspec\": {\n \"display_name\": \"Python 3.8.10 64-bit ('pymdp_env2': conda)\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.8.8\"\n },\n \"orig_nbformat\": 4\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "docs/notebooks/free_energy_calculation.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Computing the variational free energy in categorical models\\n\",\n \"\\n\",\n \"[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/infer-actively/pymdp/blob/main/docs/notebooks/free_energy_calculation.ipynb)\\n\",\n \"\\n\",\n \"*Author: Conor Heins*\\n\",\n \"\\n\",\n \"This notebook walks the user through the computation of the variational free energy (or *VFE*) for discrete generative models, composed of categorical distributions. We can represent these sorts of generative models easily in array-focused programming languages like `NumPy` and `MATLAB` using matrices and vectors.\\n\",\n \"\\n\",\n \"In the discrete state-space formulation, the variational free energy is very straightforward to compute when we take advantage of the NDarray representation of probability distributions. The highly-optimized matrix algebra built into today's numerical computing paradigms can be exploited to write simple, one-line expressions for information-theoretic terms (like Kullback-Leibler divergences, cross-entropies, log-likelihoods, etc.). All these terms end up being variants of things like inner products, matrix-vector products or matrix-matrix multiplications.\\n\",\n \"\\n\",\n \"This notebook is inspired by the supplementary MATLAB script for the paper [\\\"A Step-by-Step Tutorial on Active Inference Modelling and its Application to Empirical Data\\\"](https://www.sciencedirect.com/science/article/pii/S0022249621000973) by Ryan Smith, Karl Friston, and Christopher Whyte. The original MATLAB script is called `VFE_calculation_example.m`, and can be found on [Ryan Smith's GitHub repository](https://github.com/rssmith33/Active-Inference-Tutorial-Scripts), which also contains a set of tutorial scripts that are supplementary to their paper.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"*Note*: When running this notebook in Google Colab, you may have to run `!pip install inferactively-pymdp` at the top of the notebook, before you can `import pymdp`. That cell is left commented out below, in case you are running this notebook from Google Colab.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# ! pip install inferactively-pymdp\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Imports\\n\",\n \"\\n\",\n \"First, import `pymdp` and the modules we'll need.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import numpy as np\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"from IPython.display import display, Latex\\n\",\n \"\\n\",\n \"from pymdp import utils, maths\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### A simple generative model composed of a likelihood and a prior\\n\",\n \"\\n\",\n \"We begin by constructing a simple generative model composed of two sets of categorical distributions: a likelihood distribution $P(o|s)$ and a prior distribution $P(s)$. \\n\",\n \"\\n\",\n \"Because both of these distributions are categorical distributions, we can represent them easily in code using matrices and vectors. The likelihood distribution is a conditional distribution that tells the probability that the generative model assigns to different observations, given different hidden states. Since observations and hidden states are both discrete, this can be efficiently represented as a matrix, each of whose **columns** store the conditional probabilities of all the observations (the **rows**), given a particular hidden state. Each hidden state setting is thus indexed by a column. For this reason, each column of this matrix is a categorical probability distributions and its entries must sum to one. \\n\",\n \"\\n\",\n \"The prior is represented as a 1-D vector and stores the prior probabilities that the generative model assigns to each hidden state. \\n\",\n \"\\n\",\n \"Finally, to set ourselves up later for showing model inversion and free energy calculations, we initialize an observation that we assume the agent or generative model has \\\"gathered\\\" or \\\"seen.\\\" In `pymdp` we can represent these observations either as one-hot vectors (a `1` in one entry, and `0`'s everywhere else) or more sparsely as simple indices (integers) that represent *which* of the observations was observed. Because observations are not distributions (or technically, they are Dirac distributions), you don't need to store a whole vector of elements, you can just store a particular index.\\n\",\n \"\\n\",\n \"Below we create 3 main variables: \\n\",\n \"\\n\",\n \"- An `observation` that represents a real observation that the agent or generative model \\\"sees\\\". \\n\",\n \"- The `prior` distribution that represents the agent's prior beliefs about the hidden states\\n\",\n \"- the `likliheood_dist` that represents the agent's beliefs about how hidden states probabilistically relate to observations.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"## Define a quick helper function for printing arrays nicely (see https://gist.github.com/braingineer/d801735dac07ff3ac4d746e1f218ab75)\\n\",\n \"def matprint(mat, fmt=\\\"g\\\"):\\n\",\n \" col_maxes = [max([len((\\\"{:\\\"+fmt+\\\"}\\\").format(x)) for x in col]) for col in mat.T]\\n\",\n \" for x in mat:\\n\",\n \" for i, y in enumerate(x):\\n\",\n \" print((\\\"{:\\\"+str(col_maxes[i])+fmt+\\\"}\\\").format(y), end=\\\" \\\")\\n\",\n \" print(\\\"\\\")\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Observation: 0\\n\",\n \"\\n\",\n \"Prior:[0.5 0.5]\\n\",\n \"\\n\",\n \"Likelihood:\\n\",\n \"0.8 0.2 \\n\",\n \"0.2 0.8 \\n\"\n ]\n }\n ],\n \"source\": [\n \"num_obs = 2 # dimensionality of observations (2 possible observation levels)\\n\",\n \"num_states = 2 # dimensionality of observations (2 possible hidden state levels)\\n\",\n \"\\n\",\n \"observation = 0 # index representation\\n\",\n \"# observation = np.array([1, 0]) # one hot representation\\n\",\n \"# observation = utils.onehot(0, num_obs) # one hot representation, but use one of pymdp's utility functions to create a one-hot\\n\",\n \"\\n\",\n \"prior = np.array([0.5, 0.5]) # simply set it by hand\\n\",\n \"# prior = np.ones(num_states) / num_states # create a uniform prior distribution by creating a vector of ones and dividing each by the number of states\\n\",\n \"# prior = utils.norm_dist(np.ones(num_states)) # use one of pymdp's utility functions to normalize any vector into a probability distribution\\n\",\n \"\\n\",\n \"likelihood_dist = np.array([ [0.8, 0.2],\\n\",\n \" [0.2, 0.8] ])\\n\",\n \"\\n\",\n \"if isinstance(observation, np.ndarray):\\n\",\n \" print(f'Observation:{observation}\\\\n')\\n\",\n \"else:\\n\",\n \" print(f'Observation: {observation}\\\\n')\\n\",\n \"print(f'Prior:{prior}\\\\n')\\n\",\n \"print('Likelihood:')\\n\",\n \"matprint(likelihood_dist)\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Bayesian inference\\n\",\n \"\\n\",\n \"Before we define variational free energy for this generative model, let's step through the computations involved in inverting this model using Bayes' rule, i.e. computing the optimal Bayesian posterior over hidden states, given our sensory observation (which we will formally refer to as $o_t$). By performing exact Bayesian inference first, we can directly compares its results to that of variational free energy minimization. This will help us better understand the meaning of the free energy calculations that come later.\\n\",\n \"\\n\",\n \"#### 1. Compute the likelihood over hidden states, given the observation \\n\",\n \"\\n\",\n \"Now that we have a generative model and have fixed a particular observatio $o_t$ (`observation`), we have to perform Bayes' rule to compute the posterior. Mathematically, this can be expressed as follows:\\n\",\n \"\\n\",\n \"### $ \\\\hspace{60mm} P(s | o _t) = \\\\frac{P(o = o_t | s)P(s)}{P(o = o_t)} $\\n\",\n \"\\n\",\n \"Computing the posterior via Bayes' rule (also known as \\\"model inversion\\\") is the essence of optimal statistical inference, when one has a generative model of how one's data is caused, and some data. \\n\",\n \"\\n\",\n \"To start with, let's computing the likelihood term $P(o = o_t | s)$. We can represent the computation of the likelihood with this line of `NumPy`: ``likelihood_dist[observation,:]``. By doing so, we are providing a numerical answer to the question: \\\"What is the likelihood that State 1 vs State 2 caused the actual sensory data $o_t$ that I've observed?\\\".\\n\",\n \"\\n\",\n \" Mathematically, our likelihood function $P(o = o_t | s)$ (in the statistics literature also referred to as $L(\\\\theta)$) is a *function of the hidden states*. The particular function over hidden states we use is *defined* by the observation $o_t$. So you can think of the likelihood as a multi-dimensional function or simply a space of functions, where the particular function you use for inference is determined by your data.\\n\",\n \"\\n\",\n \"This act of computing the likelihood via an indexing operation ``likelihood_dist[observation,:]``, is similar in spirit to the operation of *conditioning*. We are, in some sense, \\\"conditioning\\\" on a particular observation (slicing out a \\\"row\\\" of our ``likelihood_dist`` matrix), and then looking at the *induced* likelihood over possible causes (hidden states) that could've have been the latent source of that observation. This operation captures the essence of what we mean when we speak of \\\"inverting\\\" generative models. Generative models are referred to as *generative* because they can be used to generate fictive observations, given some fixed setting of latent parameters. *Inversion* is thus moving in the opposite direction -- given some sensory data, what is the consequent likelihood over the *causes* or hidden states that might have generated that data?\\n\",\n \"\\n\",\n \"**Note**: We can also compute the likelihood using a matrix-vector product, if the observation is represented as a one-hot vector.\\n\",\n \"\\n\",\n \"```\\n\",\n \"likelihood_s = likelihood_dist.T @ observation\\n\",\n \"```\\n\",\n \"\\n\",\n \"You can see think of this as a weighted average of the rows of the likelihood matrix, where the weights are provided by the observations. Since we have insisted that the observations are a one-hot vector, this is equivalent to just selecting a single row of the likelihood matrix (the one indexed by the entry of the observation that is `1.0`).\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$P(o=o_t|s):$\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[0.8 0.2]\\n\",\n \"==================\\n\",\n \"\\n\"\n ]\n }\n ],\n \"source\": [\n \"\\n\",\n \"if isinstance(observation, np.ndarray): # use the matrix-vector version if your observation is a one-hot vector\\n\",\n \" likelihood_s = likelihood_dist.T @ observation\\n\",\n \"elif isinstance(observation, int): # use the index version if your observation is an integer index\\n\",\n \" likelihood_s = likelihood_dist[observation,:] \\n\",\n \"display(Latex('$P(o=o_t|s):$'))\\n\",\n \"print(f'{likelihood_s}')\\n\",\n \"print('==================\\\\n')\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### 2. The joint distribution $P(o = o_t, s) = P(o = o_t|s)P(s)$ \\n\",\n \"\\n\",\n \"To compute the full numerator on the right-hand side of the Bayes' rule equation, we need to compute the joint distribution $P(o = o_t|s)P(s)$.\\n\",\n \"\\n\",\n \"The joint distribution, which also fully defines the generative model, is the product of the likelihood and prior distributions. The joint distribution expresses the joint probability of observations and hidden states, given the likelihood distribution and the prior over hidden states. If we condition on an actual observation $o_t$, as we have done here, then this joint distribution is, like the likelihood, a function of hidden states. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$P(o = o_t,s) = P(o = o_t|s)P(s):$\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[0.4 0.1]\\n\",\n \"==================\\n\",\n \"\\n\"\n ]\n }\n ],\n \"source\": [\n \"joint_prob = likelihood_s * prior # element-wise product of the likelihood of each hidden state, given the observation, with the prior probability assigned to each hidden state\\n\",\n \"display(Latex('$P(o = o_t,s) = P(o = o_t|s)P(s):$'))\\n\",\n \"print(f'{joint_prob}')\\n\",\n \"print('==================\\\\n')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### 3. Marginal probability or marginal likelihood: $\\\\sum_s P(o = o_t, s) = P(o = o_t)$\\n\",\n \"\\n\",\n \"Let's remind ourselves of Bayes' rule below:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} P(s | o _t) = \\\\frac{P(o = o_t | s)P(s)}{P(o = o_t)} $\\n\",\n \"\\n\",\n \"So far, using the likelihood, the observation, and the prior, we have computed the numerator of this term: the unnormalized joint distribution $P(o = o_t,s)$. All that's left is to do is then divide this term by the denominator $P(o=o_t)$. This term is also referred to as the model evidence or the marginal likelihood. \\n\",\n \"\\n\",\n \"This can be thought of as the probability of having seen the particular observation you saw, under all possible settings of the hidden states. This can be computed by marginalizing the joint distribution, using the prior probabilities of the hidden states:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm}P(o) = \\\\sum_s P(o|s)P(s)$\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"p_o = joint_prob.sum()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### 4. Compute the posterior $P(s|o=o_t)$\\n\",\n \"\\n\",\n \"Now to compute the Bayes-optimal posterior, simply divide the numerator by the denominator!\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$P(s|o = o_t) = \\\\frac{P(o = o_t,s)}{P(o=o_t)}$:\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Posterior over hidden states: [0.8 0.2]\\n\",\n \"==================\\n\"\n ]\n }\n ],\n \"source\": [\n \"posterior = joint_prob / p_o # divide the joint by the marginal\\n\",\n \"display(Latex('$P(s|o = o_t) = \\\\\\\\frac{P(o = o_t,s)}{P(o=o_t)}$:'))\\n\",\n \"print(f'Posterior over hidden states: {posterior}')\\n\",\n \"print('==================')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### The variational free energy\\n\",\n \"\\n\",\n \"The variational free energy is an upper bound on **surprise**: surprise is define as $ - \\\\ln p(o)$, and is also known as the negative (log) evidence. By minimizing free energy, we are **minimizing** surprise and thus **maximizing** log evidence. This evidence is simply the (log of the) term we computed in the previous step, the normalizing denominator used in Bayes' rule. We can thus first compute the surprise associated with the observation we saw earlier:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$- \\\\ln P(o=o_t)$:\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Surprise: 0.693\\n\",\n \"==================\\n\"\n ]\n }\n ],\n \"source\": [\n \"surprise = - np.log(p_o)\\n\",\n \"\\n\",\n \"display(Latex('$- \\\\ln P(o=o_t)$:'))\\n\",\n \"print(f'Surprise: {surprise.round(3)}')\\n\",\n \"print('==================')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"By minimizing variational free energy with respect to the parameters of an arbitrary, parametrized distribution, also known as the approximate or variational posterior $Q(s)$, we are forcing the surprise to go down, and the model evidence to go up. In doing so, the approximate posterior distribution will get \\\"closer\\\" to the true posterior distribution (the $P(s|o)$ we computed above), $Q(s) \\\\approx P(s|o)$.\\n\",\n \"\\n\",\n \"This idea of minimizing a bound on surprise, is the core principle underlying the variational free energy principle, active inference, and the statistical methodology of variational principles more generally. This comes in handy because in many realistic scenarios where agents or systems need to make inferences about the hidden causes of sensory perturbations, performing Bayesian inference exactly becomes intractable (due mostly to the computation of the $P(o)$ denominator term, also known as the normalizing constant). Variational inference turns this intractable marginalization problem into a tractable optimization problem, where one only needs to change the approximate posterior $Q(s)$ in order to minimize a bound on surprise.\\n\",\n \"\\n\",\n \"But what is the variational free energy exactly, mathematically? It is commonly written as the expectation, under the approximate posterior, of the log ratio between the approximate posterior and the generative model:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} \\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln \\\\frac{Q(s)}{P(o, s)}] $\\n\",\n \"\\n\",\n \"Because of the rules of logarithms, we can also express this as an expected difference between the log posterior and the log generative model:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} \\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(o, s)] $\\n\",\n \"\\n\",\n \"By doing taking advantage of some more mathematical relationships (the factorization of the joint, rules for logarithms of products, and the definition of the conditional expectation), we can re-write this as an upper bound on surprise:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} \\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(s|o)] - \\\\ln P(o) $\\n\",\n \"\\n\",\n \"By re-arranging this equality and taking advantage of the fact that the quantity $\\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(s|o)]$ (also known as the Kullback-Leibler divergence) is greater than or equal to 0, we can easily show that the VFE is an upper bound on surprise:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} \\\\mathcal{F} \\\\geq - \\\\ln P(o) $\\n\",\n \"\\n\",\n \"Let's now compute the VFE numerically for our generative model and fixed observation. Given we already defined those two things ($o_t$ and $P(o,s)$), the last thing we need to do, is to define an initial setting of our approximate posterior $Q(s)$, and compute the variational free energy using one of the formulas above.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$\\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln \\\\frac{Q(s)}{P(o, s)}] = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(o, s)]:$\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Variational free energy (F) = 0.916\\n\",\n \"==================\\n\"\n ]\n }\n ],\n \"source\": [\n \"# to begin with, set our initial Q(s) equal to our prior distribution -- i.e. a flat/uninformative belief about hidden states\\n\",\n \"initial_qs = np.array([0.5, 0.5])\\n\",\n \"\\n\",\n \"# redefine generative model and observation, for ease\\n\",\n \"observation = 0\\n\",\n \"likelihood_dist = np.array([[0.8, 0.2], [0.2, 0.8]])\\n\",\n \"prior = utils.norm_dist(np.ones(2))\\n\",\n \"\\n\",\n \"# compute the joint or generative model using the factorization: P(o=o|s)P(s)\\n\",\n \"joint_prob = likelihood_dist[observation,:] * prior\\n\",\n \"\\n\",\n \"# compute the variational free energy using the expected log difference formulation\\n\",\n \"initial_F = initial_qs.dot(np.log(initial_qs) - np.log(joint_prob))\\n\",\n \"## @NOTE: because of log-rules, `initial_F` can also be computed using the division inside the logarithm:\\n\",\n \"# initial_F = initial_qs.dot(np.log(initial_qs/joint_prob))\\n\",\n \"\\n\",\n \"display(Latex('$\\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln \\\\\\\\frac{Q(s)}{P(o, s)}] = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(o, s)]:$'))\\n\",\n \"print(f'Variational free energy (F) = {initial_F.round(3)}')\\n\",\n \"print('==================')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's then change the approximate posterior $Q(s)$ and see what happens to the variational free energy.\\n\",\n \"\\n\",\n \"By definition, optimal inference (and 'perfect' VFE minimization) obtains when we set the approximate posterior $Q(s)$ to be equal to the true posterior, $Q(s) = P(s|o)$. \\n\",\n \"\\n\",\n \"As an extreme case, let's do this and then measure the variational free energy. We can see that it has decreased, relative to it's initial setting when the approximate posterior was equal to the prior $P(s)$.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$\\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln \\\\frac{Q(s)}{P(o, s)}] = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(o, s)]:$\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"F = 0.693\\n\",\n \"==================\\n\"\n ]\n }\n ],\n \"source\": [\n \"final_qs = posterior.copy() # now we just assert that the approximate posterior is equal to the true posterior\\n\",\n \"final_F = final_qs.dot(np.log(final_qs) - np.log(joint_prob))\\n\",\n \"\\n\",\n \"display(Latex('$\\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln \\\\\\\\frac{Q(s)}{P(o, s)}] = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(o, s)]:$'))\\n\",\n \"print(f'F = {final_F.round(3)}')\\n\",\n \"print('==================')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Notice that the free energy is 0.693 -- if you recall, this is exactly the **surprise** or negative log marginal likelihood $-\\\\ln P(o = o_t)$, related to the marginal likelihood quantity $P(o=o_t)$ that we had to compute when performing exact Bayesian inference earlier. \\n\",\n \"\\n\",\n \"It is easy to see why this equality should hold, when we consider the VFE in terms of the surprise bound:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} \\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(s|o)] - \\\\ln P(o) $\\n\",\n \"\\n\",\n \"When $Q(s) = P(s|o)$, as we have enforced with the line ``final_qs = posterior.copy()`` above, the first term $\\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(s|o)]$ will become 0. This is a property of the Kullback-Leibler divergence between two distributions $\\\\operatorname{D}_{KL}(Q \\\\parallel P) = \\\\mathbb{E}_{Q}[\\\\ln Q - \\\\ln P]$. \\n\",\n \"\\n\",\n \"So since that KL divergence is 0, this is a case when the bound on surprise is exact:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} \\\\mathcal{F} = 0 - \\\\ln P(o) = - \\\\ln P(o)$\\n\",\n \"\\n\",\n \"In other words, minimizing free energy \\\"as much as possible\\\" in the case of this generative model, means that the approximate posterior equals the true posterior, and the free energy bound becomes \\\"tight\\\", i.e. the free energy simply IS the negative log evidence!\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$-\\\\ln P(o):$\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"0.693\\n\",\n \"==================\\n\",\n \"\\n\"\n ]\n }\n ],\n \"source\": [\n \"# compute the surprise (which we can do analytically for this simple generative model)\\n\",\n \"p_o = joint_prob.sum()\\n\",\n \"surprise = - np.log(p_o)\\n\",\n \"display(Latex('$-\\\\ln P(o):$'))\\n\",\n \"print(f'{surprise.round(3)}')\\n\",\n \"print('==================\\\\n')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Bonus material: auto-differentiation to perform gradient descent on the variational free energy\\n\",\n \"\\n\",\n \"In this section, we are going to numerically differentiate the variational free energy with respect to the parameters of the approximate posterior. We can take advantage of modern autodifferentiation software, that can calculate the derivatives of arbitrary computer programs, to compute these derivatives without doing any analytic differentiation.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import autograd.numpy as np_auto # Thinly-wrapped version of Numpy that is auto-differentiable\\n\",\n \"from autograd import grad # this is the function that we use to evaluate derivatives\\n\",\n \"from functools import partial\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"First, let's create a variational free energy function, that takes as input the variational posterior `qs`, an observation `obs`, the likelihood matrix `likelihood` and a prior distribution `prior`.\\n\",\n \"\\n\",\n \"By defining this computation as a function, we can calculate its derivatives automatically using the autodifferentiation package `autograd`, which allows users to pass gradients through arbitrary Python code. It includes a special version of `numpy` (`autograd.numpy`) that has a differentiable back-end. We will thus use this \\\"special\\\" verison of `numpy` when we instantiate our arrays and perform numerical operations on them.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# define the variational free energy as a function of the approximate posterior, an observation, and the generative model\\n\",\n \"def vfe(qs, obs, likelihood, prior):\\n\",\n \" \\\"\\\"\\\"\\n\",\n \" Quick docstring below on inputs\\n\",\n \" Arguments:\\n\",\n \" =========\\n\",\n \" `qs` [1D np_auto.ndarray]: variational posterior over hidden states\\n\",\n \" `obs` [int]: index of the observation\\n\",\n \" `likelihood` [2D np_auto.ndarray]: likelihood distribution P(o|s), relating hidden states probabilistically to observations\\n\",\n \" `prior` [1D np_auto.ndarray]: prior over hidden states\\n\",\n \" \\\"\\\"\\\"\\n\",\n \"\\n\",\n \" likelihood_s = likelihood[obs,:]\\n\",\n \"\\n\",\n \" joint = likelihood_s * prior\\n\",\n \"\\n\",\n \" vfe = qs @ (np_auto.log(qs) - np_auto.log(joint))\\n\",\n \"\\n\",\n \" return vfe\\n\",\n \"\\n\",\n \"# initialize an observation, an initial variational posterior, a prior, and a likelihood matrix\\n\",\n \"obs = 0\\n\",\n \"init_qs = np_auto.array([0.5, 0.5])\\n\",\n \"prior = np_auto.array([0.5, 0.5])\\n\",\n \"likelihood_dist = np_auto.array([ [0.8, 0.2],\\n\",\n \" [0.2, 0.8] ])\\n\",\n \"\\n\",\n \"# this use of `partial` creates a version of the vfe function that is a function of Qs only, \\n\",\n \"# with the other parameters (the observation, the generative model) fixed as constant parameters\\n\",\n \"vfe_qs = partial(vfe, obs = obs, likelihood = likelihood_dist, prior = prior)\\n\",\n \"\\n\",\n \"# By calling `grad` on a function, we get out a function that can be used to compute the gradients of the VFE with respect to its input (in our case, `qs`)\\n\",\n \"grad_vfe_qs = grad(vfe_qs)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now that we have a variational free energy function, and a derivative function that will give us the gradients of the VFE, with respect $Q(s)$, we can use it to perform a gradient descent on VFE, with respect to the parameters of $Q(s)$. In other words, we will implement this discretized differential equation to update the approximate posterior:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} Q(s)_{t+1} =Q(s)_{t} - \\\\frac{\\\\partial \\\\mathcal{F}}{\\\\partial Q(s)_{t}} $\\n\",\n \"\\n\",\n \"Where the gradient term $\\\\frac{\\\\partial \\\\mathcal{F}}{\\\\partial Q(s)_{t}}$ will simply be the output of the gradient function `grad_vfe_qs` we've defined above.\\n\",\n \"\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# number of iterations of gradient descent to perform\\n\",\n \"n_iter = 40\\n\",\n \"\\n\",\n \"qs_hist = np_auto.zeros((n_iter, 2))\\n\",\n \"qs_hist[0,:] = init_qs\\n\",\n \"\\n\",\n \"vfe_hist = np_auto.zeros(n_iter)\\n\",\n \"vfe_hist[0] = vfe_qs(qs = init_qs)\\n\",\n \"\\n\",\n \"learning_rate = 0.1 # learning rate to prevent gradient steps that are too big (overshooting)\\n\",\n \"for i in range(n_iter-1): \\n\",\n \"\\n\",\n \" dFdqs = grad_vfe_qs(qs_hist[i,:])\\n\",\n \"\\n\",\n \" ln_qs = np_auto.log(qs_hist[i,:]) - learning_rate * dFdqs # transform qs to log-space to perform gradient descent\\n\",\n \" qs_hist[i+1,:] = maths.softmax(ln_qs) # re-normalize to make it a proper, categorical Q(s) again\\n\",\n \"\\n\",\n \" vfe_hist[i+1] = vfe_qs(qs = qs_hist[i+1,:]) # measure final variational free energy\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Since we were storing the history of the variational free energy over the course of the gradient descent, we can plot its trajectory below.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"Text(0.5, 1.0, 'Gradient descent on VFE')\"\n ]\n },\n \"execution_count\": 16,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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8RfPlXEiQPDxNcoXFvkno3EIz3cTOwguAsazlBoruQYCTLN3W1nz3l7r8gGOL6KYL3YjzBsUnW0TTVNvYT/K1+CHiEIBkbSvC/9VPgWHe/J/UWBsV9HOqY2cnhx3mgdDcAVB1vHNdF+pmF2ZyIiIhIt3TGQURERNKmxEFERETSpsRBRERE0qbEQURERNKmxEFERETSpttqxymrrPaZR07tfkUREZEc8PTTT29192R3WE1JiUOcwmGjaGxs7H5FERGRHGBmPR5fRk0Vcdo7nV0H2rpfUUREJE8pcUiwYvOeqEMQERHJWEocEryyeW/UIYiIiGQsJQ5xCsx4RWccREREUlLiEKe0qIAVW5Q4iIiIpKLEIU5ZcaGaKkRERLqgxCFOaXEBTXta2Lm/NepQREREMpIShzhlRYUArNiisw4iIiLJKHGIU1ocvB3qICkiIpKcEoc4JYUFlJcUskL9HERERJJS4pBgal2lzjiIiIikoMQhwfRRFbqyQkREJAUlDgmm11WydW8LO/bpygoREZFEShwSTKurANRBUkREJBklDgmm11UC8IouyRQREXkDJQ4JxlSVUVFaxEqdcRAREXkDJQ4JzIyp6iApIiKSlBKHJKbXVehmVyIiIklkROJgZvPMbLmZrTSza5Isn2Bmfzez583sITOrj1t2mZmtCKfL4spPMLMXwm1+38ws3XiCKyta2a4rK0RERA4TeeJgZoXATcA5wAzgQjObkbDat4Fb3H0WcD3w9bDuCODLwEnAXODLZjY8rPMj4MPAtHCal25M02IdJNXPQURE5DCRJw4EX/gr3X21u7cCdwDnJawzA3gwfL4obvnbgQfcfbu77wAeAOaZ2RhgmLs/4e4O3AKcn25A08NLMlcocRARETlMJiQO44D1cfMbwrJ4zwHvCZ//M1BpZjVd1B0XPu9qmwCY2ZVm1mhmjU1NTQCMHlZGZWmROkiKiIgkyITEIR2fBs4ws2eBM4CNQEd/bNjdb3b3BndvqK2tBYIrK6bVVaipQkREJEEmJA4bgfFx8/Vh2UHuvsnd3+PuxwH/FZbt7KLuxvB5ym12Z9qoSlZoECgREZHDZELisBiYZmaTzKwEmA/cG7+CmY00s1is1wI/D58vBN5mZsPDTpFvAxa6+2vAbjM7Obya4lLgnp4ENa2ugu37Wtm2t6X3eyYiIpJjIk8c3L0duIogCXgJuNPdl5rZ9Wb27nC1M4HlZvYKUAd8Nay7HfgKQfKxGLg+LAP4GPBTYCWwCri/J3EdHHpa/RxEREQOKoo6AAB3vw+4L6HsS3HP7wLuSlH35xw6AxFf3gjM7G1MscRhxZY9nDKlprebERERySmRn3HIVHXDSqksK1IHSRERkThKHFIwM6bXVaqpQkREJI4Shy5Mr6tgxeY9BGNIiYiIiBKHLkwbVcmO/W1s3at7VoiIiIAShy5N09DTIiIih1Hi0IXputmViIjIYZQ4dGFUZSnDyoo0gqSIiEhIiUMXYldWrNCVFSIiIoASh25Nq6vklS26skJERASUOHRrel0FO/e30aR7VoiIiChx6M7BoafVXCEiIqLEoTuxSzJ1ZYWIiIgSh27VVpRSNaRYQ0+LiIigxKFbwZUVFRoESkREBCUOaZlWV8krumeFiIiIEod0TB9Vwe7mdpr26MoKERHJb0oc0nBo6Gn1cxARkfymxCEN03TPChEREUCJQ1pGVpQwfGgxK7YocRARkfymxCENZhZ2kFRThYiI5DclDmmaNqpCV1aIiEjeU+KQpul1lexpbmfzbl1ZISIi+UuJQ5o09LSIiIgSh7RN15UVIiIiShzSNbKilBHlJazcog6SIiKSv5Q49ECsg6SIiEi+UuLQA9PrKlmxea+urBARkbylxKEHptdVsKelndd3N0cdioiISCQyInEws3lmttzMVprZNUmWH2Fmi8zsWTN73szODcsvMrMlcVOnmc0Jlz0UbjO2bFRf45w6SvesEBGR/BZ54mBmhcBNwDnADOBCM5uRsNoXgDvd/ThgPvBDAHf/tbvPcfc5wCXAGndfElfvothyd9/S11inh5dkrlA/BxERyVORJw7AXGClu69291bgDuC8hHUcGBY+rwI2JdnOhWHdAVNTUUpNeYk6SIqISN7KhMRhHLA+bn5DWBbvOuBiM9sA3AdcnWQ77wduTyj7RdhM8UUzs2QvbmZXmlmjmTU2NTV1G+y0ugo1VYiISN7KhMQhHRcCC9y9HjgXuNXMDsZuZicB+939xbg6F7n7scCbwumSZBt295vdvcHdG2pra7sNZHpdJSu36MoKERHJT5mQOGwExsfN14dl8a4A7gRw98eBMmBk3PL5JJxtcPeN4eMe4DaCJpE+m1ZXyd6Wdl7bpSsrREQk/2RC4rAYmGZmk8yshCAJuDdhnXXA2QBmdjRB4tAUzhcA/0Jc/wYzKzKzkeHzYuCdwIv0g+mjdM8KERHJX5EnDu7eDlwFLAReIrh6YqmZXW9m7w5X+xTwYTN7juDMwuV+qK3gzcB6d18dt9lSYKGZPQ8sITiD8ZP+iDd2z4oV6ucgIiJ5qCjqAADc/T6CTo/xZV+Ke74MOC1F3YeAkxPK9gEn9HugwPDyEkZW6MoKERHJT5GfcchGR46u5KXXd0cdhoiIyKBT4tALs+qrefm1PTS3dUQdioiIyKBS4tALs+uraO90lr2msw4iIpJflDj0wuzx1QA8v35npHGIiIgMNiUOvTB6WBm1laU8v2FX1KGIiIgMKiUOvWBmzK6vYsmGnVGHIiIiMqiUOPTS7PpqVjftY3dzW9ShiIiIDBolDr00K+zn8IKaK0REJI8oceil2fVVADyn5goREckjShx6qXpoCRNqhvL8ep1xEBGR/KHEoQ9m11frjIOIiOQVJQ59MKu+itd2NbNlt26xLSIi+UGJQx/EBoJ6Th0kRUQkTyhx6INjxg6jsMB4Xs0VIiKSJ5Q49MHQkiKmjarQGQcREckbShz6aM74ap7fsBN3jzoUERGRAafEoY9m1Vezc38b67bvjzoUERGRAafEoY9mhQNBLdGdMkVEJA8oceijI0dXUlpUoDtliohIXlDi0EfFhQUcM3aYrqwQEZG8oMShH8weX80LG3fR3tEZdSgiIiIDSolDP5hdX01zWycrtuyNOhQREZEBpcShH8Q6SD6nDpIiIpLjlDj0g4k15QwrK9JAUCIikvOUOPSDggJjVn21zjiIiEjOU+LQT2aPr2L55j00t3VEHYqIiMiAUeLQT2bVV9PR6SzdtDvqUERERAZMRiQOZjbPzJab2UozuybJ8iPMbJGZPWtmz5vZuWH5RDM7YGZLwunHcXVOMLMXwm1+38xsIPdhTuwW22quEBGRHBZ54mBmhcBNwDnADOBCM5uRsNoXgDvd/ThgPvDDuGWr3H1OOH00rvxHwIeBaeE0b6D2AaBuWBl1w0o1EJSIiOS0yBMHYC6w0t1Xu3srcAdwXsI6DgwLn1cBm7raoJmNAYa5+xMe3LbyFuD8fo06iVn11bqyQkREclomJA7jgPVx8xvCsnjXAReb2QbgPuDquGWTwiaMh83sTXHb3NDNNvvdnPHVrNm6j10H2gb6pURERCKRCYlDOi4EFrh7PXAucKuZFQCvAUeETRj/CdxmZsO62M4bmNmVZtZoZo1NTU19CjI2ENQLOusgIiI5KhMSh43A+Lj5+rAs3hXAnQDu/jhQBox09xZ33xaWPw2sAqaH9eu72SZhvZvdvcHdG2pra/u0I7PGVQPwnPo5iIhIjsqExGExMM3MJplZCUHnx3sT1lkHnA1gZkcTJA5NZlYbdq7EzCYTdIJc7e6vAbvN7OTwaopLgXsGekeqhhYzaWS5rqwQEZGcVRR1AO7ebmZXAQuBQuDn7r7UzK4HGt39XuBTwE/M7D8IOkpe7u5uZm8GrjezNqAT+Ki7bw83/TFgATAEuD+cBtys+iqeWL1tMF5KRERk0EWeOAC4+30EnR7jy74U93wZcFqSer8Dfpdim43AzP6NtHuz66u5Z8kmNu9upm5Y2WC/vIiIyIDKhKaKnDJ7vO6UKSIiuUuJQz87ZmwVhQWmDpIiIpKTlDj0s7LiQo6sq+R5XZIpIiI5SInDAJg9vorn1u8kGLRSREQkdyhxGACz66vZ3dzO2m37ow5FRESkXylxGACz6qsBdMMrERHJOUocBsD0ugrKigtYoisrREQkxyhxGABFhQXMHFulDpIiIpJzlDgMkNnjq3lx4y7aOjqjDkVERKTfKHEYILPqq2hp7+SVzXuiDkVERKTfKHEYILMPdpBUc4WIiOQOJQ4DZELNUKqGFGvoaRERySlKHAaImTGrvorndMZBRERyiBKHATRnfDWvbN7DgdaOqEMRERHpF0ocBtCs+mo6Op2lm3TWQUREcoMShwE0uz68xbaaK0REJEcocRhAo4aVMaaqTB0kRUQkZyhxGGCz6qs09LSIiOQMJQ4D7MSJI1i3fT+bdh6IOhQREZE+U+IwwE6bOhKAR1dujTgSERGRvlPiMMCOrKukpryEx1ZtizoUERGRPlPiMMAKCoxTptTw6MqtuHvU4YiIiPSJEodBcNrUkWzZ08Kqpr1RhyIiItInShwGwWlTYv0c1FwhIiLZTYnDIDiiZij1w4eog6SIiGQ9JQ6D5LQpI3li9TY6OtXPQUREspcSh0Fy6tQadje38+JGDT8tIiLZS4nDIDk11s9hlZorREQke2VE4mBm88xsuZmtNLNrkiw/wswWmdmzZva8mZ0blr/VzJ42sxfCx7Pi6jwUbnNJOI0azH1KVFtZypF1lTymDpIiIpLFiqIOwMwKgZuAtwIbgMVmdq+7L4tb7QvAne7+IzObAdwHTAS2Au9y901mNhNYCIyLq3eRuzcOxn6k49SpNdz25Dpa2jsoLSqMOhwREZEey4QzDnOBle6+2t1bgTuA8xLWcWBY+LwK2ATg7s+6+6awfCkwxMxKByHmXjltykha2jt55tWdUYciIiLSK5mQOIwD1sfNb+DwswYA1wEXm9kGgrMNVyfZznuBZ9y9Ja7sF2EzxRfNzJK9uJldaWaNZtbY1NTU651Ix0mTR1BYYDymfg4iIpKlMiFxSMeFwAJ3rwfOBW41s4Oxm9kxwDeBj8TVucjdjwXeFE6XJNuwu9/s7g3u3lBbWztgOwBQWVbMrPoqjecgIiJZKxMSh43A+Lj5+rAs3hXAnQDu/jhQBowEMLN64G7gUndfFavg7hvDxz3AbQRNIpE7dUoNz23YxZ7mtqhDERER6bFMSBwWA9PMbJKZlQDzgXsT1lkHnA1gZkcTJA5NZlYN/Bm4xt0fja1sZkVmFkssioF3Ai8O9I6k47QpI+nodJ5asz3qUERERHos8sTB3duBqwiuiHiJ4OqJpWZ2vZm9O1ztU8CHzew54Hbgcg9uNXkVMBX4UsJll6XAQjN7HlhCcAbjJ4O6YykcP2E4pUUFum+FiIhkpcgvxwRw9/sIOj3Gl30p7vky4LQk9W4Abkix2RP6M8b+UlZcSMPE4eogKSIiWSnyMw756NQpI3n59T1s3dvS/coiIiIZRIlDBE6bGgw//dgqNVeIiEh2UeIQgWPHVVFZVsRjuixTRESyjBKHCBQWGCdPrtENr0REJOsocYjIaVNqWL/9AOu37486FBERkbQpcYhIrJ+DRpEUEZFsosQhIlNHVTCqspRH1UFSRESyiBKHiJgZp06p4fFVWwnGshIREcl8ShwidOrUkWzd28orm/dGHYqIiEhalDhESP0cREQk2yhxiNC46iFMrBmq4adFRCRrKHGI2KlTR/Lk6u20d3RGHYqIiEi3lDhE7LQpI9nT0s7zG3dFHYqIiEi3lDhE7JQpNQAaflpERLKCEoeIjSgvYcaYYTy6UuM5iIhI5lPikAFOnVLD0+t20NzWEXUoIiIiXVLikAFOmzqS1vZOGtfuiDoUERGRLnWbOJjZKDP7upl91czGDEZQ+WbupBEUFZjulikiIhmvqKuFZlYA/BWYBThwIvC2QYgrr5SXFjFnfLU6SIqISMbr7ozDGcAq4GrAgHUDHlGeOnXqSF7YuItdB9qiDkVERCSl7hKHk4CfuvtNwHB3/9AgxJSXTptSQ6fDE6t1dYWIiGSu7hKHo4DnANz9sBGKzOzRgQoqHx13xHCGFBequUJERDJad4nDFCDVN9kR/RxLXispKuDESSN4dJXOOIiISObqLnGoAspSLPN+jiXvnT61hpVb9rJhx/6oQxEREUmqu8ShDPiLmX3QzCYMRkD57G0zRgPwlxdfjzgSERGR5LpLHAoIOkj+BFhtZivN7Mdm9v6BDy3/TBxZzowxw7jvhdeiDkVERCSp7hKHXQSXYRI+TgY+DNwGjDOzJ83s82Z2zADGmFfeMWsMz6zbyWu7DkQdioiIyBt0lzhsAL4CDAXOBr4NvESQRBjBgFBfAZ43s5fM7NNmVt7TIMxsnpktD89oXJNk+RFmtsjMnjWz583s3Lhl14b1lpvZ29PdZqY6Z6aaK0REJHN1lzg8Cuxw9xZ3X+Tun3X3mcBE4N+APwL7CZKII4FvAi+Y2cR0AzCzQuAm4BxgBnChmc1IWO0LwJ3ufhwwH/hhWHdGOH8MMA/4oZkVprnNjDS5toKjRldy/wtKHEREJPN0lzj8FpibWOju69z9f939PKCGYBjq7wGrCZKK7/QghrnASndf7e6twB3AeYkvCQwLn1cBm8Ln5wF3hInNGmBluL10tpmxzpk5hsWvbmfL7uaoQxERETlMl4lD+GW8rqtf6+7e6u5/c/f/dPdpBF/Qp/QghnHA+rj5DWFZvOuAi81sA3AfwRDYXdVNZ5sZ6x2zRuMOf1mqsw4iIpJZ0rmt9heBj5uZdbsm4O5/BL7ap6je6EJggbvXA+cCt4Y34OozM7vSzBrNrLGpqak/NtlnU0dVMm1Uha6uEBGRjNPtl6+7t7n7x9097QGfwntbpGsjMD5uvj4si3cFcGe47ccJxpcY2UXddLYZi/Vmd29w94ba2toehD2wzjl2DE+t2U7TnpaoQxERETmoX36199FiYJqZTTKzEoLOjvcmrLOO4KoOzOxogsShKVxvvpmVmtkkYBrwVJrbzGjvOHYMnQ4L1VwhIiIZJPLEwd3bgauAhQSXet7p7kvN7Hoze3e42qeAD5vZc8DtwOUeWEpwJmIZ8Bfg4+7ekWqbg7tnfTO9roLJteXc/6KaK0REJHNYD1ogcl5DQ4M3NjZGHcZB3164nB89vIqnPn82NRWlUYcjIiI5xsyedveGntSJ/IyDpHbOsaPp6HT+umxz1KGIiIgAShwy2owxw5hYM1RXV4iISMZQ4pDBzIxzjh3DY6u2sWNfa9ThiIiIKHHIdOfOHENHp/PAS2quEBGR6ClxyHAzxw2jfvgQNVeIiEhGUOKQ4cyMdxw7hkdXbmXX/raowxERkTynxCELnHPsGNo6nL+puUJERCKmxCELzK6vYly1mitERCR6ShyygJlxzszRPLJiK7ub1VwhIiLRUeKQJc45dgytHZ08+NKWqEMREZE8psQhSxw3vprRw8rUXCEiIpFS4pAlCgqMeTNH89ArTextaY86HBERyVNKHLLIO2aNobW9kwdfVnOFiIhEQ4lDFjnhiOGMqizlfjVXiIhIRJQ4ZJFYc8Wi5VvY36rmChERGXxKHLLMOTPH0NzWyaKXm6IORURE8pAShywzd9IIRlaUcN+Laq4QEZHBp8QhyxQWGG8/ZjSLXt7CgdaOqMMREZE8o8QhC5177Bj2t3bw8Cu6ukJERAaXEocsdNKkEYwoL+G+F16POhQREckzShyyUFFhAW8/po6/v7SZ5jY1V4iIyOBR4pCl3nHsWPa1drBwqc46iIjI4FHikKVOnVLDhJqh/PqJdVGHIiIieUSJQ5YqKDAuPmkCT63dzsuv7446HBERyRNKHLLYBQ31lBYVcOvjr0YdioiI5AklDlmsemgJ7549lruf3cju5raowxERkTygxCHLXXLKBPa3dnD3MxujDkVERPKAEocsN6u+mtn1Vdz6xKu4e9ThiIhIjsuIxMHM5pnZcjNbaWbXJFn+XTNbEk6vmNnOsPwtceVLzKzZzM4Ply0wszVxy+YM6k4NoktOmcjKLXt5fPW2qEMREZEcF3niYGaFwE3AOcAM4EIzmxG/jrv/h7vPcfc5wA+A34fli+LKzwL2A3+Nq/qZ2HJ3XzLgOxORd84aQ/XQYn71hDpJiojIwIo8cQDmAivdfbW7twJ3AOd1sf6FwO1Jyt8H3O/u+wcgxoxWVlzI+xvGs3DpZl7f1Rx1OCIiksMyIXEYB6yPm98Qlr2BmU0AJgEPJlk8nzcmFF81s+fDpo7SFNu80swazayxqamp59FniA+cdASd7tz+lAaEEhGRgZMJiUNPzAfucvfDbtBgZmOAY4GFccXXAkcBJwIjgM8l26C73+zuDe7eUFtbOzBRD4IJNeWcMb2W259aR1tHZ9ThiIhIjsqExGEjMD5uvj4sSybZWQWAfwHudveDgxm4+2seaAF+QdAkktMuPWUCW/a08Nelm6MORUREclQmJA6LgWlmNsnMSgiSg3sTVzKzo4DhwONJtvGGfg/hWQjMzIDzgRf7N+zMc8b0UdQPH8KtT6yNOhQREclRkScO7t4OXEXQzPAScKe7LzWz683s3XGrzgfu8ITBCsxsIsEZi4cTNv1rM3sBeAEYCdwwQLuQMQoLjItPnsATq7fzyuY9UYcjIiI5yDRo0CENDQ3e2NgYdRh9sn1fKyd//e/MP3E81583M+pwREQkg5nZ0+7e0JM6kZ9xkP41oryEdx47ht8/s5G9Le1RhyMiIjlGiUMOuuSUCextaefuZ3X/ChER6V9KHHLQnPHVzBw3jF89rvtXiIhI/1LikIPMjEtPnsjyzXt4as32qMMREZEcosQhR71r9liGlRVxq+5fISIi/UiJQ44aUlLIBQ3j+cuLr7Nlt+5fISIi/UOJQw67+OQJtHc6dyxe3/3KIiIiaVDikMMmjSznTdNGctuT62jX/StERKQfKHHIcZeeMpHXdzfzt5d0/woREek7JQ457qyjRjGueog6SYqISL9Q4pDjCguMD5x0BI+u3MbKLXujDkdERLKcEoc88P4Tx1NWXMBNi1ZGHYqIiGQ5JQ55YGRFKZedOpE/LNnI8td110wREek9JQ554t/OmEJFSRHf/uvyqEMREZEspsQhT1QPLeHKN0/mgWWbeXbdjqjDERGRLKXEIY988PRJ1JSX8K2FOusgIiK9o8Qhj5SXFvHxt0zlsVXbeHTl1qjDERGRLKTEIc9cdPIRjK0q438WLtctt0VEpMeUOOSZ0qJCPvlP03lu/U7+ukyjSYqISM8occhD7zl+HJNry/n2wuV0dOqsg4iIpE+JQx4qKizgU289khVb9nLPko1RhyMiIllEiUOeOmfmaI4ZO4zv/u0VWtt150wREUmPEoc8VVBgfObtR7J++wF+s3hd1OGIiEiWUOKQx86YXsvciSP4/oMrOdDaEXU4IiKSBZQ45DEz4zPzjqRpTwsLHlsbdTgiIpIFlDjkuRMnjuAtR9by44dXsetAW9ThiIhIhlPiIHz67Uey60AbP/nH6qhDERGRDJcRiYOZzTOz5Wa20syuSbL8u2a2JJxeMbOdccs64pbdG1c+ycyeDLf5GzMrGaTdyTrHjK3inbPG8PNH19C0pyXqcEREJINFnjiYWSFwE3AOMAO40MxmxK/j7v/h7nPcfQ7wA+D3cYsPxJa5+7vjyr8JfNfdpwI7gCsGcj+y3X++dTot7Z3ctGhl1KGIiEgGizxxAOYCK919tbu3AncA53Wx/oXA7V1t0MwMOAu4Kyz6JXB+30PNXZNrK7jghHpue3IdG3bsjzocERHJUJmQOIwD1sfNbwjL3sDMJgCTgAfjisvMrNHMnjCz88OyGmCnu7d3t0055N/PngYGN/5tRdShiIhIhsqExKEn5gN3uXv8oAMT3L0B+ADwPTOb0pMNmtmVYeLR2NTU1J+xZp2x1UO45OQJ/O6ZDazcsjfqcEREJANlQuKwERgfN18fliUzn4RmCnffGD6uBh4CjgO2AdVmVtTdNt39ZndvcPeG2tra3u5DzvjYmVMYWlLEdfcu1W23RUTkDTIhcVgMTAuvgighSA7uTVzJzI4ChgOPx5UNN7PS8PlI4DRgmQffeIuA94WrXgbcM6B7kSNqKkq55pyj+L+VW7lj8fruK4iISF6JPHEI+yFcBSwEXgLudPelZna9mcVfJTEfuMMP/xl8NNBoZs8RJArfcPdl4bLPAf9pZisJ+jz8bKD3JVd8YO4RnDqlhq/++SU27jwQdTgiIpJBTKejD2loaPDGxsaow8gI67fv5+3f+wcnTBjOLR+cS3ChioiI5BIzezrsJ5i2yM84SGYaP2Io1557NI+s2MqdjWqyEBGRgBIHSemiuUdwyuQabvjTS2xSk4WIiKDEQbpQUGD8z/tm0eHONb9/QVdZiIiIEgfp2vgRQ7nmnKP4xytN/LZxQ9ThiIhIxJQ4SLcuPmkCJ00awVf+tIzXdqnJQkQknylxkG4VFBjfet9s2juda9VkISKS15Q4SFqOqAmaLB5a3sRvn1aThYhIvlLiIGm75OQJzFWThYhIXlPiIGkLmixm0dbRyefVZCEikpeUOEiPTKgp53PzjmLR8iZ+90yqe5GJiEiuUuIgPXbZKROZO3EE//3Hpby+qznqcEREZBApcZAeiw0M1dbRyefvVpOFiEg+UeIgvTJxZDmffftRPPjyFu7SVRYiInlDiYP02uWnTmTupBF88Z4XeX7DzqjDERGRQaDEQXqtoMC46QPHU1NeyodvaVR/BxGRPKDEQfqktrKUn13ewN7mdj50y2L2t7ZHHZKIiAwgJQ7SZ0eNHsYPPnAcyzbt5j9/8xydneosKSKSq5Q4SL8466g6Pn/u0fxl6et8+6/Low5HREQGSFHUAUjuuOL0Saxq2scPH1rFlNoK3ntCfdQhiYhIP9MZB+k3Zsb15x3DqVNquPb3L7B47faoQxIRkX6mxEH6VXFhAT+86HjGDR/CR259mnXb9kcdkoiI9CMlDtLvqoeW8LPLGujodK745WJ2N7dFHZKIiPQTJQ4yICbXVvCji45nzdZ9XH3bs7R3dEYdkoiI9AMlDjJgTp06kq+cP5OHX2nihj+/FHU4IiLSD3RVhQyoC+cewcote/nZ/61hyqgKLjl5QtQhiYhIHyhxkAH3+XOPZs3WfVx371Im1gzlTdNqow5JRER6SU0VMuAKC4zvX3gc00ZV8JFbn+axVVujDklERHpJiYMMiorSIm754Fzqhw/h8l8s5m/LNkcdkoiI9EJGJA5mNs/MlpvZSjO7Jsny75rZknB6xcx2huVzzOxxM1tqZs+b2fvj6iwwszVx9eYM3h5JMqOGlfGbK0/hqNGVfORXT3PPko1RhyQiIj0UeR8HMysEbgLeCmwAFpvZve6+LLaOu/9H3PpXA8eFs/uBS919hZmNBZ42s4XuvjNc/hl3v2sw9kPSM7y8hF9/6CQ+9MtGPvmbJextaeeik9RhUkQkW2TCGYe5wEp3X+3urcAdwHldrH8hcDuAu7/i7ivC55uALYB63mW4yrJifvnBubzlyFH8190v8uOHV0UdkoiIpCkTEodxwPq4+Q1h2RuY2QRgEvBgkmVzgRIg/lvoq2ETxnfNrDTFNq80s0Yza2xqaurtPkgPlRUX8uOLT+Cds8bwjftf5lsLX8Zdt+MWEcl0mZA49MR84C5374gvNLMxwK3Av7p7bIjCa4GjgBOBEcDnkm3Q3W929wZ3b6it1cmKwVRSVMCN849j/onjuWnRKq67dymdnUoeREQyWeR9HICNwPi4+fqwLJn5wMfjC8xsGPBn4L/c/YlYubu/Fj5tMbNfAJ/ut4il3xQWGF9/z7FUlhXxk0fWsKelnf957yyKCrMtpxURyQ+ZkDgsBqaZ2SSChGE+8IHElczsKGA48HhcWQlwN3BLYidIMxvj7q+ZmQHnAy8O2B5In5gZnz/3aIaVFfOdB15hX0s737/wOEqLCqMOTUREEkT+s87d24GrgIXAS8Cd7r7UzK43s3fHrTofuMMPbwj/F+DNwOVJLrv8tZm9ALwAjARuGOh9kd4zM64+expfftcMFi7dzId+2cj+1vaowxIRkQSmDmmHNDQ0eGNjY9Rh5L3fNq7nc797ntnjq/nxxSdQN6ws6pBERHKSmT3t7g09qRP5GQeRRBc0jOeHFx3Py6/t4ZwbH+HhV3S1i4hIplDiIBlp3swx/PHq06itKOWynz/FN//yMu0dnd1XFBGRAaXEQTLW1FGV3HPVaVw4dzw/emgV829+gk07D0QdlohIXlPiIBmtrLiQr79nFjfOn8NLr+3m3O8/woMv6wZZIiJRUeIgWeG8OeP449WnM7ZqCB9c0MhX/7yMNjVdiIgMOiUOkjUm11bw+4+dyiUnT+Anj6zhgh8/zvrt+6MOS0QkryhxkKxSVlzIV86fyU0fOJ5VW/byju8/wsKlr0cdlohI3lDiIFnpHbPG8Kd/P50JNeV85Nanue7epRxo7ei+ooiI9IkSB8laE2rKuevfTuHyUyey4LG1nP2dh/jz86/pLpsiIgNIiYNktdKiQq579zHc+ZFTqBpawsdve4aLfvokr2zeE3VoIiI5SYmD5IS5k0bwp6tP5yvnHcPSTbs558ZHuP6Py9jd3BZ1aCIiOUWJg+SMwgLjklMmsujTZ/L+E8fzi8fWcNa3H+LOxvV0dqr5QkSkPyhxkJwzoryEr/3zsdz78dM5YsRQPnvX87znR4/x3PqdUYcmIpL1lDhIzjq2voq7Pnoq37lgNht2HOD8Hz7K5+56nm17W6IOTUQkaxVFHYDIQCooMN57Qj1vO6aOG/+2ggWPreW+F1/jitMncdkpExleXhJ1iCIiWcV06dohDQ0N3tjYGHUYMoBWbtnDN+5/mb+9tIUhxYVcOPcIPvSmSYytHhJ1aCIig87Mnnb3hh7VUeJwiBKH/LH89T3878OruOe5TRQYnD9nHB85YwpTR1VEHZqIyKBR4tBHShzyz/rt+/nZ/63hjsXraGnv5G0z6vi3M6cyZ3x11KGJiAw4JQ59pMQhf23b28IvH1vLgsfWsru5nVMm1/BvZ07hTdNGYmZRhyciMiCUOPSREgfZ29LOHU+t4yePrGbz7haOGTuMy06dyLnHjqGiVH2JRSS3KHHoIyUOEtPS3sE9z27if/+xilVN+xhSXMi8maN53wn1nDK5hoICnYUQkeynxKGPlDhIInfnmXU7+d0zG/jjc5vY09zO2Koy/vn4cbz3+Hom16ozpYhkLyUOfaTEQbrS3NbBA8s287tnNvCPV5rodDj+iGree0I975w1lqohxVGHKCLSI0oc+kiJg6Rr8+5m/vDsRu56egMrtuylpKiAt82o412zx3L61JGUqz+EiGQBJQ59pMRBesrdeWHjLu56egP3PreJnfvbKCkq4OTJNZx91CjOOmoU40cMjTpMEZGklDj0kRIH6YvW9k4a127n7y9v4e8vbWbttv0ATK+r4Kyj6jj76FEcN76aokLdIkZEMoMShz5S4iD9aXXTXh58eQt/f2kLi9dup73TqR5azJnTaznr6DrePG0k1UN1rwwRiU7WJg5mNg+4ESgEfuru30hY/l3gLeHsUGCUu1eHyy4DvhAuu8HdfxmWnwAsAIYA9wGf8G52VomDDJRdB9p4ZEUTD768hYeWN7F9XysAR9ZV0jBxOHMnjaBh4gjG6Z4ZIjKIsjJxMLNC4BXgrcAGYDFwobsvS7H+1cBx7v5BMxsBNAINgANPAye4+w4zewr4d+BJgsTh++5+f1exKHGQwdDR6SxZv4PHVm5j8as7eObVHextaQdgXPUQGiYO58SJIzhx4gimjarQmBEiMmB6kzhkQtfvucBKd18NYGZ3AOcBSRMH4ELgy+HztwMPuPv2sO4DwDwzewgY5u5PhOW3AOcDXSYOIoOhsMA4YcIITpgwAoD2jk5efn0Pi9dup3HtDh5btY17lmwCoGpIMQ0ThnP8hOEcM3YYx4ytorayNMrwRSTPZULiMA5YHze/ATgp2YpmNgGYBDzYRd1x4bQhSblIxikqLGDmuCpmjqviX0+bhLuzbvt+Fq/dweI121n8atDhMqa2spQZY4YxY+wwjhk7jBljhjGxplxnJkRkUGRC4tAT84G73L2jvzZoZlcCVwIcccQR/bVZkV4zMybUlDOhppz3nVAPwK79bSx7bXcwbdrN0k27eHTlVto7g6bGoSWFHDW6kmPGVnHUmEqm1FYwubac2opS3aRLRPpVJiQOG4HxcfP1YVky84GPJ9Q9M6HuQ2F5fTrbdPebgZsh6OOQftgig6dqaDGnTKnhlCk1B8ta2jtYsXnvwWRi2abd3P3sRvY+0X5wncrSIibVljN5ZDmTayuYNLKcybXlTBpZztCSTPj3F5FskwmfHIuBaWY2ieDLfT7wgcSVzOwoYDjweFzxQuBrZjY8nH8bcK27bzez3WZ2MkHnyEuBHwzgPogMutKiwoNNHDGdnc7GnQdYvXUfa5r2Bo9b97F47Q7+EPabiBlTVcakkeXUDx/CuOqhjBs+hHHVQ6gfPoTRVWUUa7wJEUki8sTB3dvN7CqCJKAQ+Lm7LzWz64FGd783XHU+cEf8JZVhgvAVguQD4PpYR0ngYxy6HPN+1DFS8kBBgTF+xFDGjxjKGdNrD1t2oLWDtduCRGJ1XFLx0PImtuxpOWxdM6irLDuYTIwbPoSx1UMYPayM2spSRlWWMrKilJIiJRci+SbyyzEziS7HlHzV0t7Bazub2bjzABt3HGBD+Lhx53427WzmtV0HaOt442fFiPISaitKGTWslNrK0jCpKGNUZSk1FSWMKC9h+NASqocWU1pUGMGeiUhXsvVyTBGJWGlRIRNHljNxZHnS5R2dTtOeFrbsaWbL7ha2hM+DsmBa3bSPLXuakyYYABWlRQwvL2bE0BKqhx5KKkaUF1M1tIRhZUUMG1LMsLJiqoYUMaysmMqyYsqKC9TBUySDKHEQkW4VFhijq8oYXVXW5Xruzs79bWzZ08L2fa3s2N8aPO5rZfv+VnbubztYvqppLzv2tbKvteuLpIoLjWFlxWFSUURlWTFDSwqpKC2iPDaVFFJeWkRFaRFDS+OelxQytKSIIcWFwVRSSHGhKRER6QMlDiLSb8yM4eUlDC9P/x4cLe0d7DrQxu4D7exubmNPczu7D7Sxu/lQWTDfzp7w+da9LextaWdfSzv7Wjpo7ehM+/UKC4whxYWUFRcypKSAocVFlJUUMqS4gNKiQsrCx9KiAkqLCygrKqQ0rqysOHgsKSqguDB4LIk9xsoSyosLjaLC4LG4sICiAiUvkr2UOIhIpEqLChlVWcioyt5vo7W9k/2t7WEy0XEwqdjf2s6Btg4OtHZyoK2D5raOoCxu/kBrB/vbOmhu7WDn/lZa2jtpbuugpb0zmNo6aG7vpKOzf/uDFRcaRQUFFBUaJYXBY3FhkHgUFhhFBRY8holGYYFRXGgUFgTzsbLDJuu6rMCMgoNlQWfaAgvmg/K4sgKjwIJkMFhOUP/gdGjdAguWWbh+/HyBGUZsXYBD2y0wMGL1gucFBeFjWAaHb8cS6yQrD6odNh9L1OLX5eDrBhK3BbEYOPg8vjyxXvz6uZwYKnEQkawX/NovGdC7jbZ3dB5MJprbOmjr6KQ1nI89b+3oTCh3WsPlbR2dtHc6be2dtHU67R2xcg+WxR47nY7O4HlHpx8239LWSXtnB+2dwfodnU6Hh49xU6cfqpdY3s/5j6TpYELB4UlM4vKg/LCZtNeNlR85upK7P3Zan2NORVdVxDGzPcDyqOMYQCOBrVEHMUByed9A+5fttH/ZK5f3DeBId+/R+T6dcTjc8p5elpJNzKwxV/cvl/cNtH/ZTvuXvXJ53yDYv57W0egtIiIikjYlDiIiIpI2JQ6HuznqAAZYLu9fLu8baP+ynfYve+XyvkEv9k+dI0VERCRtOuMgIiIiaVPiAJjZPDNbbmYrzeyaqOPpb2a21sxeMLMlvelBm2nM7OdmtsXMXowrG2FmD5jZivBxeFfbyGQp9u86M9sYHsMlZnZulDH2lpmNN7NFZrbMzJaa2SfC8pw4fl3sX64cvzIze8rMngv377/D8klm9mT4GfobMxu4ATUGUBf7t8DM1sQdvzkRh9prZlZoZs+a2Z/C+R4fu7xPHMysELgJOAeYAVxoZjOijWpAvMXd5+TIZUULgHkJZdcAf3f3acDfw/lstYA37h/Ad8NjOMfd7xvkmPpLO/Apd58BnAx8PPx/y5Xjl2r/IDeOXwtwlrvPBuYA88zsZOCbBPs3FdgBXBFdiH2Sav8APhN3/JZEFWA/+ATwUtx8j49d3icOwFxgpbuvdvdW4A7gvIhjki64+z+A7QnF5wG/DJ//Ejh/MGPqTyn2Lye4+2vu/kz4fA/BB9g4cuT4dbF/OcEDe8PZ4nBy4CzgrrA8m49fqv3LCWZWD7wD+Gk4b/Ti2ClxCP6p18fNbyCH/tFDDvzVzJ42syujDmaA1Ln7a+Hz14G6KIMZIFeZ2fNhU0ZWnsqPZ2YTgeOAJ8nB45ewf5Ajxy881b0E2AI8AKwCdrp7e7hKVn+GJu6fu8eO31fD4/ddMyuNLsI++R7wWSB2V7gaenHslDjkh9Pd/XiC5piPm9mbow5oIHlwqVDO/EoI/QiYQnD69DXgO5FG00dmVgH8Dviku++OX5YLxy/J/uXM8XP3DnefA9QTnLE9KtqI+lfi/pnZTOBagv08ERgBfC66CHvHzN4JbHH3p/u6LSUOsBEYHzdfH5blDHffGD5uAe4m+GfPNZvNbAxA+Lgl4nj6lbtvDj/QOoGfkMXH0MyKCb5Uf+3uvw+Lc+b4Jdu/XDp+Me6+E1gEnAJUm1nsFgY58Rkat3/zwiYod/cW4Bdk5/E7DXi3ma0laJI/C7iRXhw7JQ6wGJgW9iwtAeYD90YcU78xs3Izq4w9B94GvNh1rax0L3BZ+Pwy4J4IY+l3sS/V0D+TpccwbFP9GfCSu/+/uEU5cfxS7V8OHb9aM6sOnw8B3krQj2MR8L5wtWw+fsn27+W4pNYI+gBk3fFz92vdvd7dJxJ8zz3o7hfRi2OnAaCA8NKo7wGFwM/d/avRRtR/zGwywVkGCG5qdlu275+Z3Q6cSXDXus3Al4E/AHcCRwCvAv/i7lnZwTDF/p1JcJrbgbXAR+L6BGQNMzsdeAR4gUPtrJ8n6AeQ9cevi/27kNw4frMIOtAVEvzwvNPdrw8/Z+4gOI3/LHBx+Os8q3Sxfw8CtQR3t14CfDSuE2XWMbMzgU+7+zt7c+yUOIiIiEja1FQhIiIiaVPiICIiImlT4iAiIiJpU+IgIiIiaVPiICIiImlT4iCSYyy4G6qHl1zlLDObGO7n2qhjEcknShxE8kB4W2c3s+uijiVdZvZQPiRAItmmqPtVREQy0kbgaKAt6kBE8okSBxHJSu7eBrwcdRwi+UZNFSI5zsycYNhqgC+Hp/89WdNFeG+Tz5rZYjPbbWYHzGxp2NRRkWTbB5tAzGyCmf3CzDaYWbuZfS9cp9jMLjGz281suZntMbP9ZrbMzL5pZiMStnlmGPMZYdGihJjPDNfrso9DGM8PzWy1mbWY2Q4zW2RmH0ixfvy+1JnZ/4b70mJma8zsG2ZWlubbLpKzdMZBJPf9kuA+CbOB5wjG2o85+NzM6oGFwAygCXgcaCa4lfCXgX82szPdfUeS15hGMM59M/AowWfLznBZHXALsIPgDMESYBjQAHwWeJ+ZneTuW8P1Xw9jnhfWXRiWEbe8S2Z2MnA/UA2sIbhfywiCe36caWbzgMs8+Zj744GnCe5L8FgY6+kEt1KeAby7u9cXyWnurkmTphyaCG6i5MCZcWXXhWXXpagT+5J04AfAkLhlQ4Bbw2ULEurFtusEtxsuSbLtSuBdQHFC+RDg52HdHyWp91DifiQsnxguX5tQXgasC5d9FyiMWzaT4MZhTnCjqVT78pP4fSHoS7EnXHZa1MdYk6YoJzVViAgEv+5PAZ4APuHuB2ILwucfBbYAF5nZ8CT1twH/7u6tiQvcfY+7/9GDPgnx5QeAq4B24L39tidwAcFZg7XAZ929I+41X+RQs82nU9RfT8K+uPtLBMkTwNn9GKtI1lFThYgAnBs+/s7dOxMXuvs+M2sM1zsR+GvCKn9z9z1dvYCZHUfwpTsRKCc4ywHQCtSa2XBP3gzSU7G+EbclJiuhBcAPgalmNs7dNyYsfzA+cYoT64g5th9iFMlaShxEBGBy+PgtM/tWN+vWJil7NdXKYafKX9N934BhBP0g+mpc+Lgm2UJ3bzazTeF64wgu64y3LsV2d4eP6iApeU2Jg4gAFIaPDxOc4u9KsiQh2S/0mK8TJA3LgGuARmBr7GxA+CU+hkNnIPpLso6P6XjDGRcROUSJg4hA0K4P8Ft3v6mft31B+Pj+sI/BQWZWDozu59eLnUGYnGxheEnl2IR1RSRN6hwpkh9iHf1S/Vi4P3y8IMXyvoiN07A+ybIPkPpMQ3cxp/Jw+HihmSWre1n4miuT9G8QkW4ocRDJD7EvyKNTLP8DwdgFZ5jZjxMHZQIws9Fm9uFevHasU+HHErbXQNCMkUp3MafyW4IkZRLwdTM7+DlnZjOA/w5nv93D7YoIaqoQyRcLgf3Ae8zsH8AqoAO4193vdfdOMzsfuA/4CPABM3uO4Au4DJhOMPjRFoIxDnrieoIv86+Z2fuBlwiaCk4H7gBOAyYkqXc3cDlBh823hq8N8C13X57qxcLOj/9CcBbl0wQDVy0mOPPxFqCY4NLKm3u4HyKCzjiI5AV3fx14J8GgSrMITtdfARwft84GYC7B2ArPAscA7yMY36EZ+A7wnl689l0EX9iLCMZXeBfBFRSfBC7pot69BGcpXgb+KYz3CoKOlN295hMEo2X+mKDj53uAkwhGw7yY1KNGikg3TP87IiIiki6dcRAREZG0KXEQERGRtClxEBERkbQpcRAREZG0KXEQERGRtClxEBERkbQpcRAREZG0KXEQERGRtClxEBERkbQpcRAREZG0/f9KgPUf+cLfAgAAAABJRU5ErkJggg==\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig = plt.figure(figsize=(8,6))\\n\",\n \"plt.plot(vfe_hist)\\n\",\n \"plt.ylabel('$\\\\\\\\mathcal{F}$', fontsize = 22)\\n\",\n \"plt.xlabel(\\\"Iteration\\\", fontsize = 22)\\n\",\n \"plt.xlim(0, n_iter)\\n\",\n \"plt.ylim(vfe_hist[-1], vfe_hist[0])\\n\",\n \"plt.title('Gradient descent on VFE', fontsize = 24)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 17,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$\\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln \\\\frac{Q(s)}{P(o, s)}] = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(o, s)]:$\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Initial F = 0.916\\n\",\n \"==================\\n\",\n \"Final posterior:\\n\",\n \"[0.8 0.2]\\n\",\n \"==================\\n\",\n \"Final F = 0.693\\n\",\n \"==================\\n\"\n ]\n }\n ],\n \"source\": [\n \"final_qs, initial_F, final_F = qs_hist[-1,:], vfe_hist[0], vfe_hist[-1]\\n\",\n \"\\n\",\n \"display(Latex('$\\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln \\\\\\\\frac{Q(s)}{P(o, s)}] = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(o, s)]:$'))\\n\",\n \"print(f'Initial F = {initial_F.round(3)}')\\n\",\n \"print('==================')\\n\",\n \"\\n\",\n \"print('Final posterior:')\\n\",\n \"print(f'{final_qs.round(1)}') # note that because of numerical imprecision in the gradient descent (constant learning rate, etc.), the approximate posterior will not exactly be the optimal posterior\\n\",\n \"print('==================')\\n\",\n \"print(f'Final F = {vfe_qs(final_qs).round(3)}')\\n\",\n \"print('==================')\\n\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3.7.10 ('pymdp_env')\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.8.8\"\n },\n \"vscode\": {\n \"interpreter\": {\n \"hash\": \"43ee964e2ad3601b7244370fb08e7f23a81bd2f0e3c87ee41227da88c57ff102\"\n }\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "docs/notebooks/pymdp_fundamentals.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"6DSxgksDRLXj\"\n },\n \"source\": [\n \"# ``pymdp`` Fundamentals\\n\",\n \"\\n\",\n \"[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/infer-actively/pymdp/blob/main/docs/notebooks/pymdp_fundamentals.ipynb)\\n\",\n \"\\n\",\n \"*Author: Conor Heins*\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"*Note*: When running this notebook in Google Colab, you may have to run `!pip install inferactively-pymdp` at the top of the notebook, before you can `import pymdp`. That cell is left commented out below, in case you are running this notebook from Google Colab.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# ! pip install inferactively-pymdp\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"rKfJtPWBR4tn\"\n },\n \"source\": [\n \"## *Very brief* `pymdp` and active inference background\\n\",\n \"\\n\",\n \"`pymdp` is a Python library, written primarily in [NumPy](https://numpy.org/), for solving **P**artially-**O**bserved **M**arkov **D**ecision *P*rocesses (POMDPs) using active inference, a modelling framework for perception, learning and action, originally derived from the Free Energy Principle. POMDP models have traditionally been used in disciplines ranging from control theory and robotics, to biological fields concerned with empirically modelling human and animal behavior. \\n\",\n \"\\n\",\n \"For a theoretical overview of active inference and the motivations for developing this package, please see our companion paper: [\\\"pymdp: A Python library for active inference in discrete state spaces\\\"](https://arxiv.org/abs/2201.03904).\\n\",\n \"\\n\",\n \"More in-depth coverage of applying active inference to POMDPs can be found in the following two papers: [*Active Inference: A Process Theory*](https://direct.mit.edu/neco/article-abstract/29/1/1/8207/Active-Inference-A-Process-Theory) and [*Active Inference in Discrete State Spaces: A Synthesis*](https://www.sciencedirect.com/science/article/pii/S0022249620300857)\\n\",\n \"\\n\",\n \"Below are links to a few useful papers, talks, and blog posts that concern active inference and the free energy principle more broadly:\\n\",\n \"\\n\",\n \"* Blog post: [Tutorial on Active Inference](https://medium.com/@solopchuk/tutorial-on-active-inference-30edcf50f5dc) by Oleg Solopchuk\\n\",\n \"* Talk: [The variational foundations of movement](https://www.youtube.com/watch?v=zWFfZHqOnvM) by Karl Friston\\n\",\n \"* Podcast: [Karl Friston: Neuroscience and the Free Energy Principle](https://www.youtube.com/watch?v=NwzuibY5kUs) hosted on Lex Fridman Podcast #99\\n\",\n \"* Paper: [*A tutorial on the free-energy framework for modelling perception and learning*](https://www.sciencedirect.com/science/article/pii/S0022249615000759) by Rafal Bogacz\\n\",\n \"* Paper: [*The free energy principle for action and perception: A mathematical review*](https://www.sciencedirect.com/science/article/pii/S0022249617300962) by Christopher Buckley, Chang Sub Kim, Simon McGregor, and Anil Seth\\n\",\n \"* Paper: [*A free energy principle for the brain*](https://www.fil.ion.ucl.ac.uk/~karl/A%20free%20energy%20principle%20for%20the%20brain.pdf) by Karl Friston\\n\",\n \"* Paper: [*A Step-by-Step Tutorial on Active Inference and its Application to Empirical Data*](https://psyarxiv.com/b4jm6/) by Ryan Smith and Christopher Whyte\\n\",\n \"\\n\",\n \"Also see [Jared Tumiel's blog post](https://jaredtumiel.github.io/blog/2020/10/14/spinning-up-in-ai.html) and [Beren Millidge's github repository](https://github.com/BerenMillidge/FEP_Active_Inference_Papers) for more literature and pedagogical materials related to active inference and the free energy principle.\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"nty3Vm6YZR-X\"\n },\n \"source\": [\n \"## Data structures in `pymdp`\\n\",\n \"\\n\",\n \"In this tutorial notebook we'll be walking through the core functionalities and data structures used by `pymdp`, most of which will be easy to grasp for anyone who's familiar with array programming in `numpy` or even MATLAB, where much of the existing code related to active inference currently exists.\\n\",\n \"\\n\",\n \"We'll start by running through a full usage example of quickly building and running a random active inference agent in `pymdp`.\\n\",\n \"\\n\",\n \"In the interest of focusing on data structures and syntax, we'll just initialize the agent to have a random POMDP generative model -- we don't need to analogize this generative model to any hypothetical task environment that our agent will be behaving within. The agent will just have random beliefs about how the world evolves and how it gives rise to observations. The focus here is on how we store these objects (e.g. components of the generative model) in `pymdp`.\\n\",\n \"\\n\",\n \"For more in-depth tutorials that actually work through full, tutorial-style examples of building active inference agents and running them, please see the [Active inference from scratch](https://pymdp-rtd.readthedocs.io/en/latest/notebooks/active_inference_from_scratch.html) tutorial and [Using the agent class](https://pymdp-rtd.readthedocs.io/en/latest/notebooks/using_the_agent_class.html) tutorial. \\n\",\n \"\\n\",\n \"Other examples in the Examples section (e.g. the [T-Maze demo](https://pymdp-rtd.readthedocs.io/en/latest/notebooks/tmaze_demo.html) or the [Epistemic chaining demo](https://pymdp-rtd.readthedocs.io/en/latest/notebooks/cue_chaining_demo.html) provide walk-throughs of building active inference agents in particular task environments.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {\n \"id\": \"oDMlGXnQRuQv\"\n },\n \"outputs\": [],\n \"source\": [\n \"\\\"\\\"\\\" Quickly build a random active inference agent, give it an observation and have it do hidden state and policy inference \\\"\\\"\\\"\\n\",\n \"\\n\",\n \"from pymdp import utils\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"\\n\",\n \"num_obs = [3, 5] # observation modality dimensions\\n\",\n \"num_states = [4, 2, 3] # hidden state factor dimensions\\n\",\n \"num_controls = [4, 1, 1] # control state factor dimensions\\n\",\n \"A_array = utils.random_A_matrix(num_obs, num_states) # create sensory likelihood (A matrix)\\n\",\n \"B_array = utils.random_B_matrix(num_states, num_controls) # create transition likelihood (B matrix)\\n\",\n \"\\n\",\n \"C_vector = utils.obj_array_uniform(num_obs) # uniform preferences\\n\",\n \"\\n\",\n \"# instantiate a quick agent using your A, B and C arrays\\n\",\n \"my_agent = Agent( A = A_array, B = B_array, C = C_vector)\\n\",\n \"\\n\",\n \"# give the agent a random observation and get the optimized posterior beliefs\\n\",\n \"\\n\",\n \"observation = [1, 4] # a list specifying the indices of the observation, for each observation modality\\n\",\n \"\\n\",\n \"qs = my_agent.infer_states(observation) # get posterior over hidden states (a multi-factor belief)\\n\",\n \"\\n\",\n \"# Do active inference\\n\",\n \"\\n\",\n \"q_pi, neg_efe = my_agent.infer_policies() # return the policy posterior and return (negative) expected free energies of each policy as well\\n\",\n \"\\n\",\n \"action = my_agent.sample_action() # sample an action from the posterior over policies\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"MHIrFUuuarIA\"\n },\n \"source\": [\n \"## `numpy` object arrays \\n\",\n \"\\n\",\n \"In `pymdp`, both generative model distributions (e.g. `A` or `B`) as well as posterior distributions over hidden states (e.g. `qs`) and observations are represented as what we call \\\"object arrays\\\". Note that other conventions may refer to these arrays as \\\"arrays-of-arrays\\\", \\\"nested arrays\\\", or \\\"ragged/jagged arrays.\\\"\\n\",\n \"\\n\",\n \"Object arrays differ from more \\\"classical\\\" `numpy.ndarrays` that have numerical (e.g. `np.float64`) data types. The typical `numpy.ndarray` of float or integer data type, can only have scalar values as its entries. Object arrays (`numpy.ndarray` with `dtype = object`) however, do not have this restriction. Their array elements can be arbitrary Python data structures or objects. The entries of an object array can thus have arbitrary type and dimensionality.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"\\n\",\n \"### Deeper dive on object arrays\\n\",\n \"\\n\",\n \"Object arrays can be initialized standard `numpy` constructors, but by also explicitly declaring `dtype = object`. \\n\",\n \"\\n\",\n \"```\\n\",\n \"my_empty_array = np.empty(5, dtype = object)\\n\",\n \"```\\n\",\n \"\\n\",\n \"The `pymdp.utils` module provides a set of functions in that allow you to quickly construct, convert between, and perform mathematical operations on these object arrays. Fundamentally underpinning these `utils` operations is the assumption that the elements of the input object array are `numpy.ndarrays` with numerical data type. In other words, we simply use object arrays to store collections of multi-dimensional arrays or standard `numpy.ndarrays`. This construction is chosen to allow `pymdp` to easily perform probabilistic computations on collections of multi-dimensional arrays, where each constituent array within the collection represents a particular factor or marginal distribution within a factorized representation. In the next section we'll get into why this constructino is useful and how it's mathematically motivated.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Constructing factorized distributions with object arrays\\n\",\n \"\\n\",\n \"\\n\",\n \"For example, let's imagine a joint categorical probability distribution over some variable $\\\\mathbf{s}$ that factorizes into the product of a set of 3 marginal (i.e. univariate) distributions. Mathematically, we can express that factorization as:\\n\",\n \"\\n\",\n \"\\n\",\n \"$$\\n\",\n \" P(\\\\mathbf{s}) = \\\\prod_i^3 P(s_i)\\n\",\n \"$$\\n\",\n \"\\n\",\n \"\\n\",\n \"In `pymdp`, instead of encoding this distribution as the fully-enumerated product of marginals $P(\\\\mathbf{s}) = P(s_1) \\\\times P(s_2) \\\\times P(s_3)$, we instead exploit the factorization and *only store* the separate marginals $P(s_i)$ of the full distribution. Specifically, we store each marginal as a single `numpy.ndarray` of `ndim == 1` (i.e. a row vector) in a different entry of a `numpy.ndarray` of `dtype` object. The object array representation be easily constructed and manipulated using `utils` functions.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {\n \"id\": \"naD3NKPjbeMg\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[0.13370366 0.86629634]\\n\"\n ]\n }\n ],\n \"source\": [\n \"num_factors = 3 # we have 3 factors total\\n\",\n \"\\n\",\n \"dim_of_each_factor = [2, 2, 4] # factor 1 has 2 levels, factor 2 has 2 levels, factor 4 has 4 levels\\n\",\n \"\\n\",\n \"P_s = utils.random_single_categorical(dim_of_each_factor)\\n\",\n \"\\n\",\n \"print(P_s[0])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"IPTjskqrfi0j\"\n },\n \"source\": [\n \"Here we used the utility function `random_single_categorical(shape_list)` to create a random collection of marginal categorical distributions, representing the different factorized components of the full distribution $P(\\\\mathbf{s})$. \\n\",\n \"\\n\",\n \"Each of these marginal categorical distributions is stored in an according entry of the object array `P_s`.\\n\",\n \"\\n\",\n \"This representation is advantageous for several reasons, but one of the main advantages is sparsity / memory overhead. If we had to store the entire joint distribution $P(\\\\mathbf{s})$ as a product of all the marginals, we could either store that as a single 1D categorical distribution with `2 * 2 * 4` different levels (the combinatorics of all the hidden state dimensionalities), or as a multi-dimensional array with size `(2, 2, 4)`, where each entry of the joint `Ps[i,j,k]` stores the joint probability of $P(s^1 = i, s^2 = j, s^3 = k)$. Either way, we'd have to store polynomially more values $2 \\\\times 2 \\\\times 4$ is twice the size of $2 + 2 + 4$. But since we know that the marginals are by construction independent, we can just store them separately without losing any information.\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"HRxPg3VVj4-g\"\n },\n \"source\": [\n \"*Side note*: Here's an alternative way to generate multi-factor categorical distributions. \\n\",\n \"\\n\",\n \"if you knew what your factors were to begin with, and you wanted to construct the full distribution from the factors, you could use another utility function to build the object array from a `list` of the factorized distributions.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {\n \"id\": \"Gtr7VPjlhxIl\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[0.5 0.16666667 0.16666667 0.16666667]\\n\"\n ]\n }\n ],\n \"source\": [\n \"import numpy as np\\n\",\n \"\\n\",\n \"ps1 = np.array([0.5, 0.5])\\n\",\n \"ps2 = np.array([0.75, 0.25])\\n\",\n \"ps3 = np.array([0.5, 1./6., 1./6., 1./6.])\\n\",\n \"\\n\",\n \"P_s = utils.obj_array_from_list([ps1, ps2, ps3])\\n\",\n \"\\n\",\n \"print(P_s[2])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Object arrays and conditional distributions\\n\",\n \"\\n\",\n \"Understanding the representation of factorized probability distributions as object arrays is critical for understanding and constructing generative models in `pymdp`. This object array representation applies not only to multi-factor, unconditional categorical distributions (like the example above: a joint categorical distribution being factorized into a product of univariate marginals), but also is used to represent collections of *conditional* categorical distributions.\\n\",\n \"\\n\",\n \"In particular, we use object arrays to encode the observation and transition models (also known as the observation likelihood and transition likelihood) of the agent's generative model. Object arrays are necessary in this case, due to the convention of factorizing the observation space into multiple **observation modalities** and the hidden states into multiple **hidden state factors**. Mathematically, this can be expressed as follows:\\n\",\n \"\\n\",\n \"$$ \\n\",\n \"\\\\mathbf{o}_t = \\\\prod_{i = 1}^{M} \\\\delta_{O_i}(o^{i}_t) \\\\hspace{15 mm} \\\\mathbf{s}_t = \\\\prod_{i = 1}^{F} \\\\delta_{S_i}(s^{i}_t) \\\\\\\\\\n\",\n \"$$\\n\",\n \"\\n\",\n \"where any particular observation $\\\\mathbf{o}_t$ is actually factorized into a product of Dirac delta functions over different modality-specific observations $o^m_t$, i.e. \\\"one-hot\\\" vectors or unit vectors in $\\\\mathbb{R}^{O_m}$. The same factorization applies to multi-factorial hidden states $\\\\mathbf{s}_t$. The notation $\\\\delta_{X_i}(x^{i})$ denotes a Dirac delta function with discrete support $X_i$ evaluated at point $x^i$. \\n\",\n \"\\n\",\n \"This factorization of observations across modalities and hidden states across hidden state factors, carries forward into the specification of the `A` and `B` arrays, the representation of the conditional distributions $P(\\\\mathbf{o}_t|\\\\mathbf{s}_t)$ and $P(\\\\mathbf{s}_t|\\\\mathbf{s}_{t-1}, \\\\mathbf{u}_{t-1})$ in `pymdp`. These two arrays of conditional distributions can also be factorized by modality and factor, respectively.\\n\",\n \"\\n\",\n \"The `A` array, for instance, contains the agent's observation model, that relates hidden states $\\\\mathbf{s}_t$ to observations $\\\\mathbf{o}_t$:\\n\",\n \"\\n\",\n \"$$\\n\",\n \"\\\\mathbf{A} = \\\\{A^1, A^2, ..., A^M \\\\}, \\\\hspace{5mm} A^m = P(o^m_t | s^1_t, s^2_t, ..., s^F_t)\\n\",\n \"$$\\n\",\n \"\\n\",\n \"Therefore, we represent the `A` array as an object array whose constituent arrays are multidimensional `numpy.ndarrays` that encode conjunctive relationships between combinations of hidden states and observations.\\n\",\n \"\\n\",\n \"This is best explained using the example in the original example code at the top of this tutorial. It is custom to build lists of the dimensionalities of the modalities (resp. hidden state factors) of your model, typically using lists named `num_obs` (for the dimensionalities of the observation modalities) and `num_states` (dimensionalities of the hidden state factors). These lists can then be used to automatically construct the `A` array with the correct shape.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Dimensionality of A array for modality 1: (3, 4, 2, 3)\\n\",\n \"Dimensionality of A array for modality 2: (5, 4, 2, 3)\\n\"\n ]\n }\n ],\n \"source\": [\n \"num_obs = [3, 5] # observation modality dimensions\\n\",\n \"num_states = [4, 2, 3] # hidden state factor dimensions\\n\",\n \"\\n\",\n \"A_array = utils.random_A_matrix(num_obs, num_states) # create sensory likelihood (A array)\\n\",\n \"\\n\",\n \"for m, _ in enumerate(num_obs):\\n\",\n \" print(f'Dimensionality of A array for modality {m + 1}: {A_array[m].shape}')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For example, `A_array[0]` stores the conditional relationships between the hidden states $\\\\mathbf{s}$ and observations within the first modality $o^1_t$, which has dimensionality `3`. This explains why the `shape` of `A_array[0]` is `(3, 4, 2, 3)` -- it stores the conditional relationships between each setting of the hidden state factors (which have dimensionalities `[4, 2, 3]`) and the observations within the first modality, which has dimensionality `3`. Crucially, each sub-array `A[m]` stores the conditional dependencies between *all* the hidden state factor combinations (configurations of $s^1, s^2, ..., s^F$) and the observations along modality `m`.\\n\",\n \"\\n\",\n \"In this case, we used the `pymdp.utils` function `random_A_matrix()` to generate a random `A` array, but in most cases users will want to design their own bespoke observation models (or at least initialize them to some reasonable starting values). In such a scenario, the usual route is to initialize the `A` array to a series of identically-valued multidimensional arrays (e.g. arrays filled with 0's or uniform values), and then fill out the conditional probability entries \\\"by hand\\\", according to the task the user is interested in modelling.\\n\",\n \"\\n\",\n \"For this purpose, utility functions like `obj_array_zeros` and `obj_array_uniform` come in handy. These functions takes as inputs list of shapes, where each shape contains the dimensionality (e.g. `[2, 3, 4]`) of one of the multi-dimensional arrays that will populate the final object array. For example, creating this shape list for the `A` array, given `num_obs` and `num_states` is quite straightforward:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"A_shapes = [[o_dim] + num_states for o_dim in num_obs]\\n\",\n \"\\n\",\n \"# initialize the A array to all 0's\\n\",\n \"empty_A = utils.obj_array_zeros(A_shapes)\\n\",\n \"\\n\",\n \"# initialize the A array to uniform distributions as columns\\n\",\n \"# uniform_A = utils.obj_array_uniform(A_shapes)\\n\",\n \"\\n\",\n \"# then fill out your A matrix elements as appropriate, depending on the task\\n\",\n \"# empty_A[0][:,0,1,2] = np.array([0.7, 0.15, 0.15])\\n\",\n \"# empty_A[0][:,...] = ....\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Similarly, we can create `B` arrays that encode the temporal dependencies between the hidden state factors over time, further conditioned on control factors (or state factors that correspond to action-states). Mathematically, the `B` arrays are expressed as follows:\\n\",\n \"\\n\",\n \"$$\\n\",\n \"\\\\mathbf{B} = \\\\{B^1, B^2, ..., B^F \\\\}, \\\\hspace{5mm} B^f = P(s^f_t | s^f_{t-1}, u^f_{t-1})\\n\",\n \"$$\\n\",\n \"\\n\",\n \"where $u^f_{t-1}$ denotes the control state for control factor $f$, taken at time $t-1$.\\n\",\n \"\\n\",\n \"We can construct these matrices this by introducing an additional list `num_controls` that stores the dimensionalities of each control factor, which in combination with `num_states` can be used to specify the `B` array.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Dimensionality of B array for hidden state factor 1: (4, 4, 4)\\n\",\n \"Dimensionality of B array for hidden state factor 2: (2, 2, 1)\\n\",\n \"Dimensionality of B array for hidden state factor 3: (3, 3, 1)\\n\"\n ]\n }\n ],\n \"source\": [\n \"num_states = [4, 2, 3] # hidden state factor dimensions\\n\",\n \"num_controls = [4, 1, 1] # control state factor dimensions\\n\",\n \"\\n\",\n \"B_array = utils.random_B_matrix(num_states, num_controls) # create transition likelihood (B matrix)\\n\",\n \"\\n\",\n \"for f, _ in enumerate(num_states):\\n\",\n \" print(f'Dimensionality of B array for hidden state factor {f + 1}: {B_array[f].shape}')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"As we can see here, each factor-specific `B` array (e.g. `B[2]`) has shape `(num_states[f], num_states[f], num_controls[f])`, encoding the conditional dependencies between states for a given factor `f` at subsequent timepoints, further conditioned on actions or control states along that factor. This construction means that hidden state factors are statistically independent of one another -- i.e. hidden state factor `f` is only affected by its own state at the previous timestep, as well as the state of the `f`-th control factor.\\n\",\n \"\\n\",\n \"And of course, as with the `A` array, we can also pre-allocate our `B` arrays to have the correct shape and then fill them out by hand, using the following template:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"B_shapes = [[s_dim, s_dim, num_controls[f]] for f, s_dim in enumerate(num_states)]\\n\",\n \"\\n\",\n \"# initialize the B array to all 0's\\n\",\n \"empty_B = utils.obj_array_zeros(B_shapes)\\n\",\n \"\\n\",\n \"# initialize the B array to uniform distributions as columns\\n\",\n \"# uniform_B = utils.obj_array_uniform(B_shapes)\\n\",\n \"\\n\",\n \"# then assign your B matrix elements as appropriate, depending on the task\\n\",\n \"# empty_B[0][0,:,0] = 1.\\n\",\n \"# empty_B[0][1,:,1] = 1.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Handy functions for dealing with object arrays.\\n\",\n \"\\n\",\n \"The `utils` library is also equipped with a set of handy functions for dealing with object arrays -- this includes operations like normalization and sampling. \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Normalization\\n\",\n \"\\n\",\n \"For instance, let's imagine you generated an `A` array by hand with the following structure:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"num_obs = [3]\\n\",\n \"\\n\",\n \"num_states = [3, 2]\\n\",\n \"\\n\",\n \"A_array = utils.obj_array(len(num_obs)) # create an empty object array with as many elements as there are observation modalities (here, only 1 modality)\\n\",\n \"\\n\",\n \"A_array[0] = np.zeros(num_obs + num_states) # initialize the likelihood mapping for the single modality\\n\",\n \"\\n\",\n \"A_array[0][:,:,0] = np.eye(3) # assign the mapping between hidden states of factor 0 and observations, given factor 1 == 0\\n\",\n \"A_array[0][0,:,1] = 0.5 # assign the mapping between hidden states of factor 0 and observation of level 0, given factor 1 == 1\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This `A` array corresponds to an observation model with a single modality and two hidden state factors.\\n\",\n \"\\n\",\n \"We can check if this `A` array is a proper conditional distribution by using the `utils` function `is_normalized`, which checks to make sure each column of each sub-array within `A` sums to `1`\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"False\"\n ]\n },\n \"execution_count\": 10,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"utils.is_normalized(A_array)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This `A` is not properly normalized because of this line:\\n\",\n \"\\n\",\n \"```\\n\",\n \"A_array[0][0,:,1] = 0.5 \\n\",\n \"```\\n\",\n \"\\n\",\n \"This is problematic, because we've only assigned a single outcome to have 50% probability under all the hidden state configurations of factor 0, given factor 1 == level 1. That means each column of `A_array[0][:,:,1]` is not a proper conditional distribution, since there's still 50% of 'unaccounted' probability. In particular, the distributions encoded in the columns of this array do not each sum to 1.\\n\",\n \"\\n\",\n \"We can fix this by hand (by changing our code to allocate the remaining 50% of probability for each of those columns) or, depending on the intended final distributions, by using the `norm_dist_obj_arr` function, which column-normalizes every `numpy.ndarray` contained within an object array.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"P(o0 | s0, s1 == 1) after normalization: \\n\",\n \" [[1. 1. 1.]\\n\",\n \" [0. 0. 0.]\\n\",\n \" [0. 0. 0.]]\\n\",\n \"\\n\",\n \"Is the full distribution is now normalized? Yes!\\n\"\n ]\n }\n ],\n \"source\": [\n \"A_array = utils.norm_dist_obj_arr(A_array)\\n\",\n \"\\n\",\n \"print(f'P(o0 | s0, s1 == 1) after normalization: \\\\n {A_array[0][:,:,1]}\\\\n')\\n\",\n \"\\n\",\n \"print(f'Is the full distribution is now normalized? {\\\"Yes!\\\" if utils.is_normalized(A_array) else \\\"No!\\\"}')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Sampling\\n\",\n \"\\n\",\n \"Sometimes we will also want to sample from categorical probability distributions, for instance when sampling observations from the generative process or sampling actions from the agent's posterior over policies. We have two functions in `utils`, `sample` and `sample_obj_arr` that can deal with sampling from either single probability distributions (`numpy.ndarray` of `ndim == 1`) as well as collections of factorized distributions, stored in object arrays.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"0\\n\"\n ]\n }\n ],\n \"source\": [\n \"# sample from a single random categorical distribution\\n\",\n \"\\n\",\n \"my_categorical = np.random.rand(3)\\n\",\n \"my_categorical = utils.norm_dist(my_categorical) # the `utils.norm_dist` function works on single vectors or matrices that represent non-factorized probability distributions\\n\",\n \"sampled_outcome = utils.sample(my_categorical)\\n\",\n \"print(sampled_outcome)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[2, 2, 0]\\n\"\n ]\n }\n ],\n \"source\": [\n \"# sample from a multi-factor categorical distribution\\n\",\n \"\\n\",\n \"my_multifactor_categorical = utils.random_single_categorical([3, 4, 10]) # creates a collection of 3 marginal categorical distributions, each of different dimension\\n\",\n \"\\n\",\n \"sampled_outcome_list = utils.sample_obj_array(my_multifactor_categorical)\\n\",\n \"\\n\",\n \"print(sampled_outcome_list)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Note that when sampling from categorical distributions, the returned values are integers that represent the index of the support (i.e. which \\\"outcome\\\" or \\\"level\\\") that is sampled. In the case of multi-factor distributions, the returned value is a list of integers, one sampled outcome per marginal categorical distribution\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Conditional expectation\\n\",\n \"\\n\",\n \"We can also compute conditional expectations of single random variables that depend on a multi-factor random variables using a function from the `pymdp.maths` utility package called `spm_dot`, that is based on the original function of the same name from `SPM`, where active inference was first implemented.\\n\",\n \"\\n\",\n \"Let's imagine we have an observation model as above, with one observation modality with dimensionality `3` and two hidden state factors, with dimensionalities `3` and `2`. Given a factorized distribution over the two hidden state factors (i.e. an object array of marginal categorical distributions, one with `3` levels and the other with `2` levels), we want to generate a conditional expectation over the values of the observation distribution with dimension `3`. In other words, we want to evaluate:\\n\",\n \"\\n\",\n \"$$\\n\",\n \"\\\\mathbb{E}_{P(\\\\mathbf{s})}[P(o | \\\\mathbf{s})] = \\\\mathbb{E}_{P(s^1)P(s^2)}[P(o^1 | s^1, s^2)]\\n\",\n \"$$\\n\",\n \"\\n\",\n \"given a conditional distribution $P(o^1 | s^1, s^2)$ and some \\\"priors\\\" $P(s^1), P(s^2)$ over hidden states.\\n\",\n \"\\n\",\n \"Implementing this conditional expectation in practice can be written as a multi-dimensional dot product of the modality-specific `A` array (`A[0]`) with each of the hidden state factor distributions, $P(s^1)$ and $P(s^2)$. Under the hood, the `spm_dot` function of `pymdp.maths` achieves this using an optimized `numpy` function called [`einsum`](https://numpy.org/doc/stable/reference/generated/numpy.einsum.html), or einstein summation. Let's see what computing this conditional expectation with `spm_dot` looks like in practice:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Expected distribution over observations, given the value of Ps:\\n\",\n \" [[0.375]\\n\",\n \" [0.25 ]\\n\",\n \" [0.375]]\\n\"\n ]\n }\n ],\n \"source\": [\n \"from pymdp import maths\\n\",\n \"\\n\",\n \"num_obs = [3] # dimensionalities of observation modalities (just one here, for simplicity)\\n\",\n \"num_states = [3, 2] # dimensionalities of hidden state factors \\n\",\n \"\\n\",\n \"A_shapes = [num_obs + num_states] # shape of the A arrays (only one shape needed, (3, 3, 2))\\n\",\n \"A_array = utils.obj_array_zeros(A_shapes) # create our conditional distribution using the provided shape list\\n\",\n \"\\n\",\n \"A_array[0][:,:,0] = np.eye(3) # when s2 == 0, s1 fully determines the value of o1\\n\",\n \"A_array[0][1,:,1] = 1. # when s2 == 1, the value of o1 is always 2, regardless of the setting of s1\\n\",\n \"\\n\",\n \"Ps = utils.obj_array_from_list([np.array([0.5, 0.0, 0.5]), np.array([0.75, 0.25])]) # create our \\\"prior\\\" or beliefs about hidden states, that will be used in the expectation\\n\",\n \"\\n\",\n \"E_o_ps = maths.spm_dot(A_array[0], Ps)\\n\",\n \"\\n\",\n \"print(f\\\"Expected distribution over observations, given the value of Ps:\\\\n {E_o_ps.reshape(-1,1)}\\\")\"\n ]\n }\n ],\n \"metadata\": {\n \"colab\": {\n \"collapsed_sections\": [],\n \"name\": \"Pymdp Fundamentals.ipynb\",\n \"provenance\": []\n },\n \"kernelspec\": {\n \"display_name\": \"Python 3.7.10 ('pymdp_env')\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.8.8\"\n },\n \"vscode\": {\n \"interpreter\": {\n \"hash\": \"43ee964e2ad3601b7244370fb08e7f23a81bd2f0e3c87ee41227da88c57ff102\"\n }\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": "docs/notebooks/tmaze_demo.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Active Inference Demo: T-Maze Environment\\n\",\n \"\\n\",\n \"[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/infer-actively/pymdp/blob/main/docs/notebooks/tmaze_demo.ipynb)\\n\",\n \"\\n\",\n \"*Author: Conor Heins*\\n\",\n \"\\n\",\n \"This demo notebook provides a full walk-through of active inference using the `Agent()` class of `pymdp`. The canonical example used here is the 'T-maze' task, often used in the active inference literature in discussions of epistemic behavior (see, for example, [\\\"Active Inference and Epistemic Value\\\"](https://pubmed.ncbi.nlm.nih.gov/25689102/))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"*Note*: When running this notebook in Google Colab, you may have to run `!pip install inferactively-pymdp` at the top of the notebook, before you can `import pymdp`. That cell is left commented out below, in case you are running this notebook from Google Colab.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# ! pip install inferactively-pymdp\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Imports\\n\",\n \"\\n\",\n \"First, import `pymdp` and the modules we'll need.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import copy\\n\",\n \"\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp.utils import plot_beliefs, plot_likelihood\\n\",\n \"from pymdp import utils\\n\",\n \"from pymdp.envs import TMazeEnv\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Auxiliary Functions\\n\",\n \"\\n\",\n \"Define some utility functions that will be helpful for plotting.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Environment\\n\",\n \"\\n\",\n \"Here we consider an agent navigating a three-armed 'T-maze,' with the agent starting in a central location of the maze. The bottom arm of the maze contains an informative cue, which signals in which of the two top arms ('Left' or 'Right', the ends of the 'T') a reward is likely to be found. \\n\",\n \"\\n\",\n \"At each timestep, the environment is described by the joint occurrence of two qualitatively-different 'kinds' of states (hereafter referred to as _hidden state factors_). These hidden state factors are independent of one another.\\n\",\n \"\\n\",\n \"The first hidden state factor (`Location`) is a discrete random variable with 4 levels, that encodes the current position of the agent. Each of its four levels can be mapped to the following values: {`CENTER`, `RIGHT ARM`, `LEFT ARM`, or `CUE LOCATION`}. The random variable `Location` taking a particular value can be represented as a one-hot vector with a `1` at the appropriate level, and `0`'s everywhere else. For example, if the agent is in the `CUE LOCATION`, the current state of this factor would be $s_1 = \\\\begin{bmatrix} 0 & 0 & 0 & 1 \\\\end{bmatrix}$.\\n\",\n \"\\n\",\n \"We represent the second hidden state factor (`Reward Condition`) is a discrete random variable with 2 levels, that encodes the reward condition of the trial: {`Reward on Right`, or `Reward on Left`}. A trial where the condition is reward is `Reward on Left` is thus encoded as the state $s_2 = \\\\begin{bmatrix} 0 & 1\\\\end{bmatrix}$.\\n\",\n \"\\n\",\n \"The environment is designed such that when the agent is located in the `RIGHT ARM` and the reward condition is `Reward on Right`, the agent has a specified probability $a$ (where $a > 0.5$) of receiving a reward, and a low probability $b = 1 - a$ of receiving a 'loss' (we can think of this as an aversive or unpreferred stimulus). If the agent is in the `LEFT ARM` for the same reward condition, the reward probabilities are swapped, and the agent experiences loss with probability $a$, and reward with lower probability $b = 1 - a$. These reward contingencies are intuitively swapped for the `Reward on Left` condition. \\n\",\n \"\\n\",\n \"For instance, we can encode the state of the environment at the first time step in a `Reward on Right` trial with the following pair of hidden state vectors: $s_1 = \\\\begin{bmatrix} 1 & 0 & 0 & 0\\\\end{bmatrix}$, $s_2 = \\\\begin{bmatrix} 1 & 0\\\\end{bmatrix}$, where we assume the agent starts sitting in the central location. If the agent moved to the right arm, then the corresponding hidden state vectors would now be $s_1 = \\\\begin{bmatrix} 0 & 1 & 0 & 0\\\\end{bmatrix}$, $s_2 = \\\\begin{bmatrix} 1 & 0\\\\end{bmatrix}$. This highlights the _independence_ of the two hidden state factors. In other words, the location of the agent ($s_1$) can change without affecting the identity of the reward condition ($s_2$).\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Initialize environment\\n\",\n \"Now we can initialize the T-maze environment using the built-in `TMazeEnv` class from the `pymdp.envs` module.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Choose reward probabilities $a$ and $b$, where $a$ and $b$ are the probabilities of reward / loss in the 'correct' arm, and the probabilities of loss / reward in the 'incorrect' arm. Which arm counts as 'correct' vs. 'incorrect' depends on the reward condition (state of the 2nd hidden state factor).\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"reward_probabilities = [0.98, 0.02] # probabilities used in the original SPM T-maze demo\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Initialize an instance of the T-maze environment\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"env = TMazeEnv(reward_probs = reward_probabilities)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Structure of the state --> outcome mapping\\n\",\n \"We can 'peer into' the rules encoded by the environment (also known as the _generative process_ ) by looking at the probability distributions that map from hidden states to observations. Following the SPM version of active inference, we refer to this collection of probabilistic relationships as the `A` array. In the case of the true rules of the environment, we refer to this array as `A_gp` (where the suffix `_gp` denotes the generative process). \\n\",\n \"\\n\",\n \"It is worth outlining what constitute the agent's observations in this task. In this T-maze demo, we have three sensory channels or observation modalities: `Location`, `Reward`, and `Cue`. \\n\",\n \"\\n\",\n \"1. The `Location` observation values are identical to the `Location` hidden state values. In this case, the agent always unambiguously observes its own state - if the agent is in `RIGHT ARM`, it receives a `RIGHT ARM` observation in the corresponding modality. This might be analogized to a 'proprioceptive' sense of one's own place.\\n\",\n \"\\n\",\n \"2. The `Reward` observation modality assumes the values `No Reward`, `Reward` or `Loss`. The `No Reward` (index 0) observation is observed whenever the agent isn't occupying one of the two T-maze arms (the right or left arms). The `Reward` (index 1) and `Loss` (index 2) observations are observed in the right and left arms of the T-maze, with associated probabilities that depend on the reward condition (i.e. on the value of the second hidden state factor).\\n\",\n \"\\n\",\n \"3. The `Cue` observation modality assumes the values `Cue Right`, `Cue Left`. This observation unambiguously signals the reward condition of the trial, and therefore in which arm the `Reward` observation is more probable. When the agent occupies the other arms, the `Cue` observation will be `Cue Right` or `Cue Left` with equal probability. However (as we'll see below when we intialise the agent), the agent's beliefs about the likelihood mapping render these observations uninformative and irrelevant to state inference.\\n\",\n \"\\n\",\n \"In `pymdp`, we store the set of probability distributions encoding the conditional probabilities of observations, under different configurations of hidden states, as a set of matrices referred to as the likelihood mapping or `A` array (this is a convention borrowed from SPM). The likelihood mapping _for a single modality_ is stored as a single multidimensional array (a `numpy.ndarray`) `A[m]` with the larger likelihood array, where `m` is the index of the corresponding modality. Each modality-specific A array has `num_obs[m]` rows, and as many lagging dimensions (e.g. columns, 'slices' and higher-order dimensions) as there are hidden state factors. `num_obs[m]` tells you the number of observation values (also known as \\\"levels\\\") for observation modality `m`.\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# here, we can get the likelihood mapping directly from the environmental class. So this is the likelihood mapping that truly describes the relatinoship between the \\n\",\n \"# environment's hidden state and the observations the agent will get\\n\",\n \"\\n\",\n \"A_gp = env.get_likelihood_dist()\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": \"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\",\n 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A_gp[1][:,:,0],'Reward Right')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {\n \"scrolled\": false\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A_gp[1][:,:,1],'Reward Left')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A_gp[2][:,3,:],'Cue Mapping')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Transition Dynamics\\n\",\n \"\\n\",\n \"We represent the dynamics of the environment (e.g. changes in the location of the agent and changes to the reward condition) as conditional probability distributions that encode the likelihood of transitions between the states of a given hidden state factor. These distributions are collected into the so-called `B` array, also known as _transition likelihoods_ or _transition distribution_ . As with the `A` array, we denote the true probabilities describing the environmental dynamics as `B_gp`. Each sub-matrix `B_gp[f]` of the larger array encodes the transition probabilities between state-values of a given hidden state factor with index `f`. These matrices encode dynamics as Markovian transition probabilities, such that the entry $i,j$ of a given matrix encodes the probability of transition to state $i$ at time $t+1$, given state $j$ at $t$. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# here, we can get the transition mapping directly from the environmental class. So this is the transition mapping that truly describes the environment's dynamics\\n\",\n \"\\n\",\n \"B_gp = env.get_transition_dist()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For example, we can inspect the 'dynamics' of the `Reward Condition` factor by indexing into the appropriate sub-matrix of `B_gp`\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": \"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\",\n 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(B_gp[1][:,:,0],'Reward Condition Transitions')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The above transition array is the 'trivial' identity matrix, meaning that the reward condition doesn't change over time (it's mapped from whatever it's current value is to the same value at the next timestep).\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### (Controllable-) Transition Dynamics\\n\",\n \"\\n\",\n \"Importantly, some hidden state factors are _controllable_ by the agent, meaning that the probability of being in state $i$ at $t+1$ isn't merely a function of the state at $t$, but also of actions (or from the agent's perspective, _control states_ ). So now each transition likelihood encodes conditional probability distributions over states at $t+1$, where the conditioning variables are both the states at $t-1$ _and_ the actions at $t-1$. This extra conditioning on actions is encoded via an optional third dimension to each factor-specific `B` array.\\n\",\n \"\\n\",\n \"For example, in our case the first hidden state factor (`Location`) is under the control of the agent, which means the corresponding transition likelihoods `B[0]` are index-able by both previous state and action.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {\n \"scrolled\": false\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(B_gp[0][:,:,0],'Transition likelihood for \\\"Move to Center\\\"')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(B_gp[0][:,:,1],'Transition likelihood for \\\"Move to Right Arm\\\"')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(B_gp[0][:,:,2],'Transition likelihood for \\\"Move to Left Arm\\\"')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(B_gp[0][:,:,3],'Transition likelihood for \\\"Move to Cue Location\\\"')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## The generative model\\n\",\n \"Now we can move onto setting up the *generative model* of the agent - namely, the agent's *beliefs* or assumptions about how hidden states give rise to observations, and how hidden states transition among eachother.\\n\",\n \"\\n\",\n \"In almost all MDPs, the critical building blocks of this generative model are the agent's representation of the observation likelihood, which we'll refer to as `A_gm`, and its representation of the transition likelihood, which we'll call `B_gm`. \\n\",\n \"\\n\",\n \"Here, we assume the agent has a veridical representation of the rules of the T-maze (namely, how hidden states cause observations) as well as its ability to control its own movements with certain consequences (i.e. 'noiseless' transitions). So in other words, the agent will have a veridical representation of the \\\"rules\\\" of the environment, as encoded in the arrays `A_gp` and `B_gp` of the generative process.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"A_gm = copy.deepcopy(A_gp) # make a copy of the true observation likelihood to initialize the observation model\\n\",\n \"B_gm = copy.deepcopy(B_gp) # make a copy of the true transition likelihood to initialize the transition model\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### **Important Concept to Note Here!!!**\\n\",\n \"It is not necessary, or even in many cases _important_ , that the generative model is a veridical representation of the generative process. This distinction between generative model (essentially, beliefs entertained by the agent and its interaction with the world) and the generative process (the actual dynamical system 'out there' generating sensations) is of crucial importance to the active inference formalism and (in our experience) often overlooked in code.\\n\",\n \"\\n\",\n \"It is for notational and computational convenience that we encode the generative process using `A` and `B` matrices. By doing so, it simply puts the rules of the environment in a data structure that can easily be converted into the Markovian-style conditional distributions useful for encoding the agent's generative model.\\n\",\n \"\\n\",\n \"Strictly speaking, however, all the generative process needs to do is generate observations that are 'digestible' by the agent, and be 'perturbable' by actions issued by the agent. The way in which it does so can be arbitrarily complex, non-linear, and unaccessible by the agent. Namely, it doesn't have to be encoded by `A` and `B` arrays (what amount to Markovian, conditional probability tables), but could be described by arbitrarily complex nonlinear or non-differentiable transformations of hidden states that generate observatons.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Introducing the `Agent()` class\\n\",\n \"\\n\",\n \"In `pymdp`, we have abstracted much of the computations required for active inference into the `Agent` class, a flexible object that can be used to store necessary aspects of the generative model, the agent's instantaneous observations and actions, and perform action / perception using functions like `Agent.infer_states` and `Agent.infer_policies`. \\n\",\n \"\\n\",\n \"An instance of `Agent` is straightforwardly initialized with a call to the `Agent()` constructor with a list of optional arguments.\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"In our call to `Agent()`, we need to constrain the default behavior with some of our T-Maze-specific needs. For example, we want to make sure that the agent's beliefs about transitions are constrained by the fact that it can only control the `Location` factor - _not_ the `Reward Condition` (which we assumed stationary across an epoch of time). Therefore we specify this using a list of indices that will be passed as the `control_fac_idx` argument of the `Agent()` constructor. \\n\",\n \"\\n\",\n \"Each element in the list specifies a hidden state factor (in terms of its index) that is controllable by the agent. Hidden state factors whose indices are _not_ in this list are assumed to be uncontrollable.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"controllable_indices = [0] # this is a list of the indices of the hidden state factors that are controllable\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can construct our agent...\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 17,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"agent = Agent(A=A_gm, B=B_gm, control_fac_idx=controllable_indices)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can inspect properties (and change) of the agent as we see fit. Let's look at the initial beliefs the agent has about its starting location and reward condition, encoded in the prior over hidden states $P(s)$, known in SPM-lingo as the `D` array.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 18,\n \"metadata\": {\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_beliefs(agent.D[0],\\\"Beliefs about initial location\\\")\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 19,\n \"metadata\": {\n \"scrolled\": false\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_beliefs(agent.D[1],\\\"Beliefs about reward condition\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's make it so that agent starts with precise and accurate prior beliefs about its starting location.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 20,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"agent.D[0] = utils.onehot(0, agent.num_states[0])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The `onehot(value, dimension)` function within `pymdp.utils` is a nice function for quickly generating a one-hot vector of dimensions `dimension` with a `1` at the index `value`.\\n\",\n \"\\n\",\n \"And now confirm that our agent knows (i.e. has accurate beliefs about) its initial state by visualizing its priors again.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 21,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_beliefs(agent.D[0],\\\"Beliefs about initial location\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Another thing we want to do in this case is make sure the agent has a 'sense' of reward / loss and thus a motivation to be in the 'correct' arm (the arm that maximizes the probability of getting the reward outcome).\\n\",\n \"\\n\",\n \"We can do this by changing the prior beliefs about observations, the `C` array (also known as the _prior preferences_ ). This is represented as a collection of distributions over observations for each modality. It is initialized by default to be all 0s. This means agent has no preference for particular outcomes. Since the second modality (index `1` of the `C` array) is the `Reward` modality, with the index of the `Reward` outcome being `1`, and that of the `Loss` outcome being `2`, we populate the corresponding entries with values whose relative magnitudes encode the preference for one outcome over another (technically, this is encoded directly in terms of relative log-probabilities). \\n\",\n \"\\n\",\n \"Our ability to make the agent's prior beliefs that it tends to observe the outcome with index `1` in the `Reward` modality, more often than the outcome with index `2`, is what makes this modality a Reward modality in the first place -- otherwise, it would just be an arbitrary observation with no extrinsic value _per se_. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 22,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"agent.C[1][1] = 3.0\\n\",\n \"agent.C[1][2] = -3.0\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 23,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_beliefs(agent.C[1],\\\"Prior beliefs about observations\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Active Inference\\n\",\n \"Now we can start off the T-maze with an initial observation and run active inference via a loop over a desired time interval.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 24,\n \"metadata\": {\n \"scrolled\": false\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \" === Starting experiment === \\n\",\n \" Reward condition: Right, Observation: [CENTER, No reward, Cue Left]\\n\",\n \"[Step 0] Action: [Move to CUE LOCATION]\\n\",\n \"[Step 0] Observation: [CUE LOCATION, No reward, Cue Right]\\n\",\n \"[Step 1] Action: [Move to RIGHT ARM]\\n\",\n \"[Step 1] Observation: [RIGHT ARM, Reward!, Cue Right]\\n\",\n \"[Step 2] Action: [Move to RIGHT ARM]\\n\",\n \"[Step 2] Observation: [RIGHT ARM, Reward!, Cue Left]\\n\",\n \"[Step 3] Action: [Move to RIGHT ARM]\\n\",\n \"[Step 3] Observation: [RIGHT ARM, Reward!, Cue Right]\\n\",\n \"[Step 4] Action: [Move to RIGHT ARM]\\n\",\n \"[Step 4] Observation: [RIGHT ARM, Reward!, Cue Right]\\n\"\n ]\n }\n ],\n \"source\": [\n \"T = 5 # number of timesteps\\n\",\n \"\\n\",\n \"obs = env.reset() # reset the environment and get an initial observation\\n\",\n \"\\n\",\n \"# these are useful for displaying read-outs during the loop over time\\n\",\n \"reward_conditions = [\\\"Right\\\", \\\"Left\\\"]\\n\",\n \"location_observations = ['CENTER','RIGHT ARM','LEFT ARM','CUE LOCATION']\\n\",\n \"reward_observations = ['No reward','Reward!','Loss!']\\n\",\n \"cue_observations = ['Cue Right','Cue Left']\\n\",\n \"msg = \\\"\\\"\\\" === Starting experiment === \\\\n Reward condition: {}, Observation: [{}, {}, {}]\\\"\\\"\\\"\\n\",\n \"print(msg.format(reward_conditions[env.reward_condition], location_observations[obs[0]], reward_observations[obs[1]], cue_observations[obs[2]]))\\n\",\n \"\\n\",\n \"for t in range(T):\\n\",\n \" qx = agent.infer_states(obs)\\n\",\n \"\\n\",\n \" q_pi, efe = agent.infer_policies()\\n\",\n \"\\n\",\n \" action = agent.sample_action()\\n\",\n \"\\n\",\n \" msg = \\\"\\\"\\\"[Step {}] Action: [Move to {}]\\\"\\\"\\\"\\n\",\n \" print(msg.format(t, location_observations[int(action[0])]))\\n\",\n \"\\n\",\n \" obs = env.step(action)\\n\",\n \"\\n\",\n \" msg = \\\"\\\"\\\"[Step {}] Observation: [{}, {}, {}]\\\"\\\"\\\"\\n\",\n \" print(msg.format(t, location_observations[obs[0]], reward_observations[obs[1]], cue_observations[obs[2]]))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": []\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The agent begins by moving to the `CUE LOCATION` to resolve its uncertainty about the reward condition - this is because it knows it will get an informative cue in this location, which will signal the true reward condition unambiguously. At the beginning of the next timestep, the agent then uses this observaiton to update its posterior beliefs about states `qx[1]` to reflect the true reward condition. Having resolved its uncertainty about the reward condition, the agent then moves to `RIGHT ARM` to maximize utility and continues to do so, given its (correct) beliefs about the reward condition and the mapping between hidden states and reward observations. \\n\",\n \"\\n\",\n \"Notice, perhaps confusingly, that the agent continues to receive observations in the 3rd modality (i.e. samples from `A_gp[2]`). These are observations of the form `Cue Right` or `Cue Left`. However, these 'cue' observations are random and totally umambiguous unless the agent is in the `CUE LOCATION` - this is reflected by totally entropic distributions in the corresponding columns of `A_gp[2]` (and the agents beliefs about this ambiguity, reflected in `A_gm[2]`. See below.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 25,\n \"metadata\": {\n \"scrolled\": false\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A_gp[2][:,:,0],'Cue Observations when condition is Reward on Right, for Different Locations')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 26,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A_gp[2][:,:,1],'Cue Observations when condition is Reward on Left, for Different Locations')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The final column on the right side of these matrices represents the distribution over cue observations, conditioned on the agent being in `CUE LOCATION` and the appropriate Reward Condition. This demonstrates that cue observations are uninformative / lacking epistemic value for the agent, _unless_ they are in `CUE LOCATION.`\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can inspect the agent's final beliefs about the reward condition characterizing the 'trial,' having undergone 10 timesteps of active inference.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 27,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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6cbJmSpIWME+irga2D6W39vKGnA09P8ldJrk5y0qQKlCSNZ8Ehl13YztHAFLAGuDLJP6+q+4aNkmwANgCsWrWK6enpRe1savF1ai+w2PNKu8+OHTvslyUwTqBvB9YOptf084a2AddU1T8Cf5vka3QBf+2wUVVtBDYCrF+/vqamphZZtjQ3z6s9z/T0tP2yBMYZcrkWODrJkUn2B14JbBpp8yn6C+ckK+mGYG6dXJmSpIUsGOhV9TBwNnAZcDNwaVXdmOT8JKf2zS4D7klyE3A58Kaqumd3FS1JeqSxxtCrajOweWTeuYPbBbyh/5MkLQO/KSpJjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDXCQJekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0YK9CTnJTkliRbkpwzT7ufSVJJ1k+uREnSOBYM9CT7AhcAJwPHAGckOWaWdgcDrweumXSRkqSFjXOFfhywpapuraqHgEuA02Zp91vAu4AHJ1ifJGlMK8ZosxrYOpjeBhw/bJDkOcDaqvp0kjfNtaEkG4ANAKtWrWJ6enqXCwaYWtRa2lss9rzS7rNjxw77ZQmME+jzSrIP8PvAmQu1raqNwEaA9evX19TU1KPdvfQInld7nunpaftlCYwz5LIdWDuYXtPPm3Ew8GxgOsk3gOcBm3xjVJKW1jiBfi1wdJIjk+wPvBLYNLOwqu6vqpVVta6q1gFXA6dW1XW7pWJJ0qwWDPSqehg4G7gMuBm4tKpuTHJ+klN3d4GSpPGMNYZeVZuBzSPzzp2j7dSjL0uStKv8pqgkNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDXCQJekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEWMFepKTktySZEuSc2ZZ/oYkNyW5Icn/TnLE5EuVJM1nwUBPsi9wAXAycAxwRpJjRpr9DbC+qn4Y+CTwHyddqCRpfuNcoR8HbKmqW6vqIeAS4LRhg6q6vKq+209eDayZbJmSpIWsGKPNamDrYHobcPw87c8C/nK2BUk2ABsAVq1axfT09HhVjpha1FraWyz2vNLus2PHDvtlCYwT6GNL8gvAeuCE2ZZX1UZgI8D69etrampqkruXAPC82vNMT0/bL0tgnEDfDqwdTK/p5+0kyYnAbwInVNU/TKY8SdK4xhlDvxY4OsmRSfYHXglsGjZIcizwYeDUqrpz8mVKkhayYKBX1cPA2cBlwM3ApVV1Y5Lzk5zaN3s38ATgE0m+mGTTHJuTJO0mY42hV9VmYPPIvHMHt0+ccF2SpF3kN0UlqREGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDXCQJekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRYwV6kpOS3JJkS5JzZll+QJKP98uvSbJu4pVKkua1YKAn2Re4ADgZOAY4I8kxI83OAu6tqqOA9wDvmnShkqT5jXOFfhywpapuraqHgEuA00banAb8SX/7k8CLk2RyZUqSFrJijDarga2D6W3A8XO1qaqHk9wPPAm4e9goyQZgQz+5I8ktiylaj7CSkWO9V/NaYk/kOTo5R8y1YJxAn5iq2ghsXMp97g2SXFdV65e7DmkunqNLY5whl+3A2sH0mn7erG2SrAAOBe6ZRIGSpPGME+jXAkcnOTLJ/sArgU0jbTYBv9jfPh34bFXV5MqUJC1kwSGXfkz8bOAyYF/gI1V1Y5LzgeuqahPwx8CfJtkCfJsu9LV0HMbSns5zdAnEC2lJaoPfFJWkRhjoktQIA/0xbKGfZJCWW5KPJLkzyVeWu5a9gYH+GDXmTzJIy+1C4KTlLmJvYaA/do3zkwzSsqqqK+k++aYlYKA/ds32kwyrl6kWSXsAA12SGmGgP3aN85MMkvYiBvpj1zg/ySBpL2KgP0ZV1cPAzE8y3AxcWlU3Lm9V0s6SXAx8HnhGkm1JzlrumlrmV/8lqRFeoUtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1Ij/B+ybS8Lt4j6TAAAAAElFTkSuQmCC\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_beliefs(qx[1],\\\"Final posterior beliefs about reward condition\\\")\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3.8.8 ('base')\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.8.8\"\n },\n \"vscode\": {\n \"interpreter\": {\n \"hash\": \"70b7ceca5df5387258d861d4588082cea9500e731be001548c95afd8cd8c3af8\"\n }\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "docs/notebooks/using_the_agent_class.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Tutorial 2: the `Agent` API\\n\",\n \"\\n\",\n \"[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/infer-actively/pymdp/blob/main/docs/notebooks/using_the_agent_class.ipynb)\\n\",\n \"\\n\",\n \"*Author: Conor Heins*\\n\",\n \"\\n\",\n \"This tutorial introduces the `Agent` class, the main API offered by `pymdp` that allows you to abstract away all the mathematical nuances involved in running active inference processes. All you have to do is build a generative model in terms of `A`, `B`, `C`, and `D` arrays, plug them into the `Agent()` constructor, and then start running active inference processes using the desired functions of the `Agent` class, like `self.infer_states()` and `self.infer_policies()`. \\n\",\n \"\\n\",\n \"We demonstrate the use of the `Agent` class by building an active inference agent to play a simple explore/exploit task, what we call the \\\"epistemic 2-armed bandit\\\". The task structure is identical to the \\\"explore/exploit\\\" task described in Smith et al. (2022): [\\\"A Step-by-Step Tutorial on Active Inference Modelling and its Application to Empirical Data\\\"](https://www.sciencedirect.com/science/article/pii/S0022249621000973). The task is a modified version of a classic multi-armed bandit problem, with particular changes that make it well suited to demonstrating the information-availing nature of active inference in discrete state spaces.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"*Note*: When running this notebook in Google Colab, you may have to run `!pip install inferactively-pymdp` at the top of the notebook, before you can `import pymdp`. That cell is left commented out below, in case you are running this notebook from Google Colab.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# ! pip install inferactively-pymdp\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Imports\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {\n \"id\": \"hk0kXw1RRmTf\"\n },\n \"outputs\": [],\n \"source\": [\n \"import numpy as np\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import seaborn as sns\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"iSS6oO3RWrwp\"\n },\n \"source\": [\n \"### Define some auxiliary functions\\n\",\n \"\\n\",\n \"Here are some plotting functions that will come in handy throughout the tutorial.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {\n \"id\": \"Y0QiIF8SWxot\"\n },\n \"outputs\": [],\n \"source\": [\n \"def plot_likelihood(matrix, title_str = \\\"Likelihood distribution (A)\\\"):\\n\",\n \" \\\"\\\"\\\"\\n\",\n \" Plots a 2-D likelihood matrix as a heatmap\\n\",\n \" \\\"\\\"\\\"\\n\",\n \"\\n\",\n \" if not np.isclose(matrix.sum(axis=0), 1.0).all():\\n\",\n \" raise ValueError(\\\"Distribution not column-normalized! Please normalize (ensure matrix.sum(axis=0) == 1.0 for all columns)\\\")\\n\",\n \" \\n\",\n \" plt.figure(figsize = (6,6))\\n\",\n \" sns.heatmap(matrix, cmap = 'gray', cbar = False, vmin = 0.0, vmax = 1.0)\\n\",\n \" plt.title(title_str)\\n\",\n \" plt.show()\\n\",\n \"\\n\",\n \"\\n\",\n \"def plot_beliefs(belief_dist, title_str=\\\"\\\"):\\n\",\n \" \\\"\\\"\\\"\\n\",\n \" Plot a categorical distribution or belief distribution, stored in the 1-D numpy vector `belief_dist`\\n\",\n \" \\\"\\\"\\\"\\n\",\n \"\\n\",\n \" if not np.isclose(belief_dist.sum(), 1.0):\\n\",\n \" raise ValueError(\\\"Distribution not normalized! Please normalize\\\")\\n\",\n \"\\n\",\n \" plt.grid(zorder=0)\\n\",\n \" plt.bar(range(belief_dist.shape[0]), belief_dist, color='r', zorder=3)\\n\",\n \" plt.xticks(range(belief_dist.shape[0]))\\n\",\n \" plt.title(title_str)\\n\",\n \" plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"qknzxudf593_\"\n },\n \"source\": [\n \"## **More complex generative models**\\n\",\n \"\\n\",\n \"In this notebook we will build a more complicated generative model, with the following goals in mind:\\n\",\n \"\\n\",\n \"1. Demonstrate the unique behavior of active inference agents, as opposed to other agent-based approaches to solving POMDPs (e.g. utility-maximization / reinforcement learning)\\n\",\n \"\\n\",\n \"2. Provide a task example that is more relevant to decision-making research and computational psychiatry.\\n\",\n \"\\n\",\n \"3. Take advantage of the functionalities of `pymdp`, especially the `Agent()` class, to abstract away all the mathematical operations involved with inference and planning under active inference.\\n\",\n \"\\n\",\n \"Before we dive into specifying this generative model, we need to talk about _observation modalities_ and _hidden state factors_...\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"2YQ8gQrdkFE4\"\n },\n \"source\": [\n \"The data structure we use in `pymdp` to represent different hidden state factors and observation modalities is the `object array` (referred to in other contexts as 'arrays of arrays' or 'jagged/ragged arrays').\\n\",\n \"\\n\",\n \"They are no different than standard numpy `ndarrays` (they can arbitrarily multidimensional shape), except for the fact that their contents are unrestricted in terms of type. Their `dtype` is `object`, which means that their elements can be any kind of Python data structure -- including other arrays!\\n\",\n \"\\n\",\n \"In case you're coming from a MATLAB background: these object arrays are the equivalent of cell arrays. \\n\",\n \"\\n\",\n \"In `pymdp`, we represent a multi-factor $\\\\mathbf{B}$ array as an object array which has as many elements as there are hidden state factors. Therefore, each element `B[i]` of the object array contains the `B` matrix for hidden state factor `i`.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {\n \"id\": \"LE3k-jsQKAt3\"\n },\n \"outputs\": [],\n \"source\": [\n \"from pymdp import utils\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"Mk0dbpXibpP_\"\n },\n \"source\": [\n \"## **Explore/exploit task with a epistemic two-armed bandit**\\n\",\n \"\\n\",\n \"Now we're going to build a generative model for an active inference agent playing a two-armed bandit task. The [multi-armed bandit](https://en.wikipedia.org/wiki/Multi-armed_bandit) (or MAB) is a classic decision-making task that captures the core features of the the \\\"explore/exploit tradeoff\\\". The multi-armed bandit formulation is ubiquitous across problem spaces that require sequential decision-making under uncertainty -- this includes disciplines ranging from economics, neuroscience, machine learning, engineering all the way to advertising.\\n\",\n \"\\n\",\n \"In the standard MAB problem formulation, an agent has must choose between mutually-exclusive alternatives (also known as 'arms') in order to maximize reward over time. The probability of reward depends on which arm the agent chooses. A common real-world analogy for a MAB problem is imagining a special slot machine with three possible levers to pull (rather than the usual one), where playing each lever has different probabilities of payoff (e.g. getting a winning combination of symbols or bonus). In fact, the 'standard' slot machine, which usually only only one lever, was historically referred to as a 'one-armed bandit' -- this was the direct ancestor of the name for the generic machine learning / decision-making problem class, the MAB. \\n\",\n \"\\n\",\n \"Crucially, MAB problems are interesting and difficult because in general, the reward statistics of each arm are unknown or only partially known. In a probabilistic or Bayesian context, an agent must therefore act based on _beliefs_ about the reward statistics, since they don't have perfect access to this information. \\n\",\n \"\\n\",\n \"The inherent partial-observability of the ask creates a conflict between **exploitation** or choosing the arm that is _currently believed_ to be most rewarding, and **exploration** or gathering information about the remaining arms, in the hopes of discovering a potentially more rewarding option.\\n\",\n \"\\n\",\n \"The fact that expected reward or utility is contextualized by _beliefs_ -- i.e. which arm is currently thought to be the most rewarding -- motivates the use of active inference in this context. This is because the key objective function for action-selection, the expected free energy $\\\\mathbf{G}$, depends on the agent's beliefs about the world. And not only that, but expected free energy balances the desire to maximize rewards with the drive to resolve uncertainty about unknown parts of the agent's model. The more accurate the agent's beliefs are, the more faithfully decision-making can be guided by maximizing expected utility or rewards.\\n\",\n \"\\n\",\n \"#### **MAB with an epistemic twist**\\n\",\n \"\\n\",\n \"In the MAB formulation we'll be exploring in this tutorial, the agent must choose to play among two possible arms, each of which has unknown reward statistics. These reward statistics take the form of Bernoulli distributions over two possible reward outcomes: \\\"Loss\\\" and \\\"Reward\\\". However, one of the arms has probability $p$ of yielding \\\"Reward\\\"\\\" and probabiliity $(1-p)$ of yielding \\\"Loss\\\". The other arm has swapped statistics. In this example, agent knows that the bandit has this general reward structure, except they don't know *which* of the two arms is the rewarding one (the arm where reward probability is $p$, assuming $p \\\\in [0.5, 1]$).\\n\",\n \"\\n\",\n \"However, we introduce an additional feature in the environment, that induces an explicit trade-off in decision-making between exploration (information-seeking) and exploitation (reward-seeking). In this special \\\"epistemic bandit\\\" problem, there is an additional action available to the agent, besides playing the two arms. We call this third action \\\"Get Hint\\\", and allows the agent to acquire information reveals (potentially probabilistically) which arm is the more rewarding one. There is a trade-off here, because by choosing to acquire the hint, the agent forgoes the possibility of playing an arm and thus the possibility of getting a reward at that moment. The mutual exclusivity of hint-acquisition and arm-playing imbues the system with an explore/exploit trade-off, which active inference is particularly equipped to handle, when compared to simple reinforcement learning schemes (e.g. epsilon-greedy reward maximization).\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"WYTRxlxx4iD0\"\n },\n \"source\": [\n \"---\\n\",\n \"\\n\",\n \"Specify the dimensionalities of the hidden state factors, the control factors, and the observation modalities\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {\n \"id\": \"vOEYkFPt4gbC\"\n },\n \"outputs\": [],\n \"source\": [\n \"context_names = ['Left-Better', 'Right-Better']\\n\",\n \"choice_names = ['Start', 'Hint', 'Left Arm', 'Right Arm']\\n\",\n \"\\n\",\n \"\\\"\\\"\\\" Define `num_states` and `num_factors` below \\\"\\\"\\\"\\n\",\n \"num_states = [len(context_names), len(choice_names)]\\n\",\n \"num_factors = len(num_states)\\n\",\n \"\\n\",\n \"context_action_names = ['Do-nothing']\\n\",\n \"choice_action_names = ['Move-start', 'Get-hint', 'Play-left', 'Play-right']\\n\",\n \"\\n\",\n \"\\\"\\\"\\\" Define `num_controls` below \\\"\\\"\\\"\\n\",\n \"num_controls = [len(context_action_names), len(choice_action_names)]\\n\",\n \"\\n\",\n \"hint_obs_names = ['Null', 'Hint-left', 'Hint-right']\\n\",\n \"reward_obs_names = ['Null', 'Loss', 'Reward']\\n\",\n \"choice_obs_names = ['Start', 'Hint', 'Left Arm', 'Right Arm']\\n\",\n \"\\n\",\n \"\\\"\\\"\\\" Define `num_obs` and `num_modalities` below \\\"\\\"\\\"\\n\",\n \"num_obs = [len(hint_obs_names), len(reward_obs_names), len(choice_obs_names)]\\n\",\n \"num_modalities = len(num_obs)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"k4Tca2bJ4o0z\"\n },\n \"source\": [\n \"### The `A` array\\n\",\n \"---\\n\",\n \"\\n\",\n \"**Note**: Unlike in [Tutorial 1: Active inference from scratch](https://pymdp-rtd.readthedocs.io/en/latest/notebooks/active_inference_from_scratch.html), here we we will be building a more complex generative model more than one hidden state factor and observation modality. This leads to accordingly higher-dimensional `A` and `B` arrays. See [pymdp fundamentals](https://pymdp-rtd.readthedocs.io/en/latest/notebooks/pymdp_fundamentals.html) for more details on how we specify these high-dimensional arrays in `NumPy`.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {\n \"id\": \"zQsDxB8v6bvF\"\n },\n \"outputs\": [],\n \"source\": [\n \"\\\"\\\"\\\" Generate the A array \\\"\\\"\\\"\\n\",\n \"A = utils.obj_array( num_modalities )\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"9Vmy_Z1N6poY\"\n },\n \"source\": [\n \"Fill out the hint modality, a sub-array of `A` which we'll call `A_hint`\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {\n \"id\": \"daovgh4A6m5c\"\n },\n \"outputs\": [],\n \"source\": [\n \"p_hint = 0.7 # accuracy of the hint, according to the agent's generative model (how much does the agent trust the hint?)\\n\",\n \"\\n\",\n \"A_hint = np.zeros( (len(hint_obs_names), len(context_names), len(choice_names)) )\\n\",\n \"\\n\",\n \"for choice_id, choice_name in enumerate(choice_names):\\n\",\n \"\\n\",\n \" if choice_name == 'Start':\\n\",\n \"\\n\",\n \" A_hint[0,:,choice_id] = 1.0\\n\",\n \" \\n\",\n \" elif choice_name == 'Hint':\\n\",\n \"\\n\",\n \" A_hint[1:,:,choice_id] = np.array([[p_hint, 1.0 - p_hint],\\n\",\n \" [1.0 - p_hint, p_hint]])\\n\",\n \" elif choice_name == 'Left Arm':\\n\",\n \"\\n\",\n \" A_hint[0,:,choice_id] = 1.0\\n\",\n \" \\n\",\n \" elif choice_name == 'Right Arm':\\n\",\n \"\\n\",\n \" A_hint[0,:,choice_id] = 1.0\\n\",\n \" \\n\",\n \"A[0] = A_hint\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {\n \"id\": \"zIWcFelA7RqY\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A[0][:,:,1], title_str = \\\"Probability of the two hint types, for the two game states\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"dnVJO-Nn7zY4\"\n },\n \"source\": [\n \"Fill out the reward modality, a sub-array of `A` which we'll call `A_rew`\\n\",\n \"\\n\",\n \"\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {\n \"id\": \"fVnKm0zU8Ng3\"\n },\n \"outputs\": [],\n \"source\": [\n \"p_reward = 0.8 # probability of getting a rewarding outcome, if you are sampling the more rewarding bandit\\n\",\n \"\\n\",\n \"A_reward = np.zeros((len(reward_obs_names), len(context_names), len(choice_names)))\\n\",\n \"\\n\",\n \"for choice_id, choice_name in enumerate(choice_names):\\n\",\n \"\\n\",\n \" if choice_name == 'Start':\\n\",\n \"\\n\",\n \" A_reward[0,:,choice_id] = 1.0\\n\",\n \" \\n\",\n \" elif choice_name == 'Hint':\\n\",\n \"\\n\",\n \" A_reward[0,:,choice_id] = 1.0\\n\",\n \" \\n\",\n \" elif choice_name == 'Left Arm':\\n\",\n \"\\n\",\n \" A_reward[1:,:,choice_id] = np.array([ [1.0-p_reward, p_reward], \\n\",\n \" [p_reward, 1.0-p_reward]])\\n\",\n \" elif choice_name == 'Right Arm':\\n\",\n \"\\n\",\n \" A_reward[1:, :, choice_id] = np.array([[ p_reward, 1.0- p_reward], \\n\",\n \" [1- p_reward, p_reward]])\\n\",\n \" \\n\",\n \"A[1] = A_reward\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {\n \"id\": \"CWKQSusN9Jzk\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": \"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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A[1][:,:,2], 'Payoff structure if playing the Left Arm, for the two contexts')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"g62Zjwg0-iot\"\n },\n \"source\": [\n \"Fill out the choice observation modality, a sub-array of `A` which we'll call `A_choice`\\n\",\n \"\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {\n \"id\": \"VHdgBVSm-mOL\"\n },\n \"outputs\": [],\n \"source\": [\n \"A_choice = np.zeros((len(choice_obs_names), len(context_names), len(choice_names)))\\n\",\n \"\\n\",\n \"for choice_id in range(len(choice_names)):\\n\",\n \"\\n\",\n \" A_choice[choice_id, :, choice_id] = 1.0\\n\",\n \"\\n\",\n \"A[2] = A_choice\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {\n \"id\": \"2O5QpoC8Uc8j\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\\"\\\"\\\" Condition on context (first hidden state factor) and display the remaining indices (outcome and choice state) \\\"\\\"\\\"\\n\",\n \"\\n\",\n \"plot_likelihood(A[2][:,0,:], \\\"Mapping between sensed states and true states\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"FhP5apgR-7zN\"\n },\n \"source\": [\n \"### The `B` array\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {\n \"id\": \"JSiiIJdu4n9b\"\n },\n \"outputs\": [],\n \"source\": [\n \"B = utils.obj_array(num_factors)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"_b7Fyz0T59e0\"\n },\n \"source\": [\n \" Fill out the context state factor dynamics, a sub-array of `B` which we'll call `B_context`\\n\",\n \"\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {\n \"id\": \"lVtIXiyq6EHo\"\n },\n \"outputs\": [],\n \"source\": [\n \"B_context = np.zeros( (len(context_names), len(context_names), len(context_action_names)) )\\n\",\n \"\\n\",\n \"B_context[:,:,0] = np.eye(len(context_names))\\n\",\n \"\\n\",\n \"B[0] = B_context\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"FzDc6PLG5Mof\"\n },\n \"source\": [\n \"Fill out the choice factor dynamics, a sub-array of `B` which we'll call `B_choice`\\n\",\n \"\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {\n \"id\": \"--5HyEYt42Q8\"\n },\n \"outputs\": [],\n \"source\": [\n \"B_choice = np.zeros( (len(choice_names), len(choice_names), len(choice_action_names)) )\\n\",\n \"\\n\",\n \"for choice_i in range(len(choice_names)):\\n\",\n \" \\n\",\n \" B_choice[choice_i, :, choice_i] = 1.0\\n\",\n \"\\n\",\n \"B[1] = B_choice\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"ll-mBL_2_McK\"\n },\n \"source\": [\n \"### The `C` vectors\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {\n \"id\": \"ib54P_VFvjk0\"\n },\n \"outputs\": [],\n \"source\": [\n \"\\\"\\\"\\\" Explain `obj_array_zeros` and how you don't have to populate them necessarily \\\"\\\"\\\"\\n\",\n \"C = utils.obj_array_zeros(num_obs)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 17,\n \"metadata\": {\n \"id\": \"4JlKcepO_KgA\"\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": \"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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"from pymdp.maths import softmax\\n\",\n \"\\n\",\n \"C_reward = np.zeros(len(reward_obs_names))\\n\",\n \"C_reward[1] = -4.0 \\n\",\n \"C_reward[2] = 2.0 \\n\",\n \"\\n\",\n \"C[1] = C_reward\\n\",\n \"\\n\",\n \"plot_beliefs(softmax(C_reward), title_str = \\\"Prior preferences\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"lJXKG-IV_qm1\"\n },\n \"source\": [\n \"### The `D` vectors\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 18,\n \"metadata\": {\n \"id\": \"MJTKm27fv_Rf\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Beliefs about which arm is better: [0.5 0.5]\\n\",\n \"Beliefs about starting location: [1. 0. 0. 0.]\\n\"\n ]\n }\n ],\n \"source\": [\n \"D = utils.obj_array(num_factors)\\n\",\n \"\\n\",\n \"D_context = np.array([0.5,0.5])\\n\",\n \"\\n\",\n \"D[0] = D_context\\n\",\n \"\\n\",\n \"D_choice = np.zeros(len(choice_names))\\n\",\n \"\\n\",\n \"D_choice[choice_names.index(\\\"Start\\\")] = 1.0\\n\",\n \"\\n\",\n \"D[1] = D_choice\\n\",\n \"\\n\",\n \"print(f'Beliefs about which arm is better: {D[0]}')\\n\",\n \"print(f'Beliefs about starting location: {D[1]}')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"fP7NySzAhWgf\"\n },\n \"source\": [\n \"## **Constructing an `Agent`**\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 19,\n \"metadata\": {\n \"id\": \"ls9VoZX__0Vp\"\n },\n \"outputs\": [],\n \"source\": [\n \"from pymdp.agent import Agent\\n\",\n \"\\n\",\n \"my_agent = Agent(A = A, B = B, C = C, D = D)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"4Xu-ZVZBh_wH\"\n },\n \"source\": [\n \"Define a class for the 2-armed bandit environment (AKA the _generative process_)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 20,\n \"metadata\": {\n \"id\": \"LjxoLs67AXwR\"\n },\n \"outputs\": [],\n \"source\": [\n \"class TwoArmedBandit(object):\\n\",\n \"\\n\",\n \" def __init__(self, context = None, p_hint = 1.0, p_reward = 0.8):\\n\",\n \"\\n\",\n \" self.context_names = [\\\"Left-Better\\\", \\\"Right-Better\\\"]\\n\",\n \"\\n\",\n \" if context is None:\\n\",\n \" self.context = self.context_names[utils.sample(np.array([0.5, 0.5]))] # randomly sample which bandit arm is better (Left or Right)\\n\",\n \" else:\\n\",\n \" self.context = context\\n\",\n \"\\n\",\n \" self.p_hint = p_hint\\n\",\n \" self.p_reward = p_reward\\n\",\n \"\\n\",\n \" self.reward_obs_names = ['Null', 'Loss', 'Reward']\\n\",\n \" self.hint_obs_names = ['Null', 'Hint-left', 'Hint-right']\\n\",\n \"\\n\",\n \" def step(self, action):\\n\",\n \"\\n\",\n \" if action == \\\"Move-start\\\":\\n\",\n \" observed_hint = \\\"Null\\\"\\n\",\n \" observed_reward = \\\"Null\\\"\\n\",\n \" observed_choice = \\\"Start\\\"\\n\",\n \" elif action == \\\"Get-hint\\\":\\n\",\n \" if self.context == \\\"Left-Better\\\":\\n\",\n \" observed_hint = self.hint_obs_names[utils.sample(np.array([0.0, self.p_hint, 1.0 - self.p_hint]))]\\n\",\n \" elif self.context == \\\"Right-Better\\\":\\n\",\n \" observed_hint = self.hint_obs_names[utils.sample(np.array([0.0, 1.0 - self.p_hint, self.p_hint]))]\\n\",\n \" observed_reward = \\\"Null\\\"\\n\",\n \" observed_choice = \\\"Hint\\\"\\n\",\n \" elif action == \\\"Play-left\\\":\\n\",\n \" observed_hint = \\\"Null\\\"\\n\",\n \" observed_choice = \\\"Left Arm\\\"\\n\",\n \" if self.context == \\\"Left-Better\\\":\\n\",\n \" observed_reward = self.reward_obs_names[utils.sample(np.array([0.0, 1.0 - self.p_reward, self.p_reward]))]\\n\",\n \" elif self.context == \\\"Right-Better\\\":\\n\",\n \" observed_reward = self.reward_obs_names[utils.sample(np.array([0.0, self.p_reward, 1.0 - self.p_reward]))]\\n\",\n \" elif action == \\\"Play-right\\\":\\n\",\n \" observed_hint = \\\"Null\\\"\\n\",\n \" observed_choice = \\\"Right Arm\\\"\\n\",\n \" if self.context == \\\"Right-Better\\\":\\n\",\n \" observed_reward = self.reward_obs_names[utils.sample(np.array([0.0, 1.0 - self.p_reward, self.p_reward]))]\\n\",\n \" elif self.context == \\\"Left-Better\\\":\\n\",\n \" observed_reward = self.reward_obs_names[utils.sample(np.array([0.0, self.p_reward, 1.0 - self.p_reward]))]\\n\",\n \" \\n\",\n \" obs = [observed_hint, observed_reward, observed_choice]\\n\",\n \"\\n\",\n \" return obs\\n\",\n \" \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"h6IeX_BlhmBy\"\n },\n \"source\": [\n \"Now we'll write a function that will take the agent, the environment, and a time length and run the active inference loop\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 21,\n \"metadata\": {\n \"id\": \"In-AoaGQDdQH\"\n },\n \"outputs\": [],\n \"source\": [\n \"def run_active_inference_loop(my_agent, my_env, T = 5):\\n\",\n \"\\n\",\n \" \\\"\\\"\\\" Initialize the first observation \\\"\\\"\\\"\\n\",\n \" obs_label = [\\\"Null\\\", \\\"Null\\\", \\\"Start\\\"] # agent observes itself seeing a `Null` hint, getting a `Null` reward, and seeing itself in the `Start` location\\n\",\n \" obs = [hint_obs_names.index(obs_label[0]), reward_obs_names.index(obs_label[1]), choice_obs_names.index(obs_label[2])]\\n\",\n \" \\n\",\n \" for t in range(T):\\n\",\n \" qs = my_agent.infer_states(obs)\\n\",\n \" plot_beliefs(qs[0], title_str = f\\\"Beliefs about the context at time {t}\\\")\\n\",\n \"\\n\",\n \" q_pi, efe = my_agent.infer_policies()\\n\",\n \" chosen_action_id = my_agent.sample_action()\\n\",\n \"\\n\",\n \" movement_id = int(chosen_action_id[1])\\n\",\n \"\\n\",\n \" choice_action = choice_action_names[movement_id]\\n\",\n \"\\n\",\n \" obs_label = my_env.step(choice_action)\\n\",\n \"\\n\",\n \" obs = [hint_obs_names.index(obs_label[0]), reward_obs_names.index(obs_label[1]), choice_obs_names.index(obs_label[2])]\\n\",\n \"\\n\",\n \" print(f'Action at time {t}: {choice_action}')\\n\",\n \" print(f'Reward at time {t}: {obs_label[1]}')\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"gYeg73orwtHC\"\n },\n \"source\": [\n \"Now all we have to do is define the two-armed bandit environment, choose the length of the simulation, and run the function we wrote above.\\n\",\n \"\\n\",\n \"\\n\",\n \"* Try playing with the hint accuracy and/or reward statistics of the environment - remember this is _different_ than the agent's representation of the reward statistics (i.e. the agent's generative model, e.g. the A or B matrices).\\n\",\n \"\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 22,\n \"metadata\": {\n \"id\": \"Vy7OXyo8wvY0\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Context: Right-Better\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action at time 0: Get-hint\\n\",\n \"Reward at time 0: Null\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action at time 3: Play-right\\n\",\n \"Reward at time 3: Reward\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action at time 4: Play-right\\n\",\n \"Reward at time 4: Loss\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action at time 5: Play-right\\n\",\n \"Reward at time 5: Loss\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action at time 7: Play-right\\n\",\n \"Reward at time 7: Loss\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action at time 8: Play-right\\n\",\n \"Reward at time 8: Reward\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action at time 9: Play-right\\n\",\n \"Reward at time 9: Reward\\n\"\n ]\n }\n ],\n \"source\": [\n \"p_hint_env = 1.0 # this is the \\\"true\\\" accuracy of the hint - i.e. how often does the hint actually signal which arm is better. REMEMBER: THIS IS INDEPENDENT OF HOW YOU PARAMETERIZE THE A MATRIX FOR THE HINT MODALITY\\n\",\n \"p_reward_env = 0.7 # this is the \\\"true\\\" reward probability - i.e. how often does the better arm actually return a reward, as opposed to a loss. REMEMBER: THIS IS INDEPENDENT OF HOW YOU PARAMETERIZE THE A MATRIX FOR THE REWARD MODALITY\\n\",\n \"env = TwoArmedBandit(p_hint = p_hint_env, p_reward = p_reward_env)\\n\",\n \"print(f'Context: {env.context}')\\n\",\n \"\\n\",\n \"T = 10\\n\",\n \"\\n\",\n \"# my_agent = Agent(A = A, B = B, C = C, D = D) # in case you want to re-define the agent, you can run this again\\n\",\n \"\\n\",\n \"run_active_inference_loop(my_agent, env, T = T)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"scuxk92i3Mef\"\n },\n \"source\": [\n \"Now let's try manipulating the agent's prior preferences over reward observations ($\\\\mathbf{C}[1]$) in order to examine the tension between exploration and exploitation.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 23,\n \"metadata\": {\n \"id\": \"B1XpcHlX3Gnj\"\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Context: Right-Better\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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GgS1IjDHRJaoSBLkmNmCjQk2xNsi/J/iQ3jll+Q5KPJPmLJP8zyYbplypJWsqygZ5kFbATuBrYDFyXZPNIsw8Bc1V1OfAHwBumXagkaWmTHKFfCeyvqgeq6kngTmDbsEFVva+qvthPfgC4aLplSpKWs3qCNuuAA4Ppg8CWJdq/CnjPuAVJtgPbAdauXcvCwsJkVY6YX9GtdKZYab+apvlZF6BT2onqo5ME+sSS/DAwBzx/3PKquhW4FWBubq7m5+enuXkJAPuVTnUnqo9OEugPAesH0xf1846Q5CrgF4DnV9WXp1OeJGlSk4yh7wY2Jbk4yRrgWmDXsEGSK4C3ANdU1WemX6YkaTnLBnpVHQJ2APcA9wN3VdXeJLckuaZv9u+BpwHvSnJfkl2LrE6SdIJMNIZeVXcDd4/Mu2lw/aop1yVJOkb+UlSSGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDXCQJekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUiIkCPcnWJPuS7E9y45jl35Xkz5McSvKy6ZcpSVrOsoGeZBWwE7ga2Axcl2TzSLOPA9cD75h2gZKkyayeoM2VwP6qegAgyZ3ANuAjhxtU1YP9sq+egBolSROYJNDXAQcG0weBLSvZWJLtwHaAtWvXsrCwsJLVML+iW+lMsdJ+NU3zsy5Ap7QT1UcnCfSpqapbgVsB5ubman5+/mRuXmcI+5VOdSeqj07yoehDwPrB9EX9PEnSKWSSQN8NbEpycZI1wLXArhNbliTpWC0b6FV1CNgB3APcD9xVVXuT3JLkGoAkz0tyEHg58JYke09k0ZKko000hl5VdwN3j8y7aXB9N91QjCRpRvylqCQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqhIEuSY0w0CWpEQa6JDXCQJekRhjoktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWqEgS5JjTDQJakRBrokNWKiQE+yNcm+JPuT3Dhm+dlJ3tkv/2CSjVOvVJK0pGUDPckqYCdwNbAZuC7J5pFmrwIeqapLgDcCr592oZKkpU1yhH4lsL+qHqiqJ4E7gW0jbbYBv9df/wPge5JkemVKkpazeoI264ADg+mDwJbF2lTVoSSfB54JfHbYKMl2YHs/+ViSfSspWke5gJF9fUbzWOJUZB8dOr4+umGxBZME+tRU1a3ArSdzm2eCJHuqam7WdUiLsY+eHJMMuTwErB9MX9TPG9smyWrgfODhaRQoSZrMJIG+G9iU5OIka4BrgV0jbXYBr+ivvwx4b1XV9MqUJC1n2SGXfkx8B3APsAq4rar2JrkF2FNVu4DfBX4/yX7gc3Shr5PHYSyd6uyjJ0E8kJakNvhLUUlqhIEuSY0w0E9jy/1LBmnWktyW5DNJPjzrWs4EBvppasJ/ySDN2u3A1lkXcaYw0E9fk/xLBmmmqupP6b75ppPAQD99jfuXDOtmVIukU4CBLkmNMNBPX5P8SwZJZxAD/fQ1yb9kkHQGMdBPU1V1CDj8LxnuB+6qqr2zrUo6UpI7gP8FPCfJwSSvmnVNLfOn/5LUCI/QJakRBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqxP8H5w0AOaQW0uwAAAAASUVORK5CYII=\",\n 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action at time 0: Play-left\\n\",\n \"Reward at time 0: Reward\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action at time 3: Play-right\\n\",\n \"Reward at time 3: Reward\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action at time 4: Play-right\\n\",\n \"Reward at time 4: Reward\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action at time 5: Play-right\\n\",\n \"Reward at time 5: Reward\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action at time 6: Play-right\\n\",\n \"Reward at time 6: Reward\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action at time 7: Play-right\\n\",\n \"Reward at time 7: Reward\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Action at time 9: Play-right\\n\",\n \"Reward at time 9: Reward\\n\"\n ]\n }\n ],\n \"source\": [\n \"# change the 'shape' of the agent's reward function\\n\",\n \"C[1][1] = 0.0 # makes the Loss \\\"less aversive\\\" than before (higher prior prior probability assigned to seeing the Loss outcome). This should make the agent less risk-averse / willing to explore both arms, under uncertainty\\n\",\n \"\\n\",\n \"my_agent = Agent(A = A, B = B, C = C, D = D) # redefine the agent with the new preferences\\n\",\n \"env = TwoArmedBandit(p_hint = 0.8, p_reward = 0.8) # re-initialize the environment -- this time, the hint is not always accurate (`p_hint = 0.8`)\\n\",\n \"print(f'Context: {env.context}')\\n\",\n \"\\n\",\n \"run_active_inference_loop(my_agent, env, T = T)\"\n ]\n }\n ],\n \"metadata\": {\n \"colab\": {\n \"collapsed_sections\": [\n \"lu35jiGX4Iae\",\n \"0Icnjv8T4fpx\"\n ],\n \"name\": \"Active Inference with pymdp: Tutorial 2\",\n \"provenance\": []\n },\n \"kernelspec\": {\n \"display_name\": \"Python 3.7.10 ('pymdp_env')\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.8.8\"\n },\n \"vscode\": {\n \"interpreter\": {\n \"hash\": \"43ee964e2ad3601b7244370fb08e7f23a81bd2f0e3c87ee41227da88c57ff102\"\n }\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 0\n}\n" }, { "path": "docs/requirements.txt", "content": "# sphinx <4 required by myst-nb v0.12.0 (Feb 2021)\n# sphinx >=3 required by sphinx-autodoc-typehints v1.11.1 (Oct 2020)\n# sphinx >=3, <4 # old version of sphinx dependency, based on two comments above\n\n# New commit to myst-nb (September 2021) suggests it can work with sphinx >4 (see https://github.com/executablebooks/MyST-NB/commit/9f6fae2da3f1ce3e726320eade079b8e25a878fa)\nsphinx==4.2.0\nsphinx_rtd_theme\nsphinx-autodoc-typehints==1.11.1\njupyter-sphinx>=0.3.2\nmyst-nb\njinja2==3.0.0\n\n# Packages used for notebook execution\nmatplotlib\nnumpy\nseaborn\n." }, { "path": "docs-mkdocs/agent.html", "content": "\n\n \n \n \n \n Redirecting...\n \n \n

Redirecting to api/agent/.

\n \n\n" }, { "path": "docs-mkdocs/algos/index.html", "content": "\n\n \n \n \n \n Redirecting...\n \n \n

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\n \n\n" }, { "path": "docs-mkdocs/api/agent.md", "content": "# `pymdp.agent`\n\n::: pymdp.agent\n options:\n members:\n - Agent\n" }, { "path": "docs-mkdocs/api/algos.md", "content": "# `pymdp.algos`\n\n::: pymdp.algos\n options:\n members:\n - run_factorized_fpi\n - run_mmp\n - run_vmp\n - run_exact_single_factor_hmm_scan\n - hmm_filter_scan_colstoch\n - hmm_smoother_scan_colstoch\n" }, { "path": "docs-mkdocs/api/control.md", "content": "# `pymdp.control`\n\n::: pymdp.control\n options:\n members:\n - Policies\n - construct_policies\n - sample_action\n - sample_policy\n - get_marginals\n - update_posterior_policies\n - update_posterior_policies_inductive\n - compute_expected_state\n - compute_expected_state_and_Bs\n - compute_expected_obs\n - compute_info_gain\n - compute_expected_utility\n - calc_negative_pA_info_gain\n - calc_negative_pB_info_gain\n - compute_neg_efe_policy\n - compute_neg_efe_policy_inductive\n - generate_I_matrix\n - calc_inductive_value_t\n" }, { "path": "docs-mkdocs/api/envs-env.md", "content": "# `pymdp.envs.env`\n\n::: pymdp.envs.env\n options:\n members:\n - make\n - Env\n - PymdpEnv\n" }, { "path": "docs-mkdocs/api/envs-rollout.md", "content": "# `pymdp.envs.rollout`\n\n::: pymdp.envs.rollout\n options:\n members:\n - infer_and_plan\n - rollout\n" }, { "path": "docs-mkdocs/api/index.md", "content": "# API Reference\n\nThis reference is auto-generated from modern modules (`pymdp.*`) using mkdocstrings.\n\nLegacy modules are intentionally excluded from generated API pages and are documented in the [legacy archive](../legacy/index.md).\n\nFor end-to-end loop construction, see the dedicated [`rollout()` guide](../guides/rollout-active-inference-loop.md).\nFor environment abstractions, see `pymdp.envs.env` and `pymdp.envs.rollout` in this API section.\n" }, { "path": "docs-mkdocs/api/inference.md", "content": "# `pymdp.inference`\n\n::: pymdp.inference\n options:\n members:\n - update_posterior_states\n - joint_dist_factor\n - smoothing_ovf\n - smoothing_exact\n" }, { "path": "docs-mkdocs/api/learning.md", "content": "# `pymdp.learning`\n\n::: pymdp.learning\n options:\n members:\n - update_obs_likelihood_dirichlet_m\n - update_obs_likelihood_dirichlet\n - update_state_transition_dirichlet_f\n - update_state_transition_dirichlet\n" }, { "path": "docs-mkdocs/api/maths.md", "content": "# `pymdp.maths`\n\n::: pymdp.maths\n" }, { "path": "docs-mkdocs/api/planning-mcts.md", "content": "# MCTS Planning\n\n::: pymdp.planning.mcts\n" }, { "path": "docs-mkdocs/api/planning-si.md", "content": "# Sophisticated Inference Planning\n\n::: pymdp.planning.si\n" }, { "path": "docs-mkdocs/api/utils.md", "content": "# `pymdp.utils`\n\n::: pymdp.utils\n" }, { "path": "docs-mkdocs/control.html", "content": "\n\n \n \n \n \n Redirecting...\n \n \n

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\n \n\n" }, { "path": "docs-mkdocs/development/release-notes.md", "content": "# Release Notes\n\n## 1.0.0\n\n`pymdp` 1.0.0 is the first major release since the `0.0.7` line. The small\n`v0.0.7.1` patch was primarily packaging-oriented; the substantive story of\nthis release is that `pymdp` is now JAX-first. The primary docs, examples,\ntesting surface, and supported workflows now center on accelerator-friendly,\nbatched, differentiable active inference, while the previous NumPy/object-array\nimplementation is preserved under `pymdp.legacy`.\n\nAlongside the backend transition, this release adds a much richer environment\nand rollout workflow, upgraded inference and planning APIs, variational free\nenergy diagnostics, probabilistic model-fitting workflows built around\n`pybefit` and NumPyro, a JAX-first documentation site, and release-grade\ntesting and notebook execution gates.\n\n### Breaking Changes And Migration\n\nIf you are upgrading from the legacy NumPy backend, start with the\n[NumPy/legacy to JAX migration guide](../migration/numpy-to-jax.md).\n\n- `pymdp.*` now refers to the modern JAX implementation. Legacy NumPy code is\n still available, but it lives under `pymdp.legacy.*`.\n- The `Agent` API is now explicitly JAX- and batch-oriented. In particular,\n `batch_size` replaces the older `apply_batch` naming, and many public\n surfaces now assume a leading batch axis.\n- The `Agent`'s policy set is now stored as a dedicated Equinox module rather\n than a raw ndarray. In practice, `self.policies` is now a structured\n container, and the underlying policy array lives under\n `self.policies.policy_arr`.\n- Policy scoring is now consistently exposed as `neg_efe = -EFE`. In practice,\n `agent.infer_policies(qs)` returns `(q_pi, neg_efe)`, `rollout()` extras use\n `info[\"neg_efe\"]` instead of `info[\"G\"]`, and sophisticated-inference\n planning thresholds use `neg_efe_stop_threshold`.\n- Observation handling is stricter and more explicit. The older\n `onehot_obs` naming is now standardized as `categorical_obs`, and environment\n observations should match the `Agent`'s expected observation format.\n- Randomness is now explicit in the JAX workflow. Sampling and simulation paths\n such as `sample_action()`, `rollout()`, and environment `reset`/`step`\n methods use explicit PRNG keys.\n- JAX workflows are more functional than mutable. Existing code that assumed\n in-place stateful updates on `Agent` objects may need to be rewritten around\n returned values and updated carries.\n- Validation is stricter in several places. For example, `learn_A=True` now\n requires `pA`, and model-shape / normalization errors are surfaced earlier.\n\n### Major New Capabilities\n\n#### JAX-First Core Library And Utilities\n\n- The primary `Agent`, inference, control, learning, and planning APIs are now\n built around JAX arrays and pytrees rather than legacy object-array\n conventions.\n- The core JAX surface is designed to be JIT-friendly and autodiff-compatible,\n with tighter validation around `Distribution` shapes, normalization, and\n model structure.\n- `Agent` methods and related JAX-first library paths are now designed to be\n differentiable, which enables workflows such as fitting or training learned\n front ends around `pymdp`-defined POMDPs, including amortized neural\n encoders.\n- Generative models now support explicit sparse dependency structure through\n `A_dependencies` and `B_dependencies`, making it easier to express structured\n observation models and sparse state-transition graphs without falling back to\n dense all-to-all coupling.\n- JAX-native utility helpers now cover common model-construction workflows such\n as `random_A_array`, `random_B_array`, `make_A_full`,\n `construct_controllable_B`, and factorized categorical helpers, reducing the\n need to rely on `legacy.utils`.\n\n#### Inference, Control, And Planning\n\n- State inference was substantially upgraded. The release includes optimized\n `infer_states` paths, exact HMM associative-scan inference, corrected\n message-passing details for MMP/VMP, and better support for interacting\n `B_dependencies`.\n- Policy scoring and planning semantics were cleaned up and made more explicit.\n The release standardizes `neg_efe` naming and improves reliability in\n parameter-information-gain and inductive policy-scoring paths.\n- Sophisticated-inference planning is now JIT-friendly, and the planning stack\n supports richer deliberation and tree-search workflows.\n- Monte Carlo Tree Search (MCTS) is now part of the sophisticated-inference\n planning surface, giving users a dedicated planning workflow for more complex\n sequential search problems.\n- Canonical variational free energy is now exposed directly as part of the\n public API through `calc_vfe(...)` and `return_info=True` diagnostic paths in\n inference.\n\n#### Environments And Compiled Rollouts\n\n- `pymdp` now has a much clearer JAX-native environment and rollout surface.\n The `Env` abstraction is closer to gymnax-style workflows and is designed to\n work directly with compiled active inference loops.\n- `rollout()` is a new first-class API for compiled active inference loops over\n environments, making it much easier to express full perception-action\n rollouts in JAX-native workflows.\n- `infer_and_plan()` is also a new first-class helper for stepping agents\n through active inference loops with reusable inference-and-action logic.\n- These rollout APIs support explicit key flow, updated-agent carries, and\n learning-aware behavior for online and offline experimental setups.\n- Environments can now emit categorical observations directly, which aligns\n better with the rest of the JAX-first API surface.\n- The release also broadens the environment and demo corpus with updated\n GridWorld and T-maze workflows, plus the cue-chaining environment and\n tutorial as a new example of epistemic foraging and sequential information\n seeking.\n\n#### Model Fitting And Probabilistic Inference\n\n- `pymdp` now supports probabilistic model-fitting workflows through\n [`pybefit`](https://github.com/dimarkov/pybefit) and NumPyro-backed\n inference, making it possible to fit active-inference POMDP parameters to\n behavioral data such as observed outcomes and action sequences.\n- The shipped workflow covers both sampling-based and variational approaches.\n The `fitting_with_pybefit` notebook demonstrates Hamiltonian Monte Carlo via\n NUTS as well as stochastic variational inference with NumPyro-based guides.\n- These model-fitting workflows are designed for batched multi-agent settings,\n which makes it easier to express fitting problems over multiple synthetic or\n observed subjects in one JAX-native pipeline.\n- Installation and contributor setup now expose this workflow directly through\n the `modelfit` extra.\n\n### Docs, Tutorials, And Examples\n\n- The documentation stack was rebuilt around MkDocs and Material, replacing the\n older Sphinx-centered setup for the primary `1.0.0` docs experience.\n- The docs are now intentionally JAX-first. The landing page, quickstart,\n migration guide, rollout guide, environment guide, generated API reference,\n and legacy archive are organized around the modern backend.\n- The notebook gallery is now a first-class part of the docs site, with\n refreshed tutorials spanning environments, planning, inference, learning,\n sparse methods, advanced model construction, neural encoders, and model\n fitting.\n- Legacy material is still preserved in the docs under a dedicated archive path\n for users who need the older NumPy-oriented reference material during\n migration.\n\n### Packaging, Testing, And Contributor Workflow\n\n- The packaging surface now centers on `pyproject.toml` and setuptools-backed\n builds, with explicit optional-dependency extras for `gpu`, `docs`, `nb`,\n and `modelfit` workflows.\n- Notebook execution is now tiered and enforced through manifests: PR CI runs\n the `test/notebooks/ci_notebooks.txt` tier, while nightly coverage runs the\n `test/notebooks/nightly_notebooks.txt` tier.\n- Contributor workflow also improved through notebook sanitation hooks, strict\n docs builds, unit-test coverage reporting, and `pytest-xdist` support.\n\n### Traceability Appendix\n\nThis page is intentionally curated rather than chronological. The following\nrows identify the strongest evidence clusters behind each major section.\n\n| Section | Representative evidence | Key files |\n| --- | --- | --- |\n| JAX-first backend and migration | `57d730d`, `16985dd`, `#360`, `#361`, `#325` | `pymdp/agent.py`, `pymdp/legacy/agent.py`, `pymdp/utils.py`, `docs-mkdocs/migration/numpy-to-jax.md` |\n| Inference, control, and planning | `#315`, `#341`, `#348`, `#349`, `#365`, `#368`, `#370`, `#372` | `pymdp/inference.py`, `pymdp/control.py`, `pymdp/planning/si.py`, `pymdp/planning/mcts.py`, `pymdp/maths.py` |\n| Environments and rollout | `#334`, `#354`, `#369` plus the rollout refactor series | `pymdp/envs/env.py`, `pymdp/envs/rollout.py`, `pymdp/envs/cue_chaining.py`, `docs-mkdocs/guides/rollout-active-inference-loop.md` |\n| Model fitting and probabilistic inference | `873116a`, `ac34a1b`, `623662b` | `examples/model_fitting/fitting_with_pybefit.ipynb`, `test/test_pybefit_model_fitting.py`, `pyproject.toml`, `docs-mkdocs/index.md` |\n| Docs, tutorials, and examples | `9fa629f`, `#354`, `de6ead7` | `mkdocs.yml`, `docs-mkdocs/index.md`, `docs-mkdocs/tutorials/notebooks/index.md`, `docs-mkdocs/getting-started/quickstart-jax.md` |\n| Packaging and contributor workflow | `#364`, `#367`, `#373`, `#375` | `pyproject.toml`, `.github/workflows/test.yaml`, `.github/workflows/nightly-tests.yaml`, `test/notebooks/` |\n" }, { "path": "docs-mkdocs/development/viewing-docs.md", "content": "# Viewing Docs Locally\n\n## Quick commands\n\nFrom repo root:\n\n```bash\nuv sync --no-default-groups --extra docs\n./scripts/docs_build.sh\n./scripts/docs_serve.sh\n```\n\nLocal URL:\n- \n\n## One-shot sync + serve\n\n```bash\n./scripts/docs_sync_and_serve.sh\n```\n\n## RTD preview for PRs\n\n1. Open your PR in GitHub.\n2. Open the Read the Docs build linked to that PR.\n3. Verify nav, notebooks, API pages, and redirects.\n\n## Notes\n- `examples/` notebooks are the source of truth for the notebook gallery.\n- `docs-mkdocs/tutorials/notebooks/examples/` is generated at docs build time by `./scripts/sync_docs_notebooks.sh` and is not intended to be edited by hand.\n- `./scripts/docs_build.sh` and `./scripts/docs_serve.sh` sync curated notebooks automatically before invoking MkDocs.\n- To add notebook docs, update `docs-mkdocs/tutorials/notebooks.manifest`. The sync step will copy the listed notebooks into the generated docs tree.\n- MkDocs source-of-truth content lives in `docs-mkdocs/`.\n- `docs/` is retained as legacy Sphinx-era content for compatibility/history.\n" }, { "path": "docs-mkdocs/env.html", "content": "\n\n \n \n \n \n Redirecting...\n \n \n

Redirecting to api/envs-rollout/.

\n \n\n" }, { "path": "docs-mkdocs/getting-started/installation.md", "content": "# Installation\n\n## Recommended workflow: `uv`\n\n### 1) Create and activate a virtual environment\n```bash\n# from repo root\nuv venv .venv\nsource .venv/bin/activate\n```\n\nIf `.venv` already exists, just activate it:\n\n```bash\nsource .venv/bin/activate\n```\n\n### 2) Sync dependencies\n```bash\nuv sync --group test\n```\n\n### Dependency groups and extras\n\n- `--group test`: test and notebook tooling (`pytest`, `pytest-xdist`, `nbval`, `jupyter`, `ipykernel`) plus common visualization deps (`mediapy`, `pygraphviz`) and model-fitting dependency (`pybefit`).\n- `--extra nb`: optional notebook/media extras (`mediapy`, `pygraphviz`) when notebook visualization is needed outside test tooling.\n- `--extra modelfit`: installs `pybefit` for model-fitting workflows.\n- `--extra gpu`: installs CUDA-enabled JAX packages.\n- `--extra docs`: documentation toolchain (`mkdocs`, `mkdocs-dracula-theme`, `mkdocstrings`, `mkdocs-jupyter`, `mkdocs-redirects`).\n\n`pygraphviz` is only needed for Graphviz-backed notebook visualizations such as the MCTS graph-world demo, but it is included in the current `test` and `nb` dependency sets. On many machines `uv sync --group test` works without any extra steps; if it fails while building `pygraphviz`, use the troubleshooting notes below and then rerun the sync command.\n\nNotebook cells that call `mediapy.show_video(...)` also require a system `ffmpeg`\nbinary. If those cells fail with `Program 'ffmpeg' is not found`, install\n`ffmpeg` using the platform-specific notes below before rerunning the notebook.\n\nCommon `uv` sync patterns:\n\n```bash\n# standard dev/test work\nuv sync --group test\n\n# notebook-heavy workflows\nuv sync --group test --extra nb\n\n# model fitting workflows\nuv sync --group test --extra modelfit\n\n# docs workflow\nuv sync --group test --extra docs\n\n# GPU workflow\nuv sync --group test --extra gpu\n```\n\n## Notebook video rendering (`mediapy`)\n\nNotebook examples that render videos through `mediapy.show_video(...)` need a\nsystem `ffmpeg` binary in addition to the Python package.\n\n### macOS (Homebrew)\n\n```bash\nbrew install ffmpeg\n```\n\n### Ubuntu / Debian\n\n```bash\nsudo apt-get update\nsudo apt-get install -y ffmpeg\n```\n\nOn other platforms, install `ffmpeg` with your system package manager and make\nsure the `ffmpeg` executable is available on `PATH`.\n\n## `pygraphviz` troubleshooting\n\nIf installation fails while building `pygraphviz`, the missing dependency is usually one of:\n\n- Graphviz itself, including the C headers (`graphviz/cgraph.h`)\n- Python development headers for the exact interpreter version in your virtual environment (`Python.h`)\n\n### macOS (Homebrew)\n\nInstall Graphviz with Homebrew before syncing dependencies:\n\n```bash\nbrew install graphviz\n```\n\nIf `pygraphviz` still fails to build, install it explicitly with Homebrew's include and library paths:\n\n```bash\nuv pip install \\\n --config-settings=--global-option=build_ext \\\n --config-settings=--global-option=\"-I$(brew --prefix graphviz)/include\" \\\n --config-settings=--global-option=\"-L$(brew --prefix graphviz)/lib\" \\\n pygraphviz==1.14\n```\n\nThen rerun:\n\n```bash\nuv sync --group test\n```\n\nor, if you only need the notebook/media extras:\n\n```bash\nuv sync --extra nb\n```\n\n### Ubuntu / Debian\n\nInstall the Graphviz runtime, Graphviz development headers, `pkg-config`, and the compiler toolchain before syncing dependencies:\n\n```bash\nsudo apt-get update\nsudo apt-get install -y graphviz libgraphviz-dev pkg-config build-essential\n```\n\nInstall Python development headers that match the interpreter in your environment:\n\n```bash\nsudo apt-get install -y python3-dev\n```\n\nIf you are using a version-specific interpreter that is newer than the system default, install the matching package instead, for example:\n\n```bash\nsudo apt-get install -y python3.12-dev\n```\n\nThen rerun:\n\n```bash\nuv sync --group test\n```\n\nor install the dependency directly inside the active environment:\n\n```bash\nuv pip install pygraphviz==1.14\n```\n\nIf the build output mentions `graphviz/cgraph.h`, install or verify the Graphviz development packages above. If it mentions `Python.h`, install or verify the matching Python development headers.\n\n## Verify docs build\n```bash\n./scripts/docs_build.sh\n```\n\n## Alternative: `pip`\n\nIf you only want package installation (without the `uv` workflow):\n\n```bash\npython3 -m venv .venv\nsource .venv/bin/activate\npip install inferactively-pymdp\n```\n" }, { "path": "docs-mkdocs/getting-started/quickstart-jax.md", "content": "# Quickstart (JAX)\n\nHere are a couple of lines to quickly build an active inference agent and run state inference, policy inference (planning), and action selection. The agent is created with a random generative model comprising two observation modalities and two hidden state factors.\nThe first of the two state factors is controllable via a 3 dimensional action.\n\nThe agent also has uniform preferences (a flat `C` vector) over the observation modalities.\n\n```python\nfrom jax import numpy as jnp, random as jr\nfrom pymdp import utils\nfrom pymdp.agent import Agent\n\nkey = jr.PRNGKey(0)\nkeys = jr.split(key, 3)\n\nnum_obs = [3, 5]\nnum_states = [3, 2]\nnum_controls = [3, 1]\n\nA = utils.random_A_array(keys[0], num_obs, num_states)\nB = utils.random_B_array(keys[1], num_states, num_controls)\nC = utils.list_array_uniform([[no] for no in num_obs])\n\nagent = Agent(A=A, B=B, C=C, batch_size=1)\n\n# Discrete observation indices for each modality\nobs = [jnp.array([1]), jnp.array([2])]\n\n# Use agent.D as the initial empirical prior\nqs, info = agent.infer_states(obs, empirical_prior=agent.D, return_info=True)\n# Optional diagnostic: current variational free energy for each batch element.\nvfe = info[\"vfe\"]\nq_pi, neg_efe = agent.infer_policies(qs)\n\nsample_keys = jr.split(keys[2], agent.batch_size + 1)\naction = agent.sample_action(q_pi, rng_key=sample_keys[1:])\n```\n\nYou can also run a quick agent-environment loop with `rollout()` and\n`PymdpEnv`. For repeated calls, we recommend wrapping `rollout` in `jit`:\n\n```python\nfrom jax import jit\nfrom jax import random as jr\nfrom pymdp import utils\nfrom pymdp.agent import Agent\nfrom pymdp.envs.env import make\nfrom pymdp.envs.rollout import rollout\n\nkey = jr.PRNGKey(1)\nkey_A, key_B, key_rollout = jr.split(key, 3)\n\nnum_obs = [3, 5]\nnum_states = [3, 2]\nnum_controls = [3, 1]\n\nA = utils.random_A_array(key_A, num_obs, num_states)\nB = utils.random_B_array(key_B, num_states, num_controls)\nC = utils.list_array_uniform([[no] for no in num_obs])\nD = utils.list_array_uniform([[ns] for ns in num_states])\n\nagent = Agent(A=A, B=B, C=C, D=D, batch_size=1)\nenv, _ = make(A=A, B=B, D=D)\n\nrollout_jit = jit(rollout, static_argnums=[1, 2]) # env and num_timesteps are static\nlast, info = rollout_jit(\n agent,\n env,\n 20,\n key_rollout,\n)\n\nactions = info[\"action\"]\n```\n\nFor a more in-depth guide to compiled active inference loops, see the dedicated\n[`rollout()` guide](../guides/rollout-active-inference-loop.md).\n" }, { "path": "docs-mkdocs/guides/generative-model-structure.md", "content": "# Thinking in Generative Models in `pymdp`\n\nThis guide explains how to map Active Inference concepts onto the list-based\nmodel representation used in `pymdp`.\n\nFor a model with `F` hidden-state factors and `M` observation modalities over\n`T` timesteps, a common joint factorization is:\n\n$$\n{\\small p\\left(o_{1:T}^{1:M}, s_{1:T}^{1:F}, \\pi;\\,A,B,D\\right)\n= p(\\pi)\\underbrace{p\\left(s_1^{1:F};\\,D\\right)}_{\\text{initial state prior / }D}\n\\prod_{t=1}^{T-1}\\underbrace{p\\left(s_{t+1}^{1:F} \\mid s_t^{1:F}, u_t^\\pi;\\,B\\right)}_{\\text{transition model / }B}\n\\prod_{t=1}^{T}\\underbrace{p\\left(o_t^{1:M} \\mid s_t^{1:F};\\,A\\right)}_{\\text{observation model / }A}.}\n$$\n\nHere, $\\pi$ refers to _policies_; this is a discrete latent variable whose realizations correspond to sequences of\nactions over time, and $u_t^\\pi$ denotes the action entailed by policy $\\pi$ at time $t$.\n\nIn `pymdp`, those terms are typically factorized as:\n\n$$\np\\left(s_1^{1:F};\\,D\\right)\n= \\prod_{f=1}^{F} p\\left(s_1^f;\\,D_f\\right).\n$$\n\n$$\np\\left(s_{t+1}^{1:F} \\mid s_t^{1:F}, u_t^\\pi;\\,B\\right)\n= \\prod_{f=1}^{F}\np\\left(s_{t+1}^f \\mid s_t^{B_{\\mathrm{dependencies}}[f]}, u_t^\\pi;\\,B_f\\right).\n$$\n\n$$\np\\left(o_t^{1:M} \\mid s_t^{1:F};\\,A\\right)\n= \\prod_{m=1}^{M}\np\\left(o_t^m \\mid s_t^{A_{\\mathrm{dependencies}}[m]};\\,A_m\\right).\n$$\n\n## Mental model\n\nUse two independent indexing systems:\n\n1. **Observation modalities** (`m`) index independent sensory channels.\n2. **Hidden-state factors** (`f`) index latent causes.\n\nIn code, this means:\n\n- modality-indexed lists: `A[m]`, `observations[m]`, `C[m]`, `pA[m]`\n- factor-indexed lists: `D[f]`, `qs[f]`, `B[f]`, `pB[f]`\n\n## Observation modalities: `A[m]` and `observations[m]`\n\nEach modality gets its own likelihood tensor:\n\n- `A[m] = P(obs_m | state_{i in A_dependencies[m]})`\n- `observations[m]` is the actual observation for modality `m`\n\nSo if you have two modalities (for example, location and reward), you should\nexpect `len(A) == 2` and your observation input to have two modality entries.\n\n## Hidden-state factors: `D[f]`, `qs[f]`, `B[f]`\n\nEach hidden-state factor gets its own prior, posterior, and transition model:\n\n- `D[f]`: prior over factor-`f` states\n- `qs[f]`: posterior over factor-`f` states\n- `B[f] = P(s_{[f,t+1]} | state_{i in B_dependencies[f]}, action_{j in B_action_dependencies[f]})`\n\nThis means you can reason about each factor semantically (for example, context,\nlocation, or object identity) and keep dimensions aligned by factor index.\n\n## Dependencies connect modalities and factors\n\n`pymdp` lets you be explicit about sparse structure:\n\n- `A_dependencies[m]`: which factors modality `m` depends on\n- `B_dependencies[f]`: which previous factors influence factor `f` transitions\n- `B_action_dependencies[f]`: which action/control factors influence factor `f` transitions\n\nThis is the key to building structured models without forcing every modality to\ndepend on every factor.\n\n## Minimal indexing example\n\n```python\n# Two modalities\n# m=0 -> location observation\n# m=1 -> reward observation\nA = [A_location, A_reward]\nobs = [obs_location, obs_reward]\n\n# Two hidden-state factors\n# f=0 -> location state\n# f=1 -> context state\nD = [D_location, D_context]\nqs = [qs_location, qs_context]\nB = [B_location, B_context]\n```\n\nRead this as:\n\n- `A[1]` defines how reward observations are generated.\n- `qs[0]` is your current belief over location states.\n- `B[1]` defines context dynamics.\n\n## Common shape/indexing pitfalls\n\n1. `len(observations)` does not match `len(A)`.\n2. Mixing modality index `m` and factor index `f`.\n3. `A_dependencies`, `B_dependencies`, or `B_action_dependencies` indices not matching your list layout.\n4. Passing raw integer observations when your setup expects categorical vectors\n (or vice versa).\n\n## How this maps to the agent loop\n\nAt each step:\n\n1. infer states with `infer_states(...)` to update `qs[f]`,\n2. infer policies with `infer_policies(qs)`,\n3. sample actions and propagate beliefs through `B[f]`.\n\nFor end-to-end loops, combine this mental model with the\n[`rollout()` guide](rollout-active-inference-loop.md).\n" }, { "path": "docs-mkdocs/guides/pymdp-env.md", "content": "# `PymdpEnv`: Building JAX Environments from Generative Models\n\n`pymdp` environments implement the `Env` interface:\n\n- `reset(key, state=None, env_params=None) -> (obs, state)`\n- `step(key, state, action, env_params=None) -> (obs, next_state)`\n\nIf these methods are JAX/JIT compatible, the environment can be used directly\nwith [`rollout()`](rollout-active-inference-loop.md) for fast compiled\nagent-environment loops.\n\n## Two ways to build an environment\n\n1. Subclass `Env` for fully custom dynamics and observation logic.\n2. Use `PymdpEnv` when your environment is a discrete POMDP generative process\n defined by a discrete observation model `A`, discrete transition model `B`, and\n discrete distribution over initial states `D`.\n\n## Using `PymdpEnv`\n\n`PymdpEnv` represents environments with:\n\n- `A`: categorical emission model(s), `P(obs_m | hidden states)`\n- `B`: categorical transition model(s), `P(s_{t+1} | s_t, action)`\n- `D`: initial hidden-state priors\n\nSparse structure is controlled with:\n\n- `A_dependencies[m]`\n- `B_dependencies[f]`\n\nMinimal construction:\n\n```python\nfrom pymdp.envs.env import make\n\nenv, env_params = make(\n A=A,\n B=B,\n D=D,\n A_dependencies=A_dependencies,\n B_dependencies=B_dependencies,\n make_env_params=True,\n)\n```\n\n`env_params` can be passed to `reset`/`step` for batched or per-run parameter\ncontrol, while the `env` instance keeps default `A`, `B`, and `D`.\n\n## Writing a custom `Env`\n\nFor non-POMDP or richer simulators, subclass `Env` and implement `reset` and\n`step` directly. Keep all randomness explicit through JAX keys (`jax.random`)\nand avoid hidden stateful randomness so behavior remains JIT-safe and\nreproducible.\n\n## Practical notes\n\n- Prefer array shapes and dependency indices that match your agent model.\n- Use `env.generate_env_params(batch_size=...)` when you need batched\n environment parameters.\n- If your environment methods are not JIT-compatible, use manual loops instead\n of `rollout()`.\n" }, { "path": "docs-mkdocs/guides/rollout-active-inference-loop.md", "content": "# Using `rollout()` for compiled active inference loops\n\n`rollout()` runs repeated inference, planning, action sampling, and environment stepping for a fixed horizon.\nInternally, it uses `jax.lax.scan`, so direct calls are valid and JAX-friendly.\n\n## When to use it\n- The `.step()` and `.reset()` methods of your `Env` can be JIT-compiled.\n This includes compatibility with `pymdp`'s native `PymdpEnv`, as well as existing JAX RL environment frameworks (see for example [gymnax](https://github.com/RobertTLange/gymnax), [jumanji](https://github.com/instadeepai/jumanji), and [navix](https://github.com/epignatelli/navix)).\n- You want high-throughput simulations by compiling the full closed-loop interaction once and executing it efficiently across many rollouts.\n- You want a single, consistent API for multi-step active inference rollouts with explicit PRNG key threading.\n\n## Required inputs\n- `agent`: `pymdp.agent.Agent`\n- `env`: `pymdp.envs.env.Env`-compatible object\n- `num_timesteps`: integer horizon\n- `rng_key`: JAX PRNG key\n\n## Optional inputs\n- `initial_carry`: override initial rollout carry\n- `policy_search`: custom policy search function\n- `env_params`: batched environment parameters\n\n## Canonical usage\n\n```python\nfrom jax import random as jr\nfrom pymdp.envs.rollout import rollout\n\nrng_key = jr.PRNGKey(0)\nlast, info = rollout(agent, env, 20, rng_key)\n```\n\nFor repeated calls with fixed `env` and `num_timesteps`, we recommend wrapping\n`rollout` with `jit` so XLA can cache the compiled program:\n\n```python\nfrom jax import jit\nfrom jax import random as jr\nfrom pymdp.envs.rollout import rollout\n\nrng_key = jr.PRNGKey(0)\nrollout_jit = jit(rollout, static_argnums=[1, 2]) # env and num_timesteps are static\n\nlast, info = rollout_jit(\n agent,\n env,\n 20,\n rng_key,\n)\n```\n\n## Reproducible key flow\n\n`rollout()` internally splits keys per step and per batch. For deterministic re-runs:\n\n1. pass in the same `rng_key` seed,\n2. keep environment params/initial carry identical,\n3. avoid hidden non-JAX randomness inside your environment's `.step()` or `.reset()` methods.\n\n## Batched runs and carry\n\n- `agent.batch_size` controls parallel batch dimension.\n- `initial_carry` can override auto-initialized state (for warm-starting).\n\n## Relationship to manual loops\n\n`rollout()` repeatedly applies the one-step helper `infer_and_plan` internally\nusing `jax.lax.scan`.\n\nUse manual loops when:\n\n- your environment's `.step()` and `.reset()` methods cannot be JITTed.\n- you need custom per-step side effects that don't respect the active inference logic of `infer_and_plan`.\n\nFor JAX-based environments, we recommend using `rollout()`, as it's usually simpler and less error-prone.\n\n## Debugging checklist\n\n1. Shape mismatch: check observation/action histories and factor dimensions.\n2. Stochastic sampling errors: ensure valid RNG keys are threaded.\n3. Sequence methods (`mmp`, `vmp`): ensure `past_actions` and valid windows are correct.\n4. Learning updates: verify `learn_A`/`learn_B` flags and action alignment.\n\n## Cross-links\n- [Quickstart (JAX)](../getting-started/quickstart-jax.md)\n- [API: `pymdp.envs.rollout`](../api/envs-rollout.md)\n" }, { "path": "docs-mkdocs/index.md", "content": "# Welcome to pymdp's documentation!\n\n`pymdp` is a Python package for simulating Active Inference agents in\ndiscrete-state Markov Decision Process environments. For background and\nmotivation, see the companion JOSS paper:\n[`pymdp: A Python library for active inference in discrete state spaces`](https://joss.theoj.org/papers/10.21105/joss.04098).\n\nThis documentation focuses on the JAX backend (the default backend since the 1.0.0 release), which supports:\n\n
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\n\n![Cue-chaining demo](assets/cue-chaining-demo.gif){ width=\"880\" }\n\n## Start here\n- [Installation](getting-started/installation.md)\n- [Quickstart (JAX)](getting-started/quickstart-jax.md)\n- [NumPy/legacy to JAX migration guide](migration/numpy-to-jax.md)\n- [Using rollout() for compiled active inference loops](guides/rollout-active-inference-loop.md)\n- [PymdpEnv and custom environments](guides/pymdp-env.md)\n- [Thinking in generative models in `pymdp`](guides/generative-model-structure.md)\n- [Notebook gallery](tutorials/notebooks/index.md)\n\n## API reference\n- [API overview](api/index.md)\n\n## Legacy docs\nLegacy/NumPy material is preserved under an archive path:\n\n- [Legacy/NumPy archive](legacy/index.md)\n" }, { "path": "docs-mkdocs/inference.html", "content": "\n\n \n \n \n \n Redirecting...\n \n \n

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\n \n\n" }, { "path": "docs-mkdocs/legacy/index.md", "content": "# Legacy / NumPy Archive\n\n`pymdp/legacy` is preserved for compatibility and historical context.\n\n## Status\n- Legacy modules are frozen and not the primary API path.\n- New examples, docs, and feature development target modern JAX modules.\n\n## Mapping (legacy -> modern)\n- `pymdp.legacy.agent` -> `pymdp.agent`\n- `pymdp.legacy.inference` -> `pymdp.inference`\n- `pymdp.legacy.control` -> `pymdp.control`\n- `pymdp.legacy.learning` -> `pymdp.learning`\n- `pymdp.legacy.maths` -> `pymdp.maths`\n- `pymdp.legacy.utils` -> `pymdp.utils`\n\n## Next step\nUse the [NumPy/legacy to JAX migration guide](../migration/numpy-to-jax.md).\n" }, { "path": "docs-mkdocs/migration/numpy-to-jax.md", "content": "# NumPy/legacy to JAX Migration\n\nThis guide is for users moving from `pymdp.legacy` (NumPy/object-array style) to the [JAX](https://github.com/jax-ml/jax) backend of `pymdp`.\n\n## Key concept shifts\n\n| Legacy NumPy | JAX |\n|---|---|\n| `numpy.ndarray(dtype=object)` collections | pytrees/lists of `jax.Array` |\n| `np.random` global RNG | explicit `jr.PRNGKey` threading |\n| stateful loops with implicit mutation | functional updates with explicit returns |\n| mutable attribute assignment (`agent.x = ...`) | functional pytree updates (`eqx.tree_at(...)`) |\n| `pymdp.legacy.*` modules | `pymdp.*` modern JAX-based modules |\n\n## API differences to update\n\n1. Policy inference now takes current beliefs as inputs, since they are no longer stored internally on the agent.\n\n # legacy NumPy\n q_pi, G = agent.infer_policies()\n\n # JAX\n q_pi, neg_efe = agent.infer_policies(qs)\n\n Note: in SPM-style notation this same policy score is often called `G`\n (`G = neg_efe = -EFE`).\n\n2. Stochastic functions require explicit random keys. Common examples in\n `pymdp` include action/policy sampling (for example\n `agent.sample_action(..., rng_key=...)`), random generative model\n initialization utilities such as `utils.random_A_array(...)`,\n `utils.random_B_array(...)`, and `utils.random_factorized_categorical(...)`,\n rollout execution (`rollout(..., rng_key=...)`), and stochastic\n environment methods (`env.reset(key, ...)`, `env.step(key, ...)`).\n\n # legacy NumPy\n action = agent.sample_action()\n\n # JAX\n keys = jr.split(rng_key, agent.batch_size + 1)\n action = agent.sample_action(q_pi, rng_key=keys[1:])\n\n3. Keep observation preprocessing consistent.\n - If `categorical_obs=False`, pass discrete indices.\n - If `categorical_obs=True`, pass normalized categorical vectors.\n\n## Batching and `batch_size`\n\nMost of `pymdp`'s JAX APIs expect a leading `batch_size` dimension on most\narrays (for example state/parameter priors and posteriors). This makes it easy\nto parallelize with [`jax.vmap`](https://docs.jax.dev/en/latest/_autosummary/jax.vmap.html).\n\nDefaults to keep in mind:\n\n- `Agent(..., batch_size=1)` is the default.\n- By default, `Env` objects are typically unbatched (for example `env.A/B/D`\n have no leading batch axis), while `Agent` leaves are batch-shaped.\n- In the default single-agent case, many arrays therefore appear as `(1, ...)`.\n\nWhen migrating from legacy single-agent code, keep these points in mind:\n\n- Multi-agent simulations (including parallel parameter sweeps) require batched\n per-agent information (observations, beliefs, parameters, preferences, and\n some hyperparameters).\n- In `Agent.__init__`, if you pass unbatched `A`/`B` with `batch_size=N`, the\n tensors are broadcast to `(N, ...)`.\n- If inputs are already batched with leading dimension `1` and `batch_size>1`,\n they are also broadcast to `batch_size`.\n- If the leading dimension is batched but neither `1` nor `batch_size`, a\n `ValueError` is raised.\n\nTypical multi-agent setup pattern:\n\n```python\nbatch_size = 3\nagent = Agent(A=A, B=B, C=C, D=D, batch_size=batch_size)\n\n# One discrete modality for 3 parallel agents: shape (batch_size, 1)\nobs = [jnp.array([[0], [2], [3]])]\nqs = agent.infer_states(obs, empirical_prior=agent.D)\n```\n\nFor environment-side batching, either:\n\n- Keep a single (unbatched) environment and run batched agents against shared\n `env.A/B/D`.\n- Pass batched `env_params` (for example via\n `env.generate_env_params(batch_size=...)`) when using `rollout()`. Parameters\n inside `env_params` should also carry a leading `batch_size` dimension\n aligned to the `Agent`.\n\n## Updating `Agent` fields in JAX\n\nThe `Agent` class is an [Equinox](https://github.com/patrick-kidger/equinox)\nmodule. In practice, this means you should avoid mutable-style setter updates\nlike:\n\n```python\nagent.A = new_A\nagent.B = new_B\n```\n\nInstead, use Equinox-style functional updates with `eqx.tree_at(...)`:\n\n```python\nimport equinox as eqx\n\nagent = eqx.tree_at(lambda x: (x.A,), agent, (new_A,))\nagent = eqx.tree_at(lambda x: (x.B,), agent, (new_B,))\n```\n\nIf you change static `Agent` fields (for example model dimensions, dependency\nstructure, or static hyperparameters such as number of policies), JAX will\ntrigger recompiles of agent-specific JIT-compiled methods such as\n`infer_states`, `infer_policies`, and related methods used during rollouts.\n\nThis is the pattern used near the end of\n`infer_parameters()` in `pymdp/agent.py`, where after a learning update, the new `A`/`B` (and, when\nenabled, `I`) arrays are written back into a new `Agent` instance.\n\n## Randomness migration\n\nUse explicit key flow everywhere:\n\n```python\nrng_key = jr.PRNGKey(0)\nrng_key, key_infer, key_action = jr.split(rng_key, 3)\n\nqs = agent.infer_states(obs, empirical_prior=agent.D)\nq_pi, _ = agent.infer_policies(qs)\nkeys = jr.split(key_action, agent.batch_size + 1)\naction = agent.sample_action(q_pi, rng_key=keys[1:])\n```\n\nOther frequently used stochastic APIs that also require explicit keys:\n- `utils.random_A_array(...)`\n- `utils.random_B_array(...)`\n- `utils.random_factorized_categorical(...)`\n- `utils.generate_agent_spec(..., key=...)`\n- `rollout(..., rng_key=...)`\n- stochastic `env.reset(key, ...)` / `env.step(key, ...)`\n\nAvoid `np.random` when using the new JAX backend (see also\n[this post](https://builtin.com/data-science/numpy-random-seed), which\nencourages caution when working with `np.random`).\n\n## NumPy-to-JAX worked conversion\n\n```python\n# legacy NumPy\nfrom pymdp.legacy.agent import Agent as LegacyAgent\nfrom pymdp.legacy import utils as legacy_utils\nA = legacy_utils.random_A_matrix([3], [2])\nB = legacy_utils.random_B_matrix([2], [2])\nagent = LegacyAgent(A=A, B=B)\nobs = [1]\nqs = agent.infer_states(obs)\nq_pi, G = agent.infer_policies()\naction = agent.sample_action()\n```\n\n```python\n# JAX\nfrom jax import random as jr\nfrom pymdp.agent import Agent\nfrom pymdp import utils\n\nkey = jr.PRNGKey(0)\nkeys = jr.split(key, 3)\nA = utils.random_A_array(keys[0], [3], [2])\nB = utils.random_B_array(keys[1], [2], [2])\nagent = Agent(A=A, B=B)\nobs = [1]\nqs = agent.infer_states(obs, empirical_prior=agent.D)\nq_pi, neg_efe = agent.infer_policies(qs)\naction_keys = jr.split(keys[2], agent.batch_size + 1)\naction = agent.sample_action(q_pi, rng_key=action_keys[1:])\n```\n\n## Common migration pitfalls\n\n1. Missing batch-size dimension for `observations`, `actions`, `qs`, or parameters (`A`, `B`, `C`, `D`).\n2. Missing `empirical_prior` argument in `infer_states`.\n3. Missing `rng_key`/`key` in stochastic calls (for example `sample_action`,\n random model constructors, `rollout`, or stochastic `env.reset`/`env.step`).\n4. Mixing `numpy.ndarray` into JAX-only paths.\n5. Forgetting sequence action-history shape `(T-1, num_factors)`.\n\n## Migration done checklist\n\n1. No imports from `pymdp.legacy` in active scripts/notebooks.\n2. Randomness uses explicit `jr.PRNGKey` flow.\n3. `infer_policies(qs)` and `sample_action(q_pi, rng_key=...)` usage updated.\n4. Tests pass (`pytest test`).\n5. Notebook/docs examples run with API.\n" }, { "path": "docs-mkdocs/notebooks/active_inference_from_scratch.html", "content": "\n\n \n \n \n \n Redirecting...\n \n \n

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:nth-child(2) code,\n.doc .doc-contents > table tr > :first-child:nth-last-child(2) code {\n white-space: nowrap;\n}\n\n/* Override Dracula's default purple inline code chip for better contrast. */\narticle p code,\narticle li code,\narticle td code,\narticle th code,\narticle dt code,\narticle dd code,\narticle blockquote code,\narticle a code,\narticle h1 code,\narticle h2 code,\narticle h3 code,\narticle h4 code,\narticle h5 code,\narticle h6 code {\n background: var(--pymdp-inline-code-bg);\n border: 1px solid var(--pymdp-inline-code-border);\n border-radius: 6px;\n color: var(--pymdp-inline-code-fg);\n font-family: \"IBM Plex Mono\", \"Fira Code\", monospace;\n padding: 0.08rem 0.32rem;\n}\n\n/* Notebook pages: align mkdocs-jupyter output with the Dracula site shell. */\n.jupyter-wrapper {\n margin-block: 1.5rem;\n}\n\n.jupyter-wrapper [data-jp-theme-light=\"false\"] {\n --jp-layout-color0: #282a36;\n --jp-layout-color1: #21222c;\n --jp-layout-color2: #343746;\n --jp-layout-color3: #44475a;\n --jp-layout-color4: #6272a4;\n --jp-border-color0: rgba(139, 233, 253, 0.16);\n --jp-border-color1: rgba(139, 233, 253, 0.14);\n --jp-border-color2: rgba(139, 233, 253, 0.08);\n --jp-border-color3: rgba(139, 233, 253, 0.06);\n --jp-ui-font-color0: #f8f8f2;\n --jp-ui-font-color1: rgba(248, 248, 242, 0.92);\n --jp-ui-font-color2: rgba(248, 248, 242, 0.66);\n --jp-content-font-color0: #f8f8f2;\n --jp-content-font-color1: rgba(248, 248, 242, 0.92);\n --jp-content-font-color2: rgba(248, 248, 242, 0.7);\n --jp-content-link-color: #8be9fd;\n --jp-cell-editor-background: #191a21;\n --jp-cell-editor-active-background: #15161c;\n --jp-cell-editor-border-color: rgba(139, 233, 253, 0.14);\n --jp-rendermime-table-row-background: rgba(255, 255, 255, 0.02);\n --jp-rendermime-table-row-hover-background: rgba(139, 233, 253, 0.05);\n --jp-mirror-editor-keyword-color: #ff79c6;\n --jp-mirror-editor-atom-color: #bd93f9;\n --jp-mirror-editor-number-color: #bd93f9;\n 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{\n margin-bottom: 1rem;\n}\n\n.jupyter-wrapper .jp-Cell:last-child {\n margin-bottom: 0;\n}\n\n.jupyter-wrapper .jp-InputArea-editor,\n.jupyter-wrapper .jp-OutputArea-child,\n.jupyter-wrapper .jp-RenderedHTMLCommon table,\n.jupyter-wrapper .jp-RenderedText pre {\n border-radius: 12px;\n}\n\n.jupyter-wrapper .jp-InputArea-editor {\n border: 1px solid rgba(139, 233, 253, 0.1);\n box-shadow: none;\n}\n\n.jupyter-wrapper .jp-OutputArea-child {\n background: rgba(17, 18, 23, 0.38);\n border: 1px solid rgba(139, 233, 253, 0.06);\n padding: 0.75rem;\n}\n\n.jupyter-wrapper .jp-InputPrompt,\n.jupyter-wrapper .jp-OutputPrompt {\n color: #8be9fd;\n font-size: 0.78rem;\n opacity: 0.82;\n}\n\n.jupyter-wrapper .jp-RenderedHTMLCommon p,\n.jupyter-wrapper .jp-RenderedHTMLCommon li {\n color: var(--jp-content-font-color1);\n}\n\n.jupyter-wrapper .jp-RenderedHTMLCommon a {\n color: #8be9fd;\n}\n\n.jupyter-wrapper .jp-RenderedHTMLCommon table {\n background: rgba(17, 18, 23, 0.22);\n overflow: hidden;\n}\n\n.jupyter-wrapper .jp-RenderedImage img,\n.jupyter-wrapper .jp-RenderedSVG svg {\n border-radius: 12px;\n}\n\n.pymdp-sidebar-logo {\n display: block;\n margin: 0.35rem auto 1.4rem;\n height: auto;\n max-width: 100%;\n width: min(240px, 100%) !important;\n}\n" }, { "path": "docs-mkdocs/tutorials/index.md", "content": "# Tutorials\n\nUse this section for runnable, example-driven materials sourced from Jupyter\nnotebooks under `examples/`.\n\nFor focused conceptual/how-to docs, use the Guides section.\n\n- [Notebook gallery](notebooks/index.md)\n- [`rollout()` compiled loop guide](../guides/rollout-active-inference-loop.md)\n- [NumPy/legacy to JAX migration guide](../migration/numpy-to-jax.md)\n" }, { "path": "docs-mkdocs/tutorials/notebooks/index.header.md", "content": "## For developers\n\nThe notebook listings above are auto-generated by `./scripts/sync_docs_notebooks.sh`.\n\nSource notebooks live under `examples/`. The mirrored notebooks under\n`docs-mkdocs/tutorials/notebooks/examples/` are generated build artifacts.\n\nTo add a notebook:\n\n1. Add a path to `docs-mkdocs/tutorials/notebooks.manifest`.\n2. Run `./scripts/sync_docs_notebooks.sh`.\n" }, { "path": "docs-mkdocs/tutorials/notebooks/index.md", "content": "# Notebook Gallery\n\n## Curated notebooks\n\n### Getting started\n- [Generative Model Construction (Model/Distribution APIs)](examples/api/model_construction_tutorial.ipynb)\n- [T-Maze Demo](examples/envs/tmaze_demo.ipynb)\n- [T-Maze Task with Distractors](examples/envs/generalized_tmaze_demo.ipynb)\n- [Cue Chaining Demo](examples/envs/cue_chaining_demo.ipynb)\n- [Graph worlds](examples/envs/graph_worlds_demo.ipynb)\n- [Demo: Knapsack Problem](examples/envs/knapsack_demo.ipynb)\n\n### Sophisticated Inference\n- [Validating Sophisticated Inference (SI) Planning Algorithm using the T-Maze Task](examples/experimental/sophisticated_inference/si_tmaze_SIvalidation.ipynb)\n- [Sophisticated inference on a T-Maze Task with Distractors](examples/experimental/sophisticated_inference/si_generalized_tmaze.ipynb)\n- [Sophisticated inference on Graph Worlds](examples/experimental/sophisticated_inference/si_graph_world.ipynb)\n\n### Inductive Inference\n- [Inductive Inference Example](examples/inductive_inference/inductive_inference_example.ipynb)\n- [Inductive Inference Gridworld](examples/inductive_inference/inductive_inference_gridworld.ipynb)\n\n### Parameter Learning\n- [Learning Gridworld](examples/learning/learning_gridworld.ipynb)\n\n### Fitting POMDPs to experimental / behavioral data\n- [Fitting With `pybefit`](examples/model_fitting/fitting_with_pybefit.ipynb)\n\n### Advanced\n- [Working with complex action dependencies](examples/advanced/complex_action_dependency.ipynb)\n- [Using `pymdp` with a neural encoder](examples/advanced/pymdp_with_neural_encoder.ipynb)\n- [Testing optimized inference methods](examples/advanced/infer_states_optimization/methods_test.ipynb)\n- [Sparse Array Benchmarking](examples/sparse/sparse_benchmark.ipynb)\n- [Sophisticated inference with Monte Carlo Tree Search on TMaze with Distractors](examples/experimental/sophisticated_inference/mcts_generalized_tmaze.ipynb)\n- [Sophisticated inference with Monte Carlo Tree Search on Graph World](examples/experimental/sophisticated_inference/mcts_graph_world.ipynb)\n- [Comparing sequential inference algorithms](examples/inference_and_learning/inference_methods_comparison.ipynb)\n\n\n## For developers\n\nThe notebook listings above are auto-generated by `./scripts/sync_docs_notebooks.sh`.\n\nSource notebooks live under `examples/`. The mirrored notebooks under\n`docs-mkdocs/tutorials/notebooks/examples/` are generated build artifacts.\n\nTo add a notebook:\n\n1. Add a path to `docs-mkdocs/tutorials/notebooks.manifest`.\n2. Run `./scripts/sync_docs_notebooks.sh`.\n" }, { "path": "docs-mkdocs/tutorials/notebooks.manifest", "content": "# One notebook path per line, relative to repository root.\nexamples/advanced/complex_action_dependency.ipynb\nexamples/advanced/pymdp_with_neural_encoder.ipynb\nexamples/advanced/infer_states_optimization/methods_test.ipynb\nexamples/api/model_construction_tutorial.ipynb\nexamples/envs/cue_chaining_demo.ipynb\nexamples/envs/generalized_tmaze_demo.ipynb\nexamples/envs/graph_worlds_demo.ipynb\nexamples/envs/knapsack_demo.ipynb\nexamples/envs/tmaze_demo.ipynb\nexamples/experimental/sophisticated_inference/mcts_generalized_tmaze.ipynb\nexamples/experimental/sophisticated_inference/mcts_graph_world.ipynb\nexamples/experimental/sophisticated_inference/si_generalized_tmaze.ipynb\nexamples/experimental/sophisticated_inference/si_graph_world.ipynb\nexamples/experimental/sophisticated_inference/si_tmaze_SIvalidation.ipynb\nexamples/inductive_inference/inductive_inference_example.ipynb\nexamples/inductive_inference/inductive_inference_gridworld.ipynb\nexamples/inference_and_learning/inference_methods_comparison.ipynb\nexamples/learning/learning_gridworld.ipynb\nexamples/model_fitting/fitting_with_pybefit.ipynb\nexamples/sparse/sparse_benchmark.ipynb\n" }, { "path": "examples/__init__.py", "content": "" }, { "path": "examples/advanced/complex_action_dependency.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Complex action dependencies\\n\",\n \"\\n\",\n \"In this notebook, we will show some examples of how to specify and run agents with complex action dependencies. Complex action dependencies refer to situations where a state variables depends on multiple actions or no action. These state transitions tensors have shapes of the form: `[state_dim, *prev_state_dims, *prev_action_dims]`. \\n\",\n \"\\n\",\n \"The general strategy for dealing with this is to flatten the `prev_action_dims` while initializing the agent so that the new B tensor shapes are `[state_dim, *prev_state_dims, math.prod(prev_action_dims)]`. If a state has no action dependency, the new B tensor will have shape `[state_dim, *prev_state_dims, 1]` where 1 stands for a dummy action. All computations will be done in the flattened B tensors and actions will be sampled in the flattened action dimensions. After a flattened action is sampled, one can convert it back to the original action dimensions by calling `agent.decode_multi_actions`. To flatten multi actions, for example from collected data, one can call `agent.encode_multi_actions`.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"from pprint import pprint\\n\",\n \"import itertools\\n\",\n \"import numpy as np\\n\",\n \"from jax import numpy as jnp, random as jr\\n\",\n \"from jax import tree_util as jtu\\n\",\n \"\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp import distribution\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Multiple action dependencies\\n\",\n \"In this example, some states depend on multiple actions. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"A_dependencies [[0]]\\n\",\n \"B_dependencies [[0], [1]]\\n\",\n \"B_action_dependencies [[0, 1], [0]]\\n\",\n \"original control dims [2, 3]\\n\",\n \"flattened control dims [6, 2]\\n\",\n \"original B shapes [(4, 4, 2, 3), (4, 4, 2)]\\n\",\n \"flattened B shapes [(1, 4, 4, 6), (1, 4, 4, 2)]\\n\",\n \"B normalized [Array(True, dtype=bool), Array(True, dtype=bool)]\\n\",\n \"B flat normalized [Array(True, dtype=bool), Array(True, dtype=bool)]\\n\",\n \"\\n\",\n \"\\n\",\n \"prior\\n\",\n \"[Array([[0. , 0.25, 0.25, 0.5 ]], dtype=float32),\\n\",\n \" Array([[0. , 0.25, 0.25, 0.5 ]], dtype=float32)]\\n\",\n \"post\\n\",\n \"[Array([[[0., 0., 1., 0.]]], dtype=float32),\\n\",\n \" Array([[[0. , 0.25, 0.25, 0.5 ]]], dtype=float32)]\\n\",\n \"action\\n\",\n \"Array([[0, 0]], dtype=int32)\\n\",\n \"action_multi\\n\",\n \"Array([[0, 0]], dtype=int32)\\n\",\n \"action_reconstruct\\n\",\n \"Array([[0, 0]], dtype=int32)\\n\"\n ]\n }\n ],\n \"source\": [\n \"model_description = {\\n\",\n \" \\\"observations\\\": {\\n\",\n \" \\\"o1\\\": {\\\"elements\\\": [\\\"A\\\", \\\"B\\\", \\\"C\\\", \\\"D\\\"], \\\"depends_on\\\": [\\\"s1\\\"]},\\n\",\n \" },\\n\",\n \" \\\"controls\\\": {\\\"c1\\\": {\\\"elements\\\": [\\\"up\\\", \\\"down\\\"]}, \\\"c2\\\": {\\\"elements\\\": [\\\"left\\\", \\\"right\\\", \\\"stay\\\"]}},\\n\",\n \" \\\"states\\\": {\\n\",\n \" \\\"s1\\\": {\\\"elements\\\": [\\\"A\\\", \\\"B\\\", \\\"C\\\", \\\"D\\\"], \\\"depends_on\\\": [\\\"s1\\\"], \\\"controlled_by\\\": [\\\"c1\\\", \\\"c2\\\"]},\\n\",\n \" \\\"s2\\\": {\\\"elements\\\": [\\\"A\\\", \\\"B\\\", \\\"C\\\", \\\"D\\\"], \\\"depends_on\\\": [\\\"s2\\\"], \\\"controlled_by\\\": [\\\"c1\\\"]},\\n\",\n \" },\\n\",\n \"}\\n\",\n \"\\n\",\n \"B_action_dependencies = [\\n\",\n \" [list(model_description[\\\"controls\\\"].keys()).index(i) for i in s[\\\"controlled_by\\\"]] \\n\",\n \" for s in model_description[\\\"states\\\"].values()\\n\",\n \"]\\n\",\n \"num_controls = [len(c[\\\"elements\\\"]) for c in model_description[\\\"controls\\\"].values()]\\n\",\n \"\\n\",\n \"model = distribution.compile_model(model_description)\\n\",\n \"\\n\",\n \"# initialize tensor values\\n\",\n \"model.A[\\\"o1\\\"][\\\"A\\\", \\\"A\\\"] = 1.0\\n\",\n \"model.A[\\\"o1\\\"][\\\"B\\\", \\\"B\\\"] = 1.0\\n\",\n \"model.A[\\\"o1\\\"][\\\"C\\\", \\\"C\\\"] = 1.0\\n\",\n \"model.A[\\\"o1\\\"][\\\"D\\\", \\\"D\\\"] = 1.0\\n\",\n \"\\n\",\n \"for i, state in enumerate(model_description[\\\"states\\\"].keys()):\\n\",\n \" controls = list(itertools.product(*[\\n\",\n \" model_description[\\\"controls\\\"][c][\\\"elements\\\"] for c in model_description[\\\"states\\\"][state][\\\"controlled_by\\\"]\\n\",\n \" ]))\\n\",\n \" for control in controls:\\n\",\n \" model.B[i][(\\\"B\\\", \\\"A\\\", *control)] = 1.0\\n\",\n \" model.B[i][(\\\"C\\\", \\\"B\\\", *control)] = 1.0\\n\",\n \" model.B[i][(\\\"D\\\", \\\"C\\\", *control)] = 1.0\\n\",\n \" model.B[i][(\\\"D\\\", \\\"D\\\", *control)] = 1.0\\n\",\n \"\\n\",\n \"agent = Agent(\\n\",\n \" model.A, model.B,\\n\",\n \" B_action_dependencies=B_action_dependencies,\\n\",\n \" num_controls=num_controls,\\n\",\n \")\\n\",\n \"\\n\",\n \"# dummy history\\n\",\n \"# re-write the action sampling to be controlled by jax.random\\n\",\n \"action_key, obs_key = jr.split(jr.PRNGKey(0))\\n\",\n \"action = agent.policies[jr.choice(action_key, len(agent.policies))]\\n\",\n \"observation = [jr.randint(obs_key, (1, 1), 0, d) for d in agent.num_obs]\\n\",\n \"qs_hist = jtu.tree_map(lambda x: jnp.expand_dims(x, 0), agent.D)\\n\",\n \"\\n\",\n \"prior = agent.update_empirical_prior(action, qs_hist)\\n\",\n \"qs = agent.infer_states(observations=observation, empirical_prior=prior)\\n\",\n \"\\n\",\n \"q_pi, G = agent.infer_policies(qs)\\n\",\n \"action = agent.sample_action(q_pi)\\n\",\n \"action_multi = agent.decode_multi_actions(action)\\n\",\n \"action_reconstruct = agent.encode_multi_actions(action_multi)\\n\",\n \"\\n\",\n \"print(\\\"A_dependencies\\\", agent.A_dependencies)\\n\",\n \"print(\\\"B_dependencies\\\", agent.B_dependencies)\\n\",\n \"print(\\\"B_action_dependencies\\\", agent.B_action_dependencies)\\n\",\n \"print(\\\"original control dims\\\", agent.num_controls_multi)\\n\",\n \"print(\\\"flattened control dims\\\", agent.num_controls)\\n\",\n \"print(\\\"original B shapes\\\", [a.data.shape for a in model.B])\\n\",\n \"print(\\\"flattened B shapes\\\", [a.shape for a in agent.B])\\n\",\n \"print(\\\"B normalized\\\", [jnp.isclose(a.data.sum(0), 1.).all() for a in model.B])\\n\",\n \"print(\\\"B flat normalized\\\", [jnp.isclose(a.sum(1), 1.).all() for a in agent.B])\\n\",\n \"\\n\",\n \"print(\\\"\\\\n\\\")\\n\",\n \"print(\\\"prior\\\")\\n\",\n \"pprint([p.round(2) for p in prior])\\n\",\n \"print(\\\"post\\\")\\n\",\n \"pprint([p.round(2) for p in qs])\\n\",\n \"print(\\\"action\\\")\\n\",\n \"pprint(action)\\n\",\n \"print(\\\"action_multi\\\")\\n\",\n \"pprint(action_multi)\\n\",\n \"print(\\\"action_reconstruct\\\")\\n\",\n \"pprint(action_reconstruct)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## No action dependency\\n\",\n \"\\n\",\n \"In this example, some states do not depend on any action.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"A_dependencies [[0]]\\n\",\n \"B_dependencies [[0], [1]]\\n\",\n \"B_action_dependencies [[0, 1], []]\\n\",\n \"original control dims [2, 3]\\n\",\n \"flattened control dims [6, 1]\\n\",\n \"original B shapes [(4, 4, 2, 3), (4, 4)]\\n\",\n \"flattened B shapes [(1, 4, 4, 6), (1, 4, 4, 1)]\\n\",\n \"B normalized [Array(True, dtype=bool), Array(True, dtype=bool)]\\n\",\n \"B flat normalized [Array(True, dtype=bool), Array(True, dtype=bool)]\\n\",\n \"\\n\",\n \"\\n\",\n \"prior\\n\",\n \"[Array([[0. , 0.25, 0.25, 0.5 ]], dtype=float32),\\n\",\n \" Array([[0. , 0.25, 0.25, 0.5 ]], dtype=float32)]\\n\",\n \"post\\n\",\n \"[Array([[[0., 0., 1., 0.]]], dtype=float32),\\n\",\n \" Array([[[0. , 0.25, 0.25, 0.5 ]]], dtype=float32)]\\n\",\n \"action\\n\",\n \"Array([[0, 0]], dtype=int32)\\n\",\n \"action_multi\\n\",\n \"Array([[0, 0]], dtype=int32)\\n\",\n \"action_reconstruct\\n\",\n \"Array([[0, 0]], dtype=int32)\\n\"\n ]\n }\n ],\n \"source\": [\n \"model_description = {\\n\",\n \" \\\"observations\\\": {\\n\",\n \" \\\"o1\\\": {\\\"elements\\\": [\\\"A\\\", \\\"B\\\", \\\"C\\\", \\\"D\\\"], \\\"depends_on\\\": [\\\"s1\\\"]},\\n\",\n \" },\\n\",\n \" \\\"controls\\\": {\\\"c1\\\": {\\\"elements\\\": [\\\"up\\\", \\\"down\\\"]}, \\\"c2\\\": {\\\"elements\\\": [\\\"left\\\", \\\"right\\\", \\\"stay\\\"]}},\\n\",\n \" \\\"states\\\": {\\n\",\n \" \\\"s1\\\": {\\\"elements\\\": [\\\"A\\\", \\\"B\\\", \\\"C\\\", \\\"D\\\"], \\\"depends_on\\\": [\\\"s1\\\"], \\\"controlled_by\\\": [\\\"c1\\\", \\\"c2\\\"]},\\n\",\n \" \\\"s2\\\": {\\\"elements\\\": [\\\"A\\\", \\\"B\\\", \\\"C\\\", \\\"D\\\"], \\\"depends_on\\\": [\\\"s2\\\"], \\\"controlled_by\\\": []},\\n\",\n \" },\\n\",\n \"}\\n\",\n \"\\n\",\n \"B_action_dependencies = [ \\n\",\n \" [list(model_description[\\\"controls\\\"].keys()).index(i) for i in s[\\\"controlled_by\\\"]] \\n\",\n \" for s in model_description[\\\"states\\\"].values()\\n\",\n \"]\\n\",\n \"num_controls = [len(c[\\\"elements\\\"]) for c in model_description[\\\"controls\\\"].values()]\\n\",\n \"\\n\",\n \"model = distribution.compile_model(model_description)\\n\",\n \"\\n\",\n \"# initialize tensor values\\n\",\n \"model.A[\\\"o1\\\"][\\\"A\\\", \\\"A\\\"] = 1.0\\n\",\n \"model.A[\\\"o1\\\"][\\\"B\\\", \\\"B\\\"] = 1.0\\n\",\n \"model.A[\\\"o1\\\"][\\\"C\\\", \\\"C\\\"] = 1.0\\n\",\n \"model.A[\\\"o1\\\"][\\\"D\\\", \\\"D\\\"] = 1.0\\n\",\n \"\\n\",\n \"for i, state in enumerate(model_description[\\\"states\\\"].keys()):\\n\",\n \" controls = list(itertools.product(*[\\n\",\n \" model_description[\\\"controls\\\"][c][\\\"elements\\\"] for c in model_description[\\\"states\\\"][state][\\\"controlled_by\\\"]\\n\",\n \" ]))\\n\",\n \" for control in controls:\\n\",\n \" model.B[i][(\\\"B\\\", \\\"A\\\", *control)] = 1.0\\n\",\n \" model.B[i][(\\\"C\\\", \\\"B\\\", *control)] = 1.0\\n\",\n \" model.B[i][(\\\"D\\\", \\\"C\\\", *control)] = 1.0\\n\",\n \" model.B[i][(\\\"D\\\", \\\"D\\\", *control)] = 1.0\\n\",\n \"\\n\",\n \"agent = Agent(\\n\",\n \" model.A, model.B,\\n\",\n \" B_action_dependencies=B_action_dependencies,\\n\",\n \" num_controls=num_controls,\\n\",\n \")\\n\",\n \"\\n\",\n \"# dummy history\\n\",\n \"action_key, obs_key = jr.split(jr.PRNGKey(0))\\n\",\n \"action = agent.policies[jr.choice(action_key, len(agent.policies))]\\n\",\n \"observation = [jr.randint(obs_key, (1, 1), 0, d) for d in agent.num_obs]\\n\",\n \"qs_hist = jtu.tree_map(lambda x: jnp.expand_dims(x, 0), agent.D)\\n\",\n \"\\n\",\n \"prior = agent.update_empirical_prior(action, qs_hist)\\n\",\n \"qs = agent.infer_states(observations=observation, empirical_prior=prior)\\n\",\n \"\\n\",\n \"q_pi, G = agent.infer_policies(qs)\\n\",\n \"action = agent.sample_action(q_pi)\\n\",\n \"action_multi = agent.decode_multi_actions(action)\\n\",\n \"action_reconstruct = agent.encode_multi_actions(action_multi)\\n\",\n \"\\n\",\n \"print(\\\"A_dependencies\\\", agent.A_dependencies)\\n\",\n \"print(\\\"B_dependencies\\\", agent.B_dependencies)\\n\",\n \"print(\\\"B_action_dependencies\\\", agent.B_action_dependencies)\\n\",\n \"print(\\\"original control dims\\\", agent.num_controls_multi)\\n\",\n \"print(\\\"flattened control dims\\\", agent.num_controls)\\n\",\n \"print(\\\"original B shapes\\\", [a.data.shape for a in model.B])\\n\",\n \"print(\\\"flattened B shapes\\\", [a.shape for a in agent.B])\\n\",\n \"print(\\\"B normalized\\\", [jnp.isclose(a.data.sum(0), 1.).all() for a in model.B])\\n\",\n \"print(\\\"B flat normalized\\\", [jnp.isclose(a.sum(1), 1.).all() for a in agent.B])\\n\",\n \"\\n\",\n \"print(\\\"\\\\n\\\")\\n\",\n \"print(\\\"prior\\\")\\n\",\n \"pprint([p.round(2) for p in prior])\\n\",\n \"print(\\\"post\\\")\\n\",\n \"pprint([p.round(2) for p in qs])\\n\",\n \"print(\\\"action\\\")\\n\",\n \"pprint(action)\\n\",\n \"print(\\\"action_multi\\\")\\n\",\n \"pprint(action_multi)\\n\",\n \"print(\\\"action_reconstruct\\\")\\n\",\n \"pprint(action_reconstruct)\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"pymdp_dev_env\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/advanced/infer_states_optimization/methods_test.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"id\": \"d329903e-0caa-4ad9-8b85-92ed348f1e0f\",\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import numpy as np\\n\",\n \"import jax.numpy as jnp\\n\",\n \"import jax.tree_util as jtu\\n\",\n \"import jax.experimental.sparse as jsparse\\n\",\n \"from jax import nn, vmap, jit, block_until_ready\\n\",\n \"from functools import partial\\n\",\n \"\\n\",\n \"from pymdp.utils import init_A_and_D_from_spec, get_sample_obs, generate_agent_specs_from_parameter_sets\\n\",\n \"\\n\",\n \"# Hybrid\\n\",\n \"from pymdp.utils import apply_padding_batched\\n\",\n \"from pymdp.maths import compute_log_likelihoods_padded, deconstruct_lls\\n\",\n \"\\n\",\n \"# Hybrid block\\n\",\n \"from pymdp.utils import build_block_diag_A, preprocess_A_for_block_diag, prepare_obs_for_block_diag, concatenate_observations_block_diag\\n\",\n \"from pymdp.maths import compute_log_likelihoods_block_diag, deconstruct_log_likelihoods_block_diag\\n\",\n \"\\n\",\n \"from pymdp.algos import run_factorized_fpi_hybrid # For hybrid and hybrid block\\n\",\n \"\\n\",\n \"# End2end padded\\n\",\n \"from pymdp.utils import apply_A_end2end_padding_batched, apply_obs_end2end_padding_batched\\n\",\n \"from pymdp.maths import compute_log_likelihood_per_modality_end2end2_padded\\n\",\n \"from pymdp.algos import run_factorized_fpi_end2end_padded\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"id\": \"87d1c903-5496-4b12-a653-d6a9d8e6337b\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"{'num_factors': 10,\\n\",\n \" 'num_modalities': 10,\\n\",\n \" 'num_states': [3, 6, 2, 9, 7, 4, 7, 5, 7, 5],\\n\",\n \" 'num_obs': [4, 2, 4, 9, 7, 8, 4, 5, 7, 4],\\n\",\n \" 'A_dependencies': [[1],\\n\",\n \" [4],\\n\",\n \" [5, 6],\\n\",\n \" [0, 8],\\n\",\n \" [0, 2, 7],\\n\",\n \" [3, 5],\\n\",\n \" [6],\\n\",\n \" [2, 4, 7, 9],\\n\",\n \" [0, 2, 7, 8],\\n\",\n \" [7]],\\n\",\n \" 'metadata': {'num_factors': 'medium',\\n\",\n \" 'num_modalities': 'medium',\\n\",\n \" 'state_dim_upper_limit': 'medium',\\n\",\n \" 'obs_dim_upper_limit': 'medium',\\n\",\n \" 'dim_sampling_type': 'uniform'}}\"\n ]\n },\n \"execution_count\": 2,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"# Define coordinated parameter sets\\n\",\n \"# (num_factors, num_modalities, state_dim_upper_limit, obs_dim_upper_limit, dim_sampling_type, label)\\n\",\n \"parameter_sets = [\\n\",\n \" (5, 5, 5, 5, 'uniform', 'low'),\\n\",\n \" (10, 10, 10, 10, 'uniform', 'medium'),\\n\",\n \" (25, 25, 25, 25, 'uniform', 'high'),\\n\",\n \" # (125, 125, 125, 125, 'uniform', 'extreme'), # Uncomment to include extreme cases\\n\",\n \"]\\n\",\n \"\\n\",\n \"# Generate agent specs without dumping to file\\n\",\n \"specs = generate_agent_specs_from_parameter_sets(\\n\",\n \" parameter_sets,\\n\",\n \" num_agents_per_set=1,\\n\",\n \" output_file=None # Don't save to file\\n\",\n \")\\n\",\n \"\\n\",\n \"spec = specs['arbitrary dependencies'][1]\\n\",\n \"spec\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"id\": \"bc5d11ae-0e03-4ebc-9fb2-e31e51f29b63\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"WARNING:2025-11-20 23:52:19,919:jax._src.xla_bridge:794: An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.\\n\"\n ]\n }\n ],\n \"source\": [\n \"num_iter = 8\\n\",\n \"batch_size = 4\\n\",\n \"A_sparsity_level = None # E.g., 0.8 for 80% sparsity\\n\",\n \"\\n\",\n \"A, D = init_A_and_D_from_spec(\\n\",\n \" spec['num_obs'],\\n\",\n \" spec['num_states'],\\n\",\n \" spec['A_dependencies'],\\n\",\n \" A_sparsity_level=A_sparsity_level,\\n\",\n \" batch_size=batch_size\\n\",\n \")\\n\",\n \"\\n\",\n \"obs = get_sample_obs(spec['num_obs'], batch_size=batch_size)\\n\",\n \"o_vec = [nn.one_hot(o, spec['num_obs'][m]) for m, o in enumerate(obs)]\\n\",\n \"\\n\",\n \"# place where this happens is important!\\n\",\n \"# o_vec = jtu.tree_map(lambda x: x[-1], o_vec)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"c980e4a2-f81a-4279-a9a9-c16d1b2d7db6\",\n \"metadata\": {},\n \"source\": [\n \"### Original method imported directly from PyMDP\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"id\": \"ef656d7c-b9da-4d9b-990d-a6b7a99ca725\",\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"from pymdp.inference import update_posterior_states\\n\",\n \"\\n\",\n \"infer_states_orig_pymdp = vmap(\\n\",\n \" partial(\\n\",\n \" update_posterior_states,\\n\",\n \" A_dependencies=spec['A_dependencies'],\\n\",\n \" num_iter=num_iter,\\n\",\n \" method='fpi'\\n\",\n \" )\\n\",\n \")\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"id\": \"c2b7676f-58a7-41d3-8e66-31d2f58213b0\",\n \"metadata\": {\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"([(4, 1, 3),\\n\",\n \" (4, 1, 6),\\n\",\n \" (4, 1, 2),\\n\",\n \" (4, 1, 9),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 4),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 5),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 5)],\\n\",\n \" [Array([[[0.0911239 , 0.70235616, 0.20651992]],\\n\",\n \" \\n\",\n \" [[0.20210403, 0.22807154, 0.56982446]],\\n\",\n \" \\n\",\n \" [[0.3876841 , 0.3879837 , 0.2243322 ]],\\n\",\n \" \\n\",\n \" [[0.3751645 , 0.27490953, 0.34992597]]], dtype=float32),\\n\",\n \" Array([[[0.15824087, 0.183674 , 0.26761115, 0.09957846, 0.20257226,\\n\",\n \" 0.08832329]],\\n\",\n \" \\n\",\n \" [[0.23064205, 0.02032886, 0.13066185, 0.01698621, 0.2857863 ,\\n\",\n \" 0.31559473]],\\n\",\n \" \\n\",\n \" [[0.19148783, 0.11801518, 0.15054731, 0.13707514, 0.17550918,\\n\",\n \" 0.22736534]],\\n\",\n \" \\n\",\n \" [[0.16028336, 0.27957812, 0.16871531, 0.12887648, 0.1418996 ,\\n\",\n \" 0.12064715]]], dtype=float32),\\n\",\n \" Array([[[0.5558248 , 0.44417518]],\\n\",\n \" \\n\",\n \" [[0.549685 , 0.450315 ]],\\n\",\n \" \\n\",\n \" [[0.38312683, 0.6168732 ]],\\n\",\n \" \\n\",\n \" [[0.5388057 , 0.46119428]]], dtype=float32),\\n\",\n \" Array([[[0.07716177, 0.10925393, 0.07744848, 0.1075874 , 0.16774674,\\n\",\n \" 0.09816181, 0.09280077, 0.1271883 , 0.1426509 ]],\\n\",\n \" \\n\",\n \" [[0.12493826, 0.16711089, 0.15916635, 0.13118526, 0.06024319,\\n\",\n \" 0.04707498, 0.12128211, 0.10770807, 0.08129089]],\\n\",\n \" \\n\",\n \" [[0.1815095 , 0.10422336, 0.06684336, 0.14435901, 0.13004695,\\n\",\n \" 0.0635796 , 0.05770647, 0.09602303, 0.15570885]],\\n\",\n \" \\n\",\n \" [[0.04864096, 0.08837192, 0.09715893, 0.13307187, 0.1358143 ,\\n\",\n \" 0.18936108, 0.10949196, 0.09659162, 0.10149743]]], dtype=float32),\\n\",\n \" Array([[[0.1689375 , 0.160291 , 0.1127065 , 0.18204276, 0.21946688,\\n\",\n \" 0.08239742, 0.07415786]],\\n\",\n \" \\n\",\n \" [[0.10790369, 0.22401966, 0.21666421, 0.06581873, 0.10617904,\\n\",\n \" 0.08600897, 0.1934056 ]],\\n\",\n \" \\n\",\n \" [[0.03150751, 0.13815624, 0.12641437, 0.14349641, 0.20863566,\\n\",\n \" 0.33044106, 0.02134874]],\\n\",\n \" \\n\",\n \" [[0.09764873, 0.2943387 , 0.18542327, 0.14082205, 0.12583902,\\n\",\n \" 0.07777937, 0.0781489 ]]], dtype=float32),\\n\",\n \" Array([[[0.20188354, 0.20390284, 0.35773486, 0.23647875]],\\n\",\n \" \\n\",\n \" [[0.13832287, 0.417142 , 0.29778096, 0.14675426]],\\n\",\n \" \\n\",\n \" [[0.14250487, 0.34247938, 0.2867788 , 0.22823687]],\\n\",\n \" \\n\",\n \" [[0.33311817, 0.08985048, 0.27870888, 0.2983224 ]]], dtype=float32),\\n\",\n \" Array([[[0.25531998, 0.09805848, 0.00180036, 0.06169656, 0.30057994,\\n\",\n \" 0.10489379, 0.17765091]],\\n\",\n \" \\n\",\n \" [[0.2913621 , 0.11028862, 0.06915001, 0.06127482, 0.01146838,\\n\",\n \" 0.2958903 , 0.16056576]],\\n\",\n \" \\n\",\n \" [[0.10321112, 0.10843234, 0.09066889, 0.10762182, 0.19040616,\\n\",\n \" 0.18881004, 0.21084957]],\\n\",\n \" \\n\",\n \" [[0.0594087 , 0.15811725, 0.18402615, 0.22240478, 0.20785518,\\n\",\n \" 0.06183277, 0.10635528]]], dtype=float32),\\n\",\n \" Array([[[0.43077353, 0.01719548, 0.18029211, 0.19461532, 0.17712358]],\\n\",\n \" \\n\",\n \" [[0.20952433, 0.28238228, 0.26831535, 0.22654854, 0.01322948]],\\n\",\n \" \\n\",\n \" [[0.34862244, 0.24600431, 0.12305126, 0.11314465, 0.16917741]],\\n\",\n \" \\n\",\n \" [[0.15003231, 0.08879875, 0.19839822, 0.52532786, 0.03744285]]], dtype=float32),\\n\",\n \" Array([[[0.11571391, 0.04172199, 0.14292379, 0.21811739, 0.10899252,\\n\",\n \" 0.2847777 , 0.08775268]],\\n\",\n \" \\n\",\n \" [[0.11718995, 0.01083917, 0.22239213, 0.11398617, 0.09531911,\\n\",\n \" 0.3041632 , 0.13611032]],\\n\",\n \" \\n\",\n \" [[0.05459082, 0.1635046 , 0.13142689, 0.20870976, 0.17459586,\\n\",\n \" 0.15282223, 0.11434983]],\\n\",\n \" \\n\",\n \" [[0.1454747 , 0.0939365 , 0.19433093, 0.22500299, 0.11097856,\\n\",\n \" 0.0673811 , 0.16289519]]], dtype=float32),\\n\",\n \" Array([[[0.2335071 , 0.21891794, 0.16771059, 0.17027749, 0.20958687]],\\n\",\n \" \\n\",\n \" [[0.19165832, 0.21907933, 0.20649089, 0.19125326, 0.19151819]],\\n\",\n \" \\n\",\n \" [[0.20866643, 0.18651229, 0.23633833, 0.17361018, 0.19487286]],\\n\",\n \" \\n\",\n \" [[0.24136765, 0.17386995, 0.2222213 , 0.16080104, 0.2017401 ]]], dtype=float32)])\"\n ]\n },\n \"execution_count\": 5,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"qs = infer_states_orig_pymdp(A, None, o_vec, None, D)\\n\",\n \"[q.shape for q in qs], qs\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"5525d913-b845-4287-bd5f-d3d7dba44eb8\",\n \"metadata\": {},\n \"source\": [\n \"### Hybrid method\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"id\": \"dd83c3d3\",\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"def infer_states_hybrid(obs_padded, A_padded, D, A_shapes, A_dependencies, num_iter):\\n\",\n \" lls_padded = compute_log_likelihoods_padded(obs_padded, A_padded)\\n\",\n \" log_likelihoods = deconstruct_lls(lls_padded, A_shapes)\\n\",\n \" return vmap(partial(run_factorized_fpi_hybrid, A_dependencies=A_dependencies, num_iter=num_iter))(log_likelihoods, D)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"id\": \"6c778c1e-e373-4603-a244-6f3455a282d8\",\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"A_padded = apply_padding_batched(A)\\n\",\n \"A_shapes = [a.shape for a in A]\\n\",\n \"\\n\",\n \"if A_sparsity_level is not None:\\n\",\n \" A_padded = jsparse.BCOO.fromdense(A_padded, n_batch=1)\\n\",\n \"\\n\",\n \"# obs preprocessing\\n\",\n \"obs_padded = apply_padding_batched(jtu.tree_map(lambda x: jnp.squeeze(x, 1), o_vec))\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"id\": \"5398c4aa-77bf-438c-8be8-1a5ab72e3d89\",\n \"metadata\": {\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"([(4, 1, 3),\\n\",\n \" (4, 1, 6),\\n\",\n \" (4, 1, 2),\\n\",\n \" (4, 1, 9),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 4),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 5),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 5)],\\n\",\n \" [Array([[[0.0911239 , 0.70235616, 0.20651992]],\\n\",\n \" \\n\",\n \" [[0.20210403, 0.22807154, 0.56982446]],\\n\",\n \" \\n\",\n \" [[0.3876841 , 0.3879837 , 0.2243322 ]],\\n\",\n \" \\n\",\n \" [[0.3751645 , 0.27490953, 0.34992597]]], dtype=float32),\\n\",\n \" Array([[[0.15824087, 0.183674 , 0.26761115, 0.09957846, 0.20257226,\\n\",\n \" 0.08832329]],\\n\",\n \" \\n\",\n \" [[0.23064205, 0.02032886, 0.13066185, 0.01698621, 0.2857863 ,\\n\",\n \" 0.31559473]],\\n\",\n \" \\n\",\n \" [[0.19148783, 0.11801518, 0.15054731, 0.13707514, 0.17550918,\\n\",\n \" 0.22736534]],\\n\",\n \" \\n\",\n \" [[0.16028336, 0.27957812, 0.16871531, 0.12887648, 0.1418996 ,\\n\",\n \" 0.12064715]]], dtype=float32),\\n\",\n \" Array([[[0.5558248 , 0.44417518]],\\n\",\n \" \\n\",\n \" [[0.549685 , 0.450315 ]],\\n\",\n \" \\n\",\n \" [[0.38312683, 0.6168732 ]],\\n\",\n \" \\n\",\n \" [[0.5388057 , 0.46119428]]], dtype=float32),\\n\",\n \" Array([[[0.07716177, 0.10925393, 0.07744848, 0.1075874 , 0.16774674,\\n\",\n \" 0.09816181, 0.09280077, 0.1271883 , 0.1426509 ]],\\n\",\n \" \\n\",\n \" [[0.12493826, 0.16711089, 0.15916635, 0.13118526, 0.06024319,\\n\",\n \" 0.04707498, 0.12128211, 0.10770807, 0.08129089]],\\n\",\n \" \\n\",\n \" [[0.1815095 , 0.10422336, 0.06684336, 0.14435901, 0.13004695,\\n\",\n \" 0.0635796 , 0.05770647, 0.09602303, 0.15570885]],\\n\",\n \" \\n\",\n \" [[0.04864096, 0.08837192, 0.09715893, 0.13307187, 0.1358143 ,\\n\",\n \" 0.18936108, 0.10949196, 0.09659162, 0.10149743]]], dtype=float32),\\n\",\n \" Array([[[0.1689375 , 0.160291 , 0.1127065 , 0.18204276, 0.21946688,\\n\",\n \" 0.08239742, 0.07415786]],\\n\",\n \" \\n\",\n \" [[0.10790369, 0.22401966, 0.21666421, 0.06581873, 0.10617904,\\n\",\n \" 0.08600897, 0.1934056 ]],\\n\",\n \" \\n\",\n \" [[0.03150751, 0.13815624, 0.12641437, 0.14349641, 0.20863566,\\n\",\n \" 0.33044106, 0.02134874]],\\n\",\n \" \\n\",\n \" [[0.09764873, 0.2943387 , 0.18542327, 0.14082205, 0.12583902,\\n\",\n \" 0.07777937, 0.0781489 ]]], dtype=float32),\\n\",\n \" Array([[[0.20188354, 0.20390284, 0.35773486, 0.23647875]],\\n\",\n \" \\n\",\n \" [[0.13832287, 0.417142 , 0.29778096, 0.14675426]],\\n\",\n \" \\n\",\n \" [[0.14250487, 0.34247938, 0.2867788 , 0.22823687]],\\n\",\n \" \\n\",\n \" [[0.33311817, 0.08985048, 0.27870888, 0.2983224 ]]], dtype=float32),\\n\",\n \" Array([[[0.25531998, 0.09805848, 0.00180036, 0.06169656, 0.30057994,\\n\",\n \" 0.10489379, 0.17765091]],\\n\",\n \" \\n\",\n \" [[0.2913621 , 0.11028862, 0.06915001, 0.06127482, 0.01146838,\\n\",\n \" 0.2958903 , 0.16056576]],\\n\",\n \" \\n\",\n \" [[0.10321112, 0.10843234, 0.09066889, 0.10762182, 0.19040616,\\n\",\n \" 0.18881004, 0.21084957]],\\n\",\n \" \\n\",\n \" [[0.0594087 , 0.15811725, 0.18402615, 0.22240478, 0.20785518,\\n\",\n \" 0.06183277, 0.10635528]]], dtype=float32),\\n\",\n \" Array([[[0.43077353, 0.01719548, 0.18029211, 0.19461532, 0.17712358]],\\n\",\n \" \\n\",\n \" [[0.20952433, 0.28238228, 0.26831535, 0.22654854, 0.01322948]],\\n\",\n \" \\n\",\n \" [[0.34862244, 0.24600431, 0.12305126, 0.11314465, 0.16917741]],\\n\",\n \" \\n\",\n \" [[0.15003231, 0.08879875, 0.19839822, 0.52532786, 0.03744285]]], dtype=float32),\\n\",\n \" Array([[[0.11571391, 0.04172199, 0.14292379, 0.21811739, 0.10899252,\\n\",\n \" 0.2847777 , 0.08775268]],\\n\",\n \" \\n\",\n \" [[0.11718995, 0.01083917, 0.22239213, 0.11398617, 0.09531911,\\n\",\n \" 0.3041632 , 0.13611032]],\\n\",\n \" \\n\",\n \" [[0.05459082, 0.1635046 , 0.13142689, 0.20870976, 0.17459586,\\n\",\n \" 0.15282223, 0.11434983]],\\n\",\n \" \\n\",\n \" [[0.1454747 , 0.0939365 , 0.19433093, 0.22500299, 0.11097856,\\n\",\n \" 0.0673811 , 0.16289519]]], dtype=float32),\\n\",\n \" Array([[[0.2335071 , 0.21891794, 0.16771059, 0.17027749, 0.20958687]],\\n\",\n \" \\n\",\n \" [[0.19165832, 0.21907933, 0.20649089, 0.19125326, 0.19151819]],\\n\",\n \" \\n\",\n \" [[0.20866643, 0.18651229, 0.23633833, 0.17361018, 0.19487286]],\\n\",\n \" \\n\",\n \" [[0.24136765, 0.17386995, 0.2222213 , 0.16080104, 0.2017401 ]]], dtype=float32)])\"\n ]\n },\n \"execution_count\": 8,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"qs = infer_states_hybrid(obs_padded, A_padded, D, A_shapes, A_dependencies=spec['A_dependencies'], num_iter=num_iter)\\n\",\n \"[q.shape for q in qs], qs\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"id\": \"14c74aed\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"([(4, 1, 3),\\n\",\n \" (4, 1, 6),\\n\",\n \" (4, 1, 2),\\n\",\n \" (4, 1, 9),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 4),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 5),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 5)],\\n\",\n \" [Array([[[0.0911239 , 0.70235616, 0.20651992]],\\n\",\n \" \\n\",\n \" [[0.20210403, 0.22807154, 0.56982446]],\\n\",\n \" \\n\",\n \" [[0.3876841 , 0.3879837 , 0.2243322 ]],\\n\",\n \" \\n\",\n \" [[0.3751645 , 0.27490953, 0.34992597]]], dtype=float32),\\n\",\n \" Array([[[0.15824087, 0.183674 , 0.26761115, 0.09957846, 0.20257226,\\n\",\n \" 0.08832329]],\\n\",\n \" \\n\",\n \" [[0.23064205, 0.02032886, 0.13066185, 0.01698621, 0.2857863 ,\\n\",\n \" 0.31559473]],\\n\",\n \" \\n\",\n \" [[0.19148783, 0.11801518, 0.15054731, 0.13707514, 0.17550918,\\n\",\n \" 0.22736534]],\\n\",\n \" \\n\",\n \" [[0.16028336, 0.27957812, 0.16871531, 0.12887648, 0.1418996 ,\\n\",\n \" 0.12064715]]], dtype=float32),\\n\",\n \" Array([[[0.5558248 , 0.44417518]],\\n\",\n \" \\n\",\n \" [[0.549685 , 0.450315 ]],\\n\",\n \" \\n\",\n \" [[0.38312683, 0.6168732 ]],\\n\",\n \" \\n\",\n \" [[0.5388057 , 0.46119428]]], dtype=float32),\\n\",\n \" Array([[[0.07716177, 0.10925393, 0.07744848, 0.1075874 , 0.16774674,\\n\",\n \" 0.09816181, 0.09280077, 0.1271883 , 0.1426509 ]],\\n\",\n \" \\n\",\n \" [[0.12493826, 0.16711089, 0.15916635, 0.13118526, 0.06024319,\\n\",\n \" 0.04707498, 0.12128211, 0.10770807, 0.08129089]],\\n\",\n \" \\n\",\n \" [[0.1815095 , 0.10422336, 0.06684336, 0.14435901, 0.13004695,\\n\",\n \" 0.0635796 , 0.05770647, 0.09602303, 0.15570885]],\\n\",\n \" \\n\",\n \" [[0.04864096, 0.08837192, 0.09715893, 0.13307187, 0.1358143 ,\\n\",\n \" 0.18936108, 0.10949196, 0.09659162, 0.10149743]]], dtype=float32),\\n\",\n \" Array([[[0.1689375 , 0.160291 , 0.1127065 , 0.18204276, 0.21946688,\\n\",\n \" 0.08239742, 0.07415786]],\\n\",\n \" \\n\",\n \" [[0.10790369, 0.22401966, 0.21666421, 0.06581873, 0.10617904,\\n\",\n \" 0.08600897, 0.1934056 ]],\\n\",\n \" \\n\",\n \" [[0.03150751, 0.13815624, 0.12641437, 0.14349641, 0.20863566,\\n\",\n \" 0.33044106, 0.02134874]],\\n\",\n \" \\n\",\n \" [[0.09764873, 0.2943387 , 0.18542327, 0.14082205, 0.12583902,\\n\",\n \" 0.07777937, 0.0781489 ]]], dtype=float32),\\n\",\n \" Array([[[0.20188354, 0.20390284, 0.35773486, 0.23647875]],\\n\",\n \" \\n\",\n \" [[0.13832287, 0.417142 , 0.29778096, 0.14675426]],\\n\",\n \" \\n\",\n \" [[0.14250487, 0.34247938, 0.2867788 , 0.22823687]],\\n\",\n \" \\n\",\n \" [[0.33311817, 0.08985048, 0.27870888, 0.2983224 ]]], dtype=float32),\\n\",\n \" Array([[[0.25531998, 0.09805848, 0.00180036, 0.06169656, 0.30057994,\\n\",\n \" 0.10489379, 0.17765091]],\\n\",\n \" \\n\",\n \" [[0.2913621 , 0.11028862, 0.06915001, 0.06127482, 0.01146838,\\n\",\n \" 0.2958903 , 0.16056576]],\\n\",\n \" \\n\",\n \" [[0.10321112, 0.10843234, 0.09066889, 0.10762182, 0.19040616,\\n\",\n \" 0.18881004, 0.21084957]],\\n\",\n \" \\n\",\n \" [[0.0594087 , 0.15811725, 0.18402615, 0.22240478, 0.20785518,\\n\",\n \" 0.06183277, 0.10635528]]], dtype=float32),\\n\",\n \" Array([[[0.43077353, 0.01719548, 0.18029211, 0.19461532, 0.17712358]],\\n\",\n \" \\n\",\n \" [[0.20952433, 0.28238228, 0.26831535, 0.22654854, 0.01322948]],\\n\",\n \" \\n\",\n \" [[0.34862244, 0.24600431, 0.12305126, 0.11314465, 0.16917741]],\\n\",\n \" \\n\",\n \" [[0.15003231, 0.08879875, 0.19839822, 0.52532786, 0.03744285]]], dtype=float32),\\n\",\n \" Array([[[0.11571391, 0.04172199, 0.14292379, 0.21811739, 0.10899252,\\n\",\n \" 0.2847777 , 0.08775268]],\\n\",\n \" \\n\",\n \" [[0.11718995, 0.01083917, 0.22239213, 0.11398617, 0.09531911,\\n\",\n \" 0.3041632 , 0.13611032]],\\n\",\n \" \\n\",\n \" [[0.05459082, 0.1635046 , 0.13142689, 0.20870976, 0.17459586,\\n\",\n \" 0.15282223, 0.11434983]],\\n\",\n \" \\n\",\n \" [[0.1454747 , 0.0939365 , 0.19433093, 0.22500299, 0.11097856,\\n\",\n \" 0.0673811 , 0.16289519]]], dtype=float32),\\n\",\n \" Array([[[0.2335071 , 0.21891794, 0.16771059, 0.17027749, 0.20958687]],\\n\",\n \" \\n\",\n \" [[0.19165832, 0.21907933, 0.20649089, 0.19125326, 0.19151819]],\\n\",\n \" \\n\",\n \" [[0.20866643, 0.18651229, 0.23633833, 0.17361018, 0.19487286]],\\n\",\n \" \\n\",\n \" [[0.24136765, 0.17386995, 0.2222213 , 0.16080104, 0.2017401 ]]], dtype=float32)])\"\n ]\n },\n \"execution_count\": 9,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"# JIT\\n\",\n \"apply_padding_batched_jit = jit(partial(apply_padding_batched))\\n\",\n \"infer_states_hybrid_jit = jit(partial(infer_states_hybrid, A_shapes=A_shapes, A_dependencies=spec['A_dependencies'], num_iter=num_iter))\\n\",\n \"obs_padded = apply_padding_batched_jit(jtu.tree_map(lambda x: jnp.squeeze(x, 1), o_vec))\\n\",\n \"\\n\",\n \"qs = infer_states_hybrid_jit(obs_padded, A_padded, D)\\n\",\n \"[q.shape for q in qs], qs\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"b8ba50c5\",\n \"metadata\": {},\n \"source\": [\n \"### Hybrid Block method\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"id\": \"9485d771\",\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Infer states hybrid block\\n\",\n \"def infer_states_hybrid_block(obs, A_big, D, state_shapes, cuts, A_dependencies, num_iter, use_einsum=False):\\n\",\n \" \\\"\\\"\\\"Hybrid inference using block diagonal approach for log-likelihood computation.\\\"\\\"\\\"\\n\",\n \" log_likelihoods = compute_log_likelihoods_block_diag(A_big, obs, state_shapes, cuts, use_einsum=use_einsum)\\n\",\n \" return vmap(partial(run_factorized_fpi_hybrid, A_dependencies=A_dependencies, num_iter=num_iter))(log_likelihoods, D)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"id\": \"891743ae\",\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Create a copy with moved axes for block diagonal method (don't modify original A)\\n\",\n \"A_moveaxis = [jnp.moveaxis(a, 1, -1) for a in A]\\n\",\n \"# Preprocess A matrices for block diagonal approach\\n\",\n \"A_big, state_shapes, cuts = preprocess_A_for_block_diag(A_moveaxis)\\n\",\n \"\\n\",\n \"if A_sparsity_level is not None:\\n\",\n \" A_big = jsparse.BCOO.fromdense(A_big, n_batch=1)\\n\",\n \"\\n\",\n \"obs_tmp = jtu.tree_map(lambda x: jnp.squeeze(x, 1), o_vec)\\n\",\n \"obs_big = concatenate_observations_block_diag(obs_tmp)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"id\": \"1d52085c\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"([(4, 1, 3),\\n\",\n \" (4, 1, 6),\\n\",\n \" (4, 1, 2),\\n\",\n \" (4, 1, 9),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 4),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 5),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 5)],\\n\",\n \" [Array([[[0.0911239 , 0.70235616, 0.20651992]],\\n\",\n \" \\n\",\n \" [[0.20210403, 0.22807154, 0.56982446]],\\n\",\n \" \\n\",\n \" [[0.3876841 , 0.3879837 , 0.2243322 ]],\\n\",\n \" \\n\",\n \" [[0.3751645 , 0.27490953, 0.34992597]]], dtype=float32),\\n\",\n \" Array([[[0.15824087, 0.183674 , 0.26761115, 0.09957846, 0.20257226,\\n\",\n \" 0.08832329]],\\n\",\n \" \\n\",\n \" [[0.23064205, 0.02032886, 0.13066185, 0.01698621, 0.2857863 ,\\n\",\n \" 0.31559473]],\\n\",\n \" \\n\",\n \" [[0.19148783, 0.11801518, 0.15054731, 0.13707514, 0.17550918,\\n\",\n \" 0.22736534]],\\n\",\n \" \\n\",\n \" [[0.16028336, 0.27957812, 0.16871531, 0.12887648, 0.1418996 ,\\n\",\n \" 0.12064715]]], dtype=float32),\\n\",\n \" Array([[[0.5558248 , 0.44417518]],\\n\",\n \" \\n\",\n \" [[0.549685 , 0.450315 ]],\\n\",\n \" \\n\",\n \" [[0.38312683, 0.6168732 ]],\\n\",\n \" \\n\",\n \" [[0.5388057 , 0.46119428]]], dtype=float32),\\n\",\n \" Array([[[0.07716177, 0.10925393, 0.07744848, 0.1075874 , 0.16774674,\\n\",\n \" 0.09816181, 0.09280077, 0.1271883 , 0.1426509 ]],\\n\",\n \" \\n\",\n \" [[0.12493826, 0.16711089, 0.15916635, 0.13118526, 0.06024319,\\n\",\n \" 0.04707498, 0.12128211, 0.10770807, 0.08129089]],\\n\",\n \" \\n\",\n \" [[0.1815095 , 0.10422336, 0.06684336, 0.14435901, 0.13004695,\\n\",\n \" 0.0635796 , 0.05770647, 0.09602303, 0.15570885]],\\n\",\n \" \\n\",\n \" [[0.04864096, 0.08837192, 0.09715893, 0.13307187, 0.1358143 ,\\n\",\n \" 0.18936108, 0.10949196, 0.09659162, 0.10149743]]], dtype=float32),\\n\",\n \" Array([[[0.1689375 , 0.160291 , 0.1127065 , 0.18204276, 0.21946688,\\n\",\n \" 0.08239742, 0.07415786]],\\n\",\n \" \\n\",\n \" [[0.10790369, 0.22401966, 0.21666421, 0.06581873, 0.10617904,\\n\",\n \" 0.08600897, 0.1934056 ]],\\n\",\n \" \\n\",\n \" [[0.03150751, 0.13815624, 0.12641437, 0.14349641, 0.20863566,\\n\",\n \" 0.33044106, 0.02134874]],\\n\",\n \" \\n\",\n \" [[0.09764873, 0.2943387 , 0.18542327, 0.14082205, 0.12583902,\\n\",\n \" 0.07777937, 0.0781489 ]]], dtype=float32),\\n\",\n \" Array([[[0.20188354, 0.20390284, 0.35773486, 0.23647875]],\\n\",\n \" \\n\",\n \" [[0.13832287, 0.417142 , 0.29778096, 0.14675426]],\\n\",\n \" \\n\",\n \" [[0.14250487, 0.34247938, 0.2867788 , 0.22823687]],\\n\",\n \" \\n\",\n \" [[0.33311817, 0.08985048, 0.27870888, 0.2983224 ]]], dtype=float32),\\n\",\n \" Array([[[0.25531998, 0.09805848, 0.00180036, 0.06169656, 0.30057994,\\n\",\n \" 0.10489379, 0.17765091]],\\n\",\n \" \\n\",\n \" [[0.2913621 , 0.11028862, 0.06915001, 0.06127482, 0.01146838,\\n\",\n \" 0.2958903 , 0.16056576]],\\n\",\n \" \\n\",\n \" [[0.10321112, 0.10843234, 0.09066889, 0.10762182, 0.19040616,\\n\",\n \" 0.18881004, 0.21084957]],\\n\",\n \" \\n\",\n \" [[0.0594087 , 0.15811725, 0.18402615, 0.22240478, 0.20785518,\\n\",\n \" 0.06183277, 0.10635528]]], dtype=float32),\\n\",\n \" Array([[[0.43077353, 0.01719548, 0.18029211, 0.19461532, 0.17712358]],\\n\",\n \" \\n\",\n \" [[0.20952433, 0.28238228, 0.26831535, 0.22654854, 0.01322948]],\\n\",\n \" \\n\",\n \" [[0.34862244, 0.24600431, 0.12305126, 0.11314465, 0.16917741]],\\n\",\n \" \\n\",\n \" [[0.15003231, 0.08879875, 0.19839822, 0.52532786, 0.03744285]]], dtype=float32),\\n\",\n \" Array([[[0.11571391, 0.04172199, 0.14292379, 0.21811739, 0.10899252,\\n\",\n \" 0.2847777 , 0.08775268]],\\n\",\n \" \\n\",\n \" [[0.11718995, 0.01083917, 0.22239213, 0.11398617, 0.09531911,\\n\",\n \" 0.3041632 , 0.13611032]],\\n\",\n \" \\n\",\n \" [[0.05459082, 0.1635046 , 0.13142689, 0.20870976, 0.17459586,\\n\",\n \" 0.15282223, 0.11434983]],\\n\",\n \" \\n\",\n \" [[0.1454747 , 0.0939365 , 0.19433093, 0.22500299, 0.11097856,\\n\",\n \" 0.0673811 , 0.16289519]]], dtype=float32),\\n\",\n \" Array([[[0.2335071 , 0.21891794, 0.16771059, 0.17027749, 0.20958687]],\\n\",\n \" \\n\",\n \" [[0.19165832, 0.21907933, 0.20649089, 0.19125326, 0.19151819]],\\n\",\n \" \\n\",\n \" [[0.20866643, 0.18651229, 0.23633833, 0.17361018, 0.19487286]],\\n\",\n \" \\n\",\n \" [[0.24136765, 0.17386995, 0.2222213 , 0.16080104, 0.2017401 ]]], dtype=float32)])\"\n ]\n },\n \"execution_count\": 12,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"qs = infer_states_hybrid_block(obs_big, A_big, D, \\n\",\n \" state_shapes=state_shapes, cuts=cuts, A_dependencies=spec['A_dependencies'], \\n\",\n \" num_iter=num_iter, use_einsum=False\\n\",\n \")\\n\",\n \"\\n\",\n \"[q.shape for q in qs], qs\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"id\": \"78beb618\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"([(4, 1, 3),\\n\",\n \" (4, 1, 6),\\n\",\n \" (4, 1, 2),\\n\",\n \" (4, 1, 9),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 4),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 5),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 5)],\\n\",\n \" [Array([[[0.0911239 , 0.70235616, 0.20651992]],\\n\",\n \" \\n\",\n \" [[0.20210403, 0.22807154, 0.56982446]],\\n\",\n \" \\n\",\n \" [[0.3876841 , 0.3879837 , 0.2243322 ]],\\n\",\n \" \\n\",\n \" [[0.3751645 , 0.27490953, 0.34992597]]], dtype=float32),\\n\",\n \" Array([[[0.15824087, 0.183674 , 0.26761115, 0.09957846, 0.20257226,\\n\",\n \" 0.08832329]],\\n\",\n \" \\n\",\n \" [[0.23064205, 0.02032886, 0.13066185, 0.01698621, 0.2857863 ,\\n\",\n \" 0.31559473]],\\n\",\n \" \\n\",\n \" [[0.19148783, 0.11801518, 0.15054731, 0.13707514, 0.17550918,\\n\",\n \" 0.22736534]],\\n\",\n \" \\n\",\n \" [[0.16028336, 0.27957812, 0.16871531, 0.12887648, 0.1418996 ,\\n\",\n \" 0.12064715]]], dtype=float32),\\n\",\n \" Array([[[0.5558248 , 0.44417518]],\\n\",\n \" \\n\",\n \" [[0.549685 , 0.450315 ]],\\n\",\n \" \\n\",\n \" [[0.38312683, 0.6168732 ]],\\n\",\n \" \\n\",\n \" [[0.5388057 , 0.46119428]]], dtype=float32),\\n\",\n \" Array([[[0.07716177, 0.10925393, 0.07744848, 0.1075874 , 0.16774674,\\n\",\n \" 0.09816181, 0.09280077, 0.1271883 , 0.1426509 ]],\\n\",\n \" \\n\",\n \" [[0.12493826, 0.16711089, 0.15916635, 0.13118526, 0.06024319,\\n\",\n \" 0.04707498, 0.12128211, 0.10770807, 0.08129089]],\\n\",\n \" \\n\",\n \" [[0.1815095 , 0.10422336, 0.06684336, 0.14435901, 0.13004695,\\n\",\n \" 0.0635796 , 0.05770647, 0.09602303, 0.15570885]],\\n\",\n \" \\n\",\n \" [[0.04864096, 0.08837192, 0.09715893, 0.13307187, 0.1358143 ,\\n\",\n \" 0.18936108, 0.10949196, 0.09659162, 0.10149743]]], dtype=float32),\\n\",\n \" Array([[[0.1689375 , 0.160291 , 0.1127065 , 0.18204276, 0.21946688,\\n\",\n \" 0.08239742, 0.07415786]],\\n\",\n \" \\n\",\n \" [[0.10790369, 0.22401966, 0.21666421, 0.06581873, 0.10617904,\\n\",\n \" 0.08600897, 0.1934056 ]],\\n\",\n \" \\n\",\n \" [[0.03150751, 0.13815624, 0.12641437, 0.14349641, 0.20863566,\\n\",\n \" 0.33044106, 0.02134874]],\\n\",\n \" \\n\",\n \" [[0.09764873, 0.2943387 , 0.18542327, 0.14082205, 0.12583902,\\n\",\n \" 0.07777937, 0.0781489 ]]], dtype=float32),\\n\",\n \" Array([[[0.20188354, 0.20390284, 0.35773486, 0.23647875]],\\n\",\n \" \\n\",\n \" [[0.13832287, 0.417142 , 0.29778096, 0.14675426]],\\n\",\n \" \\n\",\n \" [[0.14250487, 0.34247938, 0.2867788 , 0.22823687]],\\n\",\n \" \\n\",\n \" [[0.33311817, 0.08985048, 0.27870888, 0.2983224 ]]], dtype=float32),\\n\",\n \" Array([[[0.25531998, 0.09805848, 0.00180036, 0.06169656, 0.30057994,\\n\",\n \" 0.10489379, 0.17765091]],\\n\",\n \" \\n\",\n \" [[0.2913621 , 0.11028862, 0.06915001, 0.06127482, 0.01146838,\\n\",\n \" 0.2958903 , 0.16056576]],\\n\",\n \" \\n\",\n \" [[0.10321112, 0.10843234, 0.09066889, 0.10762182, 0.19040616,\\n\",\n \" 0.18881004, 0.21084957]],\\n\",\n \" \\n\",\n \" [[0.0594087 , 0.15811725, 0.18402615, 0.22240478, 0.20785518,\\n\",\n \" 0.06183277, 0.10635528]]], dtype=float32),\\n\",\n \" Array([[[0.43077353, 0.01719548, 0.18029211, 0.19461532, 0.17712358]],\\n\",\n \" \\n\",\n \" [[0.20952433, 0.28238228, 0.26831535, 0.22654854, 0.01322948]],\\n\",\n \" \\n\",\n \" [[0.34862244, 0.24600431, 0.12305126, 0.11314465, 0.16917741]],\\n\",\n \" \\n\",\n \" [[0.15003231, 0.08879875, 0.19839822, 0.52532786, 0.03744285]]], dtype=float32),\\n\",\n \" Array([[[0.11571391, 0.04172199, 0.14292379, 0.21811739, 0.10899252,\\n\",\n \" 0.2847777 , 0.08775268]],\\n\",\n \" \\n\",\n \" [[0.11718995, 0.01083917, 0.22239213, 0.11398617, 0.09531911,\\n\",\n \" 0.3041632 , 0.13611032]],\\n\",\n \" \\n\",\n \" [[0.05459082, 0.1635046 , 0.13142689, 0.20870976, 0.17459586,\\n\",\n \" 0.15282223, 0.11434983]],\\n\",\n \" \\n\",\n \" [[0.1454747 , 0.0939365 , 0.19433093, 0.22500299, 0.11097856,\\n\",\n \" 0.0673811 , 0.16289519]]], dtype=float32),\\n\",\n \" Array([[[0.2335071 , 0.21891794, 0.16771059, 0.17027749, 0.20958687]],\\n\",\n \" \\n\",\n \" [[0.19165832, 0.21907933, 0.20649089, 0.19125326, 0.19151819]],\\n\",\n \" \\n\",\n \" [[0.20866643, 0.18651229, 0.23633833, 0.17361018, 0.19487286]],\\n\",\n \" \\n\",\n \" [[0.24136765, 0.17386995, 0.2222213 , 0.16080104, 0.2017401 ]]], dtype=float32)])\"\n ]\n },\n \"execution_count\": 13,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"# JIT\\n\",\n \"use_einsum=False\\n\",\n \"concatenate_observations_block_diag_jit = jit(partial(concatenate_observations_block_diag)) # just for obs\\n\",\n \"infer_states_hybrid_block_jit = jit(partial(infer_states_hybrid_block, state_shapes=state_shapes, cuts=cuts, A_dependencies=spec['A_dependencies'], num_iter=num_iter, use_einsum=use_einsum))\\n\",\n \"obs_big = concatenate_observations_block_diag_jit(obs_tmp) # add padding of obs before running the infer states\\n\",\n \"\\n\",\n \"qs = infer_states_hybrid_block_jit(obs_big, A_big, D)\\n\",\n \"[q.shape for q in qs], qs\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"0020c0e3-4baa-45f7-a920-2640dcc958b9\",\n \"metadata\": {},\n \"source\": [\n \"### End2End padded method\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"id\": \"1e91bf02\",\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"def infer_states_end2end_padded(A_padded, obs_padded, D, A_dependencies, max_obs_dim, max_state_dim, num_iter, sparsity=None):\\n\",\n \" lls_padded = compute_log_likelihood_per_modality_end2end2_padded(obs_padded, A_padded, sparsity=sparsity)\\n\",\n \" return run_factorized_fpi_end2end_padded(lls_padded, D, A_dependencies, max_obs_dim, max_state_dim, num_iter)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"id\": \"96d162ed-b35e-44d3-9106-1c37158aab4d\",\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"A_padded = apply_A_end2end_padding_batched(A)\\n\",\n \"\\n\",\n \"if A_sparsity_level is not None:\\n\",\n \" A_padded = jsparse.BCOO.fromdense(A_padded)\\n\",\n \"\\n\",\n \"max_obs_dim = A_padded.shape[2]\\n\",\n \"max_state_dim = max(A_padded.shape[3:])\\n\",\n \"\\n\",\n \"# obs preprocessing\\n\",\n \"obs_padded = apply_obs_end2end_padding_batched(jtu.tree_map(lambda x: jnp.squeeze(x, 1), o_vec), max_obs_dim)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"id\": \"72bc7f44-52e9-4843-aef8-f8255fe785fd\",\n \"metadata\": {\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"([(4, 1, 3),\\n\",\n \" (4, 1, 6),\\n\",\n \" (4, 1, 2),\\n\",\n \" (4, 1, 9),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 4),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 5),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 5)],\\n\",\n \" [Array([[[0.09112392, 0.70235604, 0.20652005]],\\n\",\n \" \\n\",\n \" [[0.202104 , 0.22807139, 0.56982464]],\\n\",\n \" \\n\",\n \" [[0.3876841 , 0.3879837 , 0.2243322 ]],\\n\",\n \" \\n\",\n \" [[0.37516478, 0.27490932, 0.34992588]]], dtype=float32),\\n\",\n \" Array([[[0.15824087, 0.183674 , 0.26761115, 0.09957846, 0.20257226,\\n\",\n \" 0.08832329]],\\n\",\n \" \\n\",\n \" [[0.23064205, 0.02032886, 0.13066185, 0.01698621, 0.2857863 ,\\n\",\n \" 0.31559473]],\\n\",\n \" \\n\",\n \" [[0.19148783, 0.11801518, 0.15054731, 0.13707514, 0.17550918,\\n\",\n \" 0.22736534]],\\n\",\n \" \\n\",\n \" [[0.16028336, 0.27957812, 0.16871531, 0.12887648, 0.1418996 ,\\n\",\n \" 0.12064715]]], dtype=float32),\\n\",\n \" Array([[[0.55582505, 0.44417495]],\\n\",\n \" \\n\",\n \" [[0.549685 , 0.450315 ]],\\n\",\n \" \\n\",\n \" [[0.3831266 , 0.6168734 ]],\\n\",\n \" \\n\",\n \" [[0.5388056 , 0.4611944 ]]], dtype=float32),\\n\",\n \" Array([[[0.07716177, 0.10925393, 0.07744848, 0.1075874 , 0.16774674,\\n\",\n \" 0.09816181, 0.09280077, 0.1271883 , 0.1426509 ]],\\n\",\n \" \\n\",\n \" [[0.12493826, 0.16711089, 0.15916635, 0.13118526, 0.06024319,\\n\",\n \" 0.04707498, 0.12128211, 0.10770807, 0.08129089]],\\n\",\n \" \\n\",\n \" [[0.1815095 , 0.10422336, 0.06684336, 0.14435901, 0.13004695,\\n\",\n \" 0.0635796 , 0.05770647, 0.09602303, 0.15570885]],\\n\",\n \" \\n\",\n \" [[0.04864096, 0.08837192, 0.09715893, 0.13307187, 0.1358143 ,\\n\",\n \" 0.18936108, 0.10949196, 0.09659162, 0.10149743]]], dtype=float32),\\n\",\n \" Array([[[0.16893746, 0.16029103, 0.11270652, 0.18204279, 0.21946692,\\n\",\n \" 0.0823974 , 0.07415791]],\\n\",\n \" \\n\",\n \" [[0.10790369, 0.2240197 , 0.21666422, 0.06581873, 0.10617904,\\n\",\n \" 0.08600904, 0.1934056 ]],\\n\",\n \" \\n\",\n \" [[0.03150751, 0.13815625, 0.12641439, 0.14349648, 0.20863557,\\n\",\n \" 0.33044103, 0.02134874]],\\n\",\n \" \\n\",\n \" [[0.09764872, 0.29433855, 0.18542336, 0.14082211, 0.12583902,\\n\",\n \" 0.07777937, 0.07814886]]], dtype=float32),\\n\",\n \" Array([[[0.20188354, 0.20390284, 0.35773486, 0.23647875]],\\n\",\n \" \\n\",\n \" [[0.13832287, 0.417142 , 0.29778096, 0.14675426]],\\n\",\n \" \\n\",\n \" [[0.14250487, 0.34247938, 0.2867788 , 0.22823687]],\\n\",\n \" \\n\",\n \" [[0.33311817, 0.08985048, 0.27870888, 0.2983224 ]]], dtype=float32),\\n\",\n \" Array([[[0.25531998, 0.09805848, 0.00180036, 0.06169656, 0.30057994,\\n\",\n \" 0.10489379, 0.17765091]],\\n\",\n \" \\n\",\n \" [[0.2913621 , 0.11028862, 0.06915001, 0.06127482, 0.01146838,\\n\",\n \" 0.2958903 , 0.16056576]],\\n\",\n \" \\n\",\n \" [[0.10321112, 0.10843234, 0.09066889, 0.10762182, 0.19040616,\\n\",\n \" 0.18881004, 0.21084957]],\\n\",\n \" \\n\",\n \" [[0.0594087 , 0.15811725, 0.18402615, 0.22240478, 0.20785518,\\n\",\n \" 0.06183277, 0.10635528]]], dtype=float32),\\n\",\n \" Array([[[0.43077335, 0.01719547, 0.18029204, 0.19461544, 0.17712368]],\\n\",\n \" \\n\",\n \" [[0.20952433, 0.28238228, 0.26831535, 0.22654854, 0.01322947]],\\n\",\n \" \\n\",\n \" [[0.34862235, 0.24600424, 0.12305134, 0.11314452, 0.16917753]],\\n\",\n \" \\n\",\n \" [[0.15003254, 0.08879873, 0.19839816, 0.5253277 , 0.03744284]]], dtype=float32),\\n\",\n \" Array([[[0.11571389, 0.04172199, 0.14292377, 0.21811737, 0.1089925 ,\\n\",\n \" 0.2847778 , 0.08775266]],\\n\",\n \" \\n\",\n \" [[0.11719004, 0.01083917, 0.22239207, 0.11398614, 0.09531904,\\n\",\n \" 0.30416313, 0.13611037]],\\n\",\n \" \\n\",\n \" [[0.05459085, 0.16350462, 0.13142684, 0.20870967, 0.17459588,\\n\",\n \" 0.15282223, 0.11434983]],\\n\",\n \" \\n\",\n \" [[0.1454746 , 0.09393647, 0.19433096, 0.22500303, 0.11097853,\\n\",\n \" 0.06738115, 0.16289523]]], dtype=float32),\\n\",\n \" Array([[[0.23350713, 0.21891789, 0.16771066, 0.17027755, 0.20958683]],\\n\",\n \" \\n\",\n \" [[0.19165839, 0.2190793 , 0.20649076, 0.19125327, 0.19151816]],\\n\",\n \" \\n\",\n \" [[0.20866643, 0.18651229, 0.23633833, 0.17361015, 0.19487286]],\\n\",\n \" \\n\",\n \" [[0.24136762, 0.17386994, 0.22222117, 0.1608011 , 0.20174012]]], dtype=float32)])\"\n ]\n },\n \"execution_count\": 16,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"qs = infer_states_end2end_padded(A_padded, obs_padded, D, spec['A_dependencies'], max_obs_dim, max_state_dim, num_iter, sparsity='ll_only')\\n\",\n \"\\n\",\n \"[q.shape for q in qs], qs\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 17,\n \"id\": \"5f161096\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"([(4, 1, 3),\\n\",\n \" (4, 1, 6),\\n\",\n \" (4, 1, 2),\\n\",\n \" (4, 1, 9),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 4),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 5),\\n\",\n \" (4, 1, 7),\\n\",\n \" (4, 1, 5)],\\n\",\n \" [Array([[[0.09112392, 0.70235604, 0.20652005]],\\n\",\n \" \\n\",\n \" [[0.202104 , 0.22807139, 0.56982464]],\\n\",\n \" \\n\",\n \" [[0.3876841 , 0.3879837 , 0.2243322 ]],\\n\",\n \" \\n\",\n \" [[0.37516478, 0.27490932, 0.34992588]]], dtype=float32),\\n\",\n \" Array([[[0.15824087, 0.183674 , 0.26761115, 0.09957846, 0.20257226,\\n\",\n \" 0.08832329]],\\n\",\n \" \\n\",\n \" [[0.23064205, 0.02032886, 0.13066185, 0.01698621, 0.2857863 ,\\n\",\n \" 0.31559473]],\\n\",\n \" \\n\",\n \" [[0.19148783, 0.11801518, 0.15054731, 0.13707514, 0.17550918,\\n\",\n \" 0.22736534]],\\n\",\n \" \\n\",\n \" [[0.16028336, 0.27957812, 0.16871531, 0.12887648, 0.1418996 ,\\n\",\n \" 0.12064715]]], dtype=float32),\\n\",\n \" Array([[[0.55582505, 0.44417495]],\\n\",\n \" \\n\",\n \" [[0.549685 , 0.450315 ]],\\n\",\n \" \\n\",\n \" [[0.3831266 , 0.6168734 ]],\\n\",\n \" \\n\",\n \" [[0.5388056 , 0.4611944 ]]], dtype=float32),\\n\",\n \" Array([[[0.07716177, 0.10925393, 0.07744848, 0.1075874 , 0.16774674,\\n\",\n \" 0.09816181, 0.09280077, 0.1271883 , 0.1426509 ]],\\n\",\n \" \\n\",\n \" [[0.12493826, 0.16711089, 0.15916635, 0.13118526, 0.06024319,\\n\",\n \" 0.04707498, 0.12128211, 0.10770807, 0.08129089]],\\n\",\n \" \\n\",\n \" [[0.1815095 , 0.10422336, 0.06684336, 0.14435901, 0.13004695,\\n\",\n \" 0.0635796 , 0.05770647, 0.09602303, 0.15570885]],\\n\",\n \" \\n\",\n \" [[0.04864096, 0.08837192, 0.09715893, 0.13307187, 0.1358143 ,\\n\",\n \" 0.18936108, 0.10949196, 0.09659162, 0.10149743]]], dtype=float32),\\n\",\n \" Array([[[0.16893746, 0.16029103, 0.11270652, 0.18204279, 0.21946692,\\n\",\n \" 0.0823974 , 0.07415791]],\\n\",\n \" \\n\",\n \" [[0.10790369, 0.2240197 , 0.21666422, 0.06581873, 0.10617904,\\n\",\n \" 0.08600904, 0.1934056 ]],\\n\",\n \" \\n\",\n \" [[0.03150751, 0.13815625, 0.12641439, 0.14349648, 0.20863557,\\n\",\n \" 0.33044103, 0.02134874]],\\n\",\n \" \\n\",\n \" [[0.09764872, 0.29433855, 0.18542336, 0.14082211, 0.12583902,\\n\",\n \" 0.07777937, 0.07814886]]], dtype=float32),\\n\",\n \" Array([[[0.20188354, 0.20390284, 0.35773486, 0.23647875]],\\n\",\n \" \\n\",\n \" [[0.13832287, 0.417142 , 0.29778096, 0.14675426]],\\n\",\n \" \\n\",\n \" [[0.14250487, 0.34247938, 0.2867788 , 0.22823687]],\\n\",\n \" \\n\",\n \" [[0.33311817, 0.08985048, 0.27870888, 0.2983224 ]]], dtype=float32),\\n\",\n \" Array([[[0.25531998, 0.09805848, 0.00180036, 0.06169656, 0.30057994,\\n\",\n \" 0.10489379, 0.17765091]],\\n\",\n \" \\n\",\n \" [[0.2913621 , 0.11028862, 0.06915001, 0.06127482, 0.01146838,\\n\",\n \" 0.2958903 , 0.16056576]],\\n\",\n \" \\n\",\n \" [[0.10321112, 0.10843234, 0.09066889, 0.10762182, 0.19040616,\\n\",\n \" 0.18881004, 0.21084957]],\\n\",\n \" \\n\",\n \" [[0.0594087 , 0.15811725, 0.18402615, 0.22240478, 0.20785518,\\n\",\n \" 0.06183277, 0.10635528]]], dtype=float32),\\n\",\n \" Array([[[0.43077335, 0.01719547, 0.18029204, 0.19461544, 0.17712368]],\\n\",\n \" \\n\",\n \" [[0.20952433, 0.28238228, 0.26831535, 0.22654854, 0.01322947]],\\n\",\n \" \\n\",\n \" [[0.34862235, 0.24600424, 0.12305134, 0.11314452, 0.16917753]],\\n\",\n \" \\n\",\n \" [[0.15003254, 0.08879873, 0.19839816, 0.5253277 , 0.03744284]]], dtype=float32),\\n\",\n \" Array([[[0.11571389, 0.04172199, 0.14292377, 0.21811737, 0.1089925 ,\\n\",\n \" 0.2847778 , 0.08775266]],\\n\",\n \" \\n\",\n \" [[0.11719004, 0.01083917, 0.22239207, 0.11398614, 0.09531904,\\n\",\n \" 0.30416313, 0.13611037]],\\n\",\n \" \\n\",\n \" [[0.05459085, 0.16350462, 0.13142684, 0.20870967, 0.17459588,\\n\",\n \" 0.15282223, 0.11434983]],\\n\",\n \" \\n\",\n \" [[0.1454746 , 0.09393647, 0.19433096, 0.22500303, 0.11097853,\\n\",\n \" 0.06738115, 0.16289523]]], dtype=float32),\\n\",\n \" Array([[[0.23350713, 0.21891789, 0.16771066, 0.17027755, 0.20958683]],\\n\",\n \" \\n\",\n \" [[0.19165839, 0.2190793 , 0.20649076, 0.19125327, 0.19151816]],\\n\",\n \" \\n\",\n \" [[0.20866643, 0.18651229, 0.23633833, 0.17361015, 0.19487286]],\\n\",\n \" \\n\",\n \" [[0.24136762, 0.17386994, 0.22222117, 0.1608011 , 0.20174012]]], dtype=float32)])\"\n ]\n },\n \"execution_count\": 17,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"# JIT\\n\",\n \"apply_obs_padding_batched_jit = jit(partial(apply_obs_end2end_padding_batched, max_obs_dim=max_obs_dim))\\n\",\n \"infer_states_partially_padded_jit = jit(partial(infer_states_end2end_padded, A_dependencies=spec['A_dependencies'], max_obs_dim=max_obs_dim, max_state_dim=max_state_dim, num_iter=num_iter, sparsity='ll_only'))\\n\",\n \"obs_padded = apply_obs_padding_batched_jit(jtu.tree_map(lambda x: jnp.squeeze(x, 1), o_vec))\\n\",\n \"\\n\",\n \"qs = infer_states_partially_padded_jit(A_padded, obs_padded, D)\\n\",\n \"[q.shape for q in qs], qs\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"venv\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.10.18\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 5\n}\n" }, { "path": "examples/advanced/pymdp_with_neural_encoder.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"id\": \"0\",\n \"metadata\": {},\n \"source\": [\n \"# Training a neural network to transform continuous into discrete observations for a `pymdp` Agent\\n\",\n \"\\n\",\n \"With `pymdp`'s JAX backend, it's straightforward to combine differentiable modules with `pymdp`'s active inference processes. We can use tools from `JAX`'s rich neural network ecosystem (`flax`, `optax`, and `equinox`, to name a few) and combine them with active inference agents in creative ways.\\n\",\n \"\\n\",\n \"In this tutorial, we use a simple neural network to embed continuous observations into an `pymdp` agent's observation space; we can train the encoder end-to-end, enabled by JAX's native compatibility with autodifferentiable programs and `pymdp`'s autodifferentiable `Agent` and `Agent` methods.\\n\",\n \"\\n\",\n \"For this simple demo, we fix a discrete generative model (fixed/known `A`, `B`) and train a simple MLP (in `equinox`) to map continuous observations into categorical classes, which can be ingested as observations by the `pymdp` Agent. Because the inference path is differentiable, gradients from a variational objective can flow back through `Agent`-level methods (like `Agent.infer_states`) into encoder parameters.\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"1\",\n \"metadata\": {},\n \"source\": [\n \"## 1. Imports\\n\",\n \"\\n\",\n \"We use JAX/Equinox for pymdp and building our neural network, `pymdp.Agent` for active inference, and Matplotlib for diagnostics and animations.\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"id\": \"2\",\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import time\\n\",\n \"from itertools import permutations\\n\",\n \"\\n\",\n \"import equinox as eqx\\n\",\n \"import jax\\n\",\n \"import jax.nn as jnn\\n\",\n \"import jax.numpy as jnp\\n\",\n \"import jax.random as jr\\n\",\n \"import jax.tree_util as jtu\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"from matplotlib import animation\\n\",\n \"\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"plt.rcParams['animation.html'] = 'jshtml'\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"3\",\n \"metadata\": {},\n \"source\": [\n \"## 2. Setup\\n\",\n \"\\n\",\n \"We define a 5-state line world with local controls (`back`, `stay`, `forward`) and set some training hyperparameters.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"id\": \"4\",\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Reproducibility\\n\",\n \"GLOBAL_KEY = jr.PRNGKey(1)\\n\",\n \"\\n\",\n \"# Problem size\\n\",\n \"K = 5\\n\",\n \"O = K\\n\",\n \"U = 3\\n\",\n \"BACK_ACTION = 0\\n\",\n \"STAY_ACTION = 1\\n\",\n \"FORWARD_ACTION = 2\\n\",\n \"D = 2\\n\",\n \"T = 6\\n\",\n \"POLICY_LEN = 4\\n\",\n \"\\n\",\n \"# Data and training settings\\n\",\n \"N_TRAIN = 640\\n\",\n \"N_VAL = 320\\n\",\n \"BATCH_SIZE = 16\\n\",\n \"TRAIN_STEPS = 200\\n\",\n \"CHECKPOINT_EVERY = 20\\n\",\n \"LR = 1e-3\\n\",\n \"\\n\",\n \"# Encoder architecture\\n\",\n \"ENCODER_WIDTH = 256\\n\",\n \"ENCODER_DEPTH = 3\\n\",\n \"LOGIT_TEMPERATURE = 0.15\\n\",\n \"\\n\",\n \"# Loss weights\\n\",\n \"TEMPORAL_CONSISTENCY_WEIGHT = 8.0\\n\",\n \"\\n\",\n \"# Numerical stability\\n\",\n \"EPS_A = 1e-4\\n\",\n \"EPS = 1e-8\\n\",\n \"\\n\",\n \"# Observation model / dynamics assumptions\\n\",\n \"TRANSITION_NOISE = 0.1\\n\",\n \"\\n\",\n \"# Continuous emissions: one Gaussian mean per discrete state\\n\",\n \"GAUSSIAN_MEANS = jnp.array([\\n\",\n \" [ 0.0, 3.2],\\n\",\n \" [ 3.0, 1.0],\\n\",\n \" [ 1.9, -2.6],\\n\",\n \" [-1.9, -2.6],\\n\",\n \" [-3.0, 1.0],\\n\",\n \"])\\n\",\n \"GAUSSIAN_SCALE = 1.0\\n\",\n \"\\n\",\n \"TARGET_STATE = K - 1\\n\",\n \"START_STATE = 0\\n\",\n \"ROLLOUT_HORIZON = 8\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"5\",\n \"metadata\": {},\n \"source\": [\n \"## 3. Build the Fixed Discrete Agent\\n\",\n \"\\n\",\n \"The agent's generative model is fixed throughout training:\\n\",\n \"\\n\",\n \"- `A`: epsilon-smoothed identity (observation categories aligned with hidden states)\\n\",\n \"- `B`: line dynamics with action-conditioned transitions\\n\",\n \"- `C`: preference for the terminal state\\n\",\n \"- `D`: uniform prior over initial hidden states\\n\",\n \"\\n\",\n \"Only the front-end encoder is optimized.\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"id\": \"6\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"A fixed diagonal: [1.0, 1.0, 1.0, 1.0, 1.0]\\n\",\n \"Local transitions by state:\\n\",\n \" state 0: back -> 0, stay -> 0, forward -> 1\\n\",\n \" state 1: back -> 0, stay -> 1, forward -> 2\\n\",\n \" state 2: back -> 1, stay -> 2, forward -> 3\\n\",\n \" state 3: back -> 2, stay -> 3, forward -> 4\\n\",\n \" state 4: back -> 3, stay -> 4, forward -> 4\\n\"\n ]\n }\n ],\n \"source\": [\n \"def make_eps_identity_A(num_states: int, eps: float) -> jnp.ndarray:\\n\",\n \" eye = jnp.eye(num_states)\\n\",\n \" off = (1.0 - eye) * (eps / (num_states - 1))\\n\",\n \" return (1.0 - eps) * eye + off\\n\",\n \"\\n\",\n \"\\n\",\n \"def make_B_line(num_states: int, num_controls: int, transition_noise: float) -> jnp.ndarray:\\n\",\n \"\\n\",\n \" B_det = jnp.zeros((num_states, num_states, num_controls))\\n\",\n \"\\n\",\n \" for s in range(num_states):\\n\",\n \" back_next = max(s - 1, 0)\\n\",\n \" stay_next = s\\n\",\n \" forward_next = min(s + 1, num_states - 1)\\n\",\n \"\\n\",\n \" B_det = B_det.at[back_next, s, BACK_ACTION].set(1.0)\\n\",\n \" B_det = B_det.at[stay_next, s, STAY_ACTION].set(1.0)\\n\",\n \" B_det = B_det.at[forward_next, s, FORWARD_ACTION].set(1.0)\\n\",\n \"\\n\",\n \" B = (1.0 - transition_noise) * B_det + transition_noise * (jnp.ones_like(B_det) / num_states)\\n\",\n \" B = B / jnp.sum(B, axis=0, keepdims=True)\\n\",\n \" return B\\n\",\n \"\\n\",\n \"\\n\",\n \"A_FIXED_SINGLE = make_eps_identity_A(K, EPS_A)\\n\",\n \"B_TRUE = make_B_line(K, U, TRANSITION_NOISE)\\n\",\n \"\\n\",\n \"\\n\",\n \"def build_agent(batch_size: int) -> Agent:\\n\",\n \" A = [jnp.broadcast_to(A_FIXED_SINGLE, (batch_size, O, K))]\\n\",\n \" B = [jnp.broadcast_to(B_TRUE, (batch_size, K, K, U))]\\n\",\n \"\\n\",\n \" C_single = jnp.zeros((O,)).at[TARGET_STATE].set(8.0)\\n\",\n \" C = [jnp.broadcast_to(C_single, (batch_size, O))]\\n\",\n \"\\n\",\n \" D_single = jnp.ones((K,)) / K\\n\",\n \" D = [jnp.broadcast_to(D_single, (batch_size, K))]\\n\",\n \"\\n\",\n \" return Agent(\\n\",\n \" A=A,\\n\",\n \" B=B,\\n\",\n \" C=C,\\n\",\n \" D=D,\\n\",\n \" A_dependencies=[[0]],\\n\",\n \" B_dependencies=[[0]],\\n\",\n \" num_controls=[U],\\n\",\n \" batch_size=batch_size,\\n\",\n \" policy_len=POLICY_LEN,\\n\",\n \" categorical_obs=True,\\n\",\n \" inference_algo='fpi',\\n\",\n \" num_iter=1,\\n\",\n \" action_selection='deterministic',\\n\",\n \" sampling_mode='full',\\n\",\n \" use_utility=True,\\n\",\n \" use_states_info_gain=True, # although it doesn't matter here\\n\",\n \" use_param_info_gain=False,\\n\",\n \" learn_A=False,\\n\",\n \" learn_B=False,\\n\",\n \" )\\n\",\n \"\\n\",\n \"\\n\",\n \"print('A fixed diagonal:', jnp.round(jnp.diag(A_FIXED_SINGLE), 3).tolist())\\n\",\n \"print('Local transitions by state:')\\n\",\n \"for s in range(K):\\n\",\n \" to_back = int(jnp.argmax(B_TRUE[:, s, BACK_ACTION]))\\n\",\n \" to_stay = int(jnp.argmax(B_TRUE[:, s, STAY_ACTION]))\\n\",\n \" to_fwd = int(jnp.argmax(B_TRUE[:, s, FORWARD_ACTION]))\\n\",\n \" print(f' state {s}: back -> {to_back}, stay -> {to_stay}, forward -> {to_fwd}')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"7\",\n \"metadata\": {},\n \"source\": [\n \"## 4. Generate Offline Continuous Trajectories\\n\",\n \"\\n\",\n \"We simulate offline sequences with balanced state coverage and random actions.\\n\",\n \"\\n\",\n \"Each discrete state emits a 2D Gaussian sample, giving paired trajectories of:\\n\",\n \"\\n\",\n \"- continuous observations `x_t`\\n\",\n \"- latent states `s_t` (for evaluation only)\\n\",\n \"- actions `a_t` (used to propagate empirical priors during training)\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"id\": \"8\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"W0310 14:07:59.095707 1229360 cpp_gen_intrinsics.cc:74] Empty bitcode string provided for eigen. Optimizations relying on this IR will be disabled.\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"train x_seq: (640, 6, 2)\\n\",\n \"train s_seq: (640, 6)\\n\",\n \"train a_seq: (640, 6, 1)\\n\",\n \"train state proportions: [0.21300001 0.201 0.194 0.19600001 0.19500001]\\n\",\n \"val state proportions: [0.21100001 0.20300001 0.20500001 0.19500001 0.186 ]\\n\",\n \"train action proportions: [0.34600002 0.324 0.33 ]\\n\",\n \"val action proportions: [0.356 0.312 0.33100003]\\n\"\n ]\n }\n ],\n \"source\": [\n \"def sample_categorical_batch(key: jnp.ndarray, probs: jnp.ndarray) -> jnp.ndarray:\\n\",\n \" keys = jr.split(key, probs.shape[0])\\n\",\n \" return jax.vmap(lambda k, p: jr.categorical(k, jnp.log(jnp.clip(p, a_min=EPS))))(keys, probs).astype(jnp.int32)\\n\",\n \"\\n\",\n \"\\n\",\n \"def sample_balanced_initial_states(key: jnp.ndarray, num_sequences: int) -> jnp.ndarray:\\n\",\n \" reps = (num_sequences + K - 1) // K\\n\",\n \" base = jnp.tile(jnp.arange(K, dtype=jnp.int32), reps)[:num_sequences]\\n\",\n \" perm = jr.permutation(key, num_sequences)\\n\",\n \" return base[perm]\\n\",\n \"\\n\",\n \"\\n\",\n \"def sample_uniform_actions(key: jnp.ndarray, num_sequences: int) -> jnp.ndarray:\\n\",\n \" return jr.randint(key, shape=(num_sequences,), minval=0, maxval=U).astype(jnp.int32)\\n\",\n \"\\n\",\n \"\\n\",\n \"def simulate_gaussian_sequences(\\n\",\n \" key: jnp.ndarray,\\n\",\n \" num_sequences: int,\\n\",\n \" seq_len: int,\\n\",\n \" means: jnp.ndarray,\\n\",\n \" scale: float,\\n\",\n \"):\\n\",\n \" key_init, key_loop = jr.split(key, 2)\\n\",\n \" s_t = sample_balanced_initial_states(key_init, num_sequences)\\n\",\n \"\\n\",\n \" xs, ss, acts = [], [], []\\n\",\n \"\\n\",\n \" for _ in range(seq_len):\\n\",\n \" key_loop, key_action, key_obs, key_trans = jr.split(key_loop, 4)\\n\",\n \"\\n\",\n \" a_t = sample_uniform_actions(key_action, num_sequences)\\n\",\n \" x_t = means[s_t] + scale * jr.normal(key_obs, (num_sequences, D))\\n\",\n \"\\n\",\n \" xs.append(x_t)\\n\",\n \" ss.append(s_t)\\n\",\n \" acts.append(a_t[:, None])\\n\",\n \"\\n\",\n \" next_probs = jax.vmap(lambda s, a: B_TRUE[:, s, a])(s_t, a_t)\\n\",\n \" s_t = sample_categorical_batch(key_trans, next_probs)\\n\",\n \"\\n\",\n \" return {\\n\",\n \" 'x_seq': jnp.stack(xs, axis=1),\\n\",\n \" 's_seq': jnp.stack(ss, axis=1),\\n\",\n \" 'a_seq': jnp.stack(acts, axis=1),\\n\",\n \" }\\n\",\n \"\\n\",\n \"\\n\",\n \"def state_props(data):\\n\",\n \" counts = jnp.bincount(data['s_seq'].reshape(-1), length=K)\\n\",\n \" return counts / jnp.sum(counts)\\n\",\n \"\\n\",\n \"\\n\",\n \"def action_props(data):\\n\",\n \" counts = jnp.bincount(data['a_seq'][..., 0].reshape(-1), length=U)\\n\",\n \" return counts / jnp.sum(counts)\\n\",\n \"\\n\",\n \"\\n\",\n \"GLOBAL_KEY, key_train, key_val, key_encoder = jr.split(GLOBAL_KEY, 4)\\n\",\n \"train_data = simulate_gaussian_sequences(key_train, N_TRAIN, T, GAUSSIAN_MEANS, GAUSSIAN_SCALE)\\n\",\n \"val_data = simulate_gaussian_sequences(key_val, N_VAL, T, GAUSSIAN_MEANS, GAUSSIAN_SCALE)\\n\",\n \"\\n\",\n \"print('train x_seq:', train_data['x_seq'].shape)\\n\",\n \"print('train s_seq:', train_data['s_seq'].shape)\\n\",\n \"print('train a_seq:', train_data['a_seq'].shape)\\n\",\n \"\\n\",\n \"print('train state proportions:', jnp.round(state_props(train_data), 3))\\n\",\n \"print('val state proportions:', jnp.round(state_props(val_data), 3))\\n\",\n \"print('train action proportions:', jnp.round(action_props(train_data), 3))\\n\",\n \"print('val action proportions:', jnp.round(action_props(val_data), 3))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"9\",\n \"metadata\": {},\n \"source\": [\n \"## 5. Define the Differentiable Front-End\\n\",\n \"\\n\",\n \"The encoder is an Equinox MLP:\\n\",\n \"\\n\",\n \"`x_t -> logits_o_t -> softmax -> o_hat_t`\\n\",\n \"\\n\",\n \"`o_hat_t` is passed directly to `Agent.infer_states` as a categorical observation distribution.\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"id\": \"10\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"encoder initialized\\n\"\n ]\n }\n ],\n \"source\": [\n \"class ObservationEncoder(eqx.Module):\\n\",\n \" mlp: eqx.nn.MLP\\n\",\n \"\\n\",\n \" def __init__(self, key: jnp.ndarray, width: int = ENCODER_WIDTH, depth: int = ENCODER_DEPTH):\\n\",\n \" self.mlp = eqx.nn.MLP(\\n\",\n \" in_size=D,\\n\",\n \" out_size=O,\\n\",\n \" width_size=width,\\n\",\n \" depth=depth,\\n\",\n \" activation=jnn.tanh,\\n\",\n \" final_activation=lambda x: x,\\n\",\n \" key=key,\\n\",\n \" )\\n\",\n \"\\n\",\n \" def __call__(self, x: jnp.ndarray) -> jnp.ndarray:\\n\",\n \" return self.mlp(x)\\n\",\n \"\\n\",\n \"\\n\",\n \"class FrontendModel(eqx.Module):\\n\",\n \" encoder: ObservationEncoder\\n\",\n \"\\n\",\n \" def __init__(self, key_encoder: jnp.ndarray):\\n\",\n \" self.encoder = ObservationEncoder(key_encoder)\\n\",\n \"\\n\",\n \"\\n\",\n \"def model_obs_categorical(model: FrontendModel, x_t: jnp.ndarray):\\n\",\n \" logits = jax.vmap(model.encoder)(x_t) / LOGIT_TEMPERATURE\\n\",\n \" probs = jnn.softmax(logits, axis=-1)\\n\",\n \" probs = jnp.clip(probs, a_min=EPS)\\n\",\n \" probs = probs / probs.sum(axis=-1, keepdims=True)\\n\",\n \" return [probs]\\n\",\n \"\\n\",\n \"\\n\",\n \"key_encoder, _ = jr.split(key_encoder)\\n\",\n \"model_init = FrontendModel(key_encoder)\\n\",\n \"print('encoder initialized')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"11\",\n \"metadata\": {},\n \"source\": [\n \"## 6. Define the Training Objective\\n\",\n \"\\n\",\n \"We optimize a label-free objective composed of:\\n\",\n \"\\n\",\n \"- canonical state-level variational free energy (via `Agent.infer_states(..., return_info=True)`) (still ignores complexity / KL terms related to parameters A, B, D)\\n\",\n \"- temporal observation consistency between `o_hat_{t+1}` and dynamics-predicted next-state beliefs projected through `A`\\n\",\n \"\\n\",\n \"Objective:\\n\",\n \"\\n\",\n \"`loss = mean_t VFE_t + lambda_temp * KL_temporal`\\n\",\n \"\\n\",\n \"This is the key mechanism that encourages the encoder to partition continuous space into discrete categories compatible with the fixed agent model.\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"id\": \"12\",\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"def temporal_obs_consistency_kl(obs_seq: jnp.ndarray, pred_next_state_seq: jnp.ndarray):\\n\",\n \" if obs_seq.shape[1] <= 1:\\n\",\n \" return jnp.array(0.0)\\n\",\n \"\\n\",\n \" pred_obs_next = jnp.einsum('btk,ok->bto', pred_next_state_seq, A_FIXED_SINGLE)\\n\",\n \" pred_obs_next = jnp.clip(pred_obs_next, a_min=EPS)\\n\",\n \" pred_obs_next = pred_obs_next / pred_obs_next.sum(axis=-1, keepdims=True)\\n\",\n \"\\n\",\n \" obs_next = jnp.clip(obs_seq[:, 1:, :], a_min=EPS)\\n\",\n \" kl = jnp.sum(obs_next * (jnp.log(obs_next) - jnp.log(pred_obs_next)), axis=-1)\\n\",\n \" return jnp.mean(kl)\\n\",\n \"\\n\",\n \"\\n\",\n \"def sequence_loss_terms(model: FrontendModel, batch: dict, agent: Agent):\\n\",\n \" batch_size = batch['x_seq'].shape[0]\\n\",\n \"\\n\",\n \" prior = agent.D\\n\",\n \" total_vfe = jnp.array(0.0)\\n\",\n \" obs_seq = []\\n\",\n \" pred_next_state = []\\n\",\n \"\\n\",\n \" n_steps = batch['x_seq'].shape[1]\\n\",\n \"\\n\",\n \" for t in range(n_steps):\\n\",\n \" x_t = batch['x_seq'][:, t, :]\\n\",\n \" obs_t = model_obs_categorical(model, x_t)\\n\",\n \" obs_seq.append(obs_t[0])\\n\",\n \"\\n\",\n \" qs_hist_t, info_t = agent.infer_states(\\n\",\n \" obs_t,\\n\",\n \" empirical_prior=prior,\\n\",\n \" return_info=True,\\n\",\n \" )\\n\",\n \"\\n\",\n \" F_t = info_t['vfe']\\n\",\n \" total_vfe = total_vfe + jnp.mean(F_t)\\n\",\n \"\\n\",\n \" a_t = batch['a_seq'][:, t, :]\\n\",\n \" prior_next = agent.update_empirical_prior(a_t, qs_hist_t)\\n\",\n \" if t < n_steps - 1:\\n\",\n \" pred_next_state.append(prior_next[0])\\n\",\n \" prior = prior_next\\n\",\n \"\\n\",\n \" obs_seq = jnp.stack(obs_seq, axis=1)\\n\",\n \" pred_next_state = jnp.stack(pred_next_state, axis=1) if n_steps > 1 else jnp.zeros((batch_size, 0, K))\\n\",\n \"\\n\",\n \" mean_vfe = total_vfe / n_steps\\n\",\n \" temporal_kl = temporal_obs_consistency_kl(obs_seq, pred_next_state)\\n\",\n \" total = mean_vfe + TEMPORAL_CONSISTENCY_WEIGHT * temporal_kl\\n\",\n \"\\n\",\n \" return total, mean_vfe, temporal_kl, obs_seq\\n\",\n \"\\n\",\n \"\\n\",\n \"def sequence_objective(model: FrontendModel, batch: dict, agent: Agent):\\n\",\n \" total, _, _, _ = sequence_loss_terms(model, batch, agent)\\n\",\n \" return total\\n\",\n \"\\n\",\n \"\\n\",\n \"def sample_batch(key: jnp.ndarray, data: dict, batch_size: int):\\n\",\n \" idx = jr.choice(key, data['x_seq'].shape[0], shape=(batch_size,), replace=False)\\n\",\n \" return {k: v[idx] for k, v in data.items()}\\n\",\n \"\\n\",\n \"\\n\",\n \"def best_aligned_accuracy(true_labels: jnp.ndarray, pred_labels: jnp.ndarray):\\n\",\n \" t = true_labels.reshape(-1).astype(jnp.int32)\\n\",\n \" p = pred_labels.reshape(-1).astype(jnp.int32)\\n\",\n \"\\n\",\n \" best_acc = -1.0\\n\",\n \" best_perm = tuple(range(K))\\n\",\n \" for perm in permutations(range(K)):\\n\",\n \" p_mapped = jnp.array(perm)[p]\\n\",\n \" acc = float(jnp.mean(p_mapped == t))\\n\",\n \" if acc > best_acc:\\n\",\n \" best_acc = acc\\n\",\n \" best_perm = perm\\n\",\n \" return best_acc, best_perm\\n\",\n \"\\n\",\n \"\\n\",\n \"def infer_qs_sequence(model: FrontendModel, batch: dict, agent: Agent):\\n\",\n \" prior = agent.D\\n\",\n \" qs_all = []\\n\",\n \"\\n\",\n \" for t in range(batch['x_seq'].shape[1]):\\n\",\n \" x_t = batch['x_seq'][:, t, :]\\n\",\n \" obs_t = model_obs_categorical(model, x_t)\\n\",\n \" qs_hist_t = agent.infer_states(obs_t, empirical_prior=prior)\\n\",\n \" qs_t = qs_hist_t[0][:, -1, :]\\n\",\n \" qs_all.append(qs_t)\\n\",\n \"\\n\",\n \" a_t = batch['a_seq'][:, t, :]\\n\",\n \" prior = agent.update_empirical_prior(a_t, qs_hist_t)\\n\",\n \"\\n\",\n \" return jnp.stack(qs_all, axis=1)\\n\",\n \"\\n\",\n \"\\n\",\n \"def predict_obs_idx(model: FrontendModel, x_points: jnp.ndarray):\\n\",\n \" logits = jax.vmap(model.encoder)(x_points) / LOGIT_TEMPERATURE\\n\",\n \" return jnp.argmax(logits, axis=-1)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"13\",\n \"metadata\": {},\n \"source\": [\n \"## 7. Train the Encoder\\n\",\n \"\\n\",\n \"We train with minibatches sampled from offline trajectories.\\n\",\n \"\\n\",\n \"At each timestep in a sequence, the notebook:\\n\",\n \"\\n\",\n \"1. encodes `x_t` to `o_hat_t`\\n\",\n \"2. runs `infer_states(o_hat_t, prior_t)`\\n\",\n \"3. accumulates VFE\\n\",\n \"4. updates prior using observed `a_t`\\n\",\n \"5. accumulates temporal consistency across steps\\n\",\n \"\\n\",\n \"Gradients are computed with `eqx.filter_value_and_grad` and applied directly to encoder parameters.\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"id\": \"14\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_16049/1731807479.py:39: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" return Agent(\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"initial objective: 15.04537582397461\\n\",\n \"training finished in 5.10s\\n\",\n \"final train total/vfe/temp: 6.0631256103515625 1.2384639978408813 0.6030827164649963\\n\",\n \"final val total/vfe/temp: 4.517769813537598 1.1381111145019531 0.42245736718177795\\n\"\n ]\n }\n ],\n \"source\": [\n \"train_agent = build_agent(BATCH_SIZE)\\n\",\n \"\\n\",\n \"@eqx.filter_jit\\n\",\n \"def train_step(model: FrontendModel, batch: dict):\\n\",\n \" loss, grads = eqx.filter_value_and_grad(sequence_objective)(model, batch, train_agent)\\n\",\n \" updates = jtu.tree_map(lambda g: -LR * g if g is not None else None, grads)\\n\",\n \" model = eqx.apply_updates(model, updates)\\n\",\n \" return model, loss, grads\\n\",\n \"\\n\",\n \"\\n\",\n \"def evaluate_model(model_eval: FrontendModel, batch: dict, agent: Agent):\\n\",\n \" qs_seq = infer_qs_sequence(model_eval, batch, agent)\\n\",\n \" pred_states = jnp.argmax(qs_seq, axis=-1)\\n\",\n \" raw_acc = float(jnp.mean(pred_states == batch['s_seq']))\\n\",\n \" aligned_acc, best_perm = best_aligned_accuracy(batch['s_seq'], pred_states)\\n\",\n \"\\n\",\n \" total, mean_vfe, temporal_kl, _ = sequence_loss_terms(model_eval, batch, agent)\\n\",\n \"\\n\",\n \" return {\\n\",\n \" 'raw_acc': raw_acc,\\n\",\n \" 'aligned_acc': float(aligned_acc),\\n\",\n \" 'best_perm': best_perm,\\n\",\n \" 'total': float(total),\\n\",\n \" 'vfe': float(mean_vfe),\\n\",\n \" 'temporal_kl': float(temporal_kl),\\n\",\n \" 'pred_states': pred_states,\\n\",\n \" }\\n\",\n \"\\n\",\n \"\\n\",\n \"GLOBAL_KEY, key_probe = jr.split(GLOBAL_KEY)\\n\",\n \"probe_batch = sample_batch(key_probe, train_data, BATCH_SIZE)\\n\",\n \"probe_loss, probe_grads = eqx.filter_value_and_grad(sequence_objective)(model_init, probe_batch, train_agent)\\n\",\n \"print('initial objective:', float(probe_loss))\\n\",\n \"\\n\",\n \"model = model_init\\n\",\n \"train_total_curve = []\\n\",\n \"train_vfe_curve = []\\n\",\n \"train_temp_curve = []\\n\",\n \"val_total_curve = []\\n\",\n \"val_vfe_curve = []\\n\",\n \"val_temp_curve = []\\n\",\n \"curve_steps = []\\n\",\n \"\\n\",\n \"start = time.time()\\n\",\n \"for step in range(TRAIN_STEPS):\\n\",\n \" GLOBAL_KEY, key_batch, key_val = jr.split(GLOBAL_KEY, 3)\\n\",\n \" train_batch = sample_batch(key_batch, train_data, BATCH_SIZE)\\n\",\n \" model, loss, grads = train_step(model, train_batch)\\n\",\n \"\\n\",\n \" if (step % CHECKPOINT_EVERY == 0) or (step == TRAIN_STEPS - 1):\\n\",\n \" val_batch = sample_batch(key_val, val_data, BATCH_SIZE)\\n\",\n \"\\n\",\n \" train_metrics = evaluate_model(model, train_batch, train_agent)\\n\",\n \" val_metrics = evaluate_model(model, val_batch, train_agent)\\n\",\n \"\\n\",\n \" train_total_curve.append(train_metrics['total'])\\n\",\n \" train_vfe_curve.append(train_metrics['vfe'])\\n\",\n \" train_temp_curve.append(train_metrics['temporal_kl'])\\n\",\n \" val_total_curve.append(val_metrics['total'])\\n\",\n \" val_vfe_curve.append(val_metrics['vfe'])\\n\",\n \" val_temp_curve.append(val_metrics['temporal_kl'])\\n\",\n \" curve_steps.append(step)\\n\",\n \"\\n\",\n \"elapsed = time.time() - start\\n\",\n \"print(f'training finished in {elapsed:.2f}s')\\n\",\n \"print('final train total/vfe/temp:', train_total_curve[-1], train_vfe_curve[-1], train_temp_curve[-1])\\n\",\n \"print('final val total/vfe/temp:', val_total_curve[-1], val_vfe_curve[-1], val_temp_curve[-1])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"15\",\n \"metadata\": {},\n \"source\": [\n \"## 8. Evaluate Representation Quality\\n\",\n \"\\n\",\n \"We evaluate both:\\n\",\n \"\\n\",\n \"- encoder-level discrete assignments (`argmax` over encoder logits)\\n\",\n \"- inferred-state assignments (`argmax` over `q(s_t)`)\\n\",\n \"\\n\",\n \"To account for permutation symmetry, accuracy is reported after best label alignment.\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"id\": \"16\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_16049/1731807479.py:39: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" return Agent(\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Encoder aligned acc (pre/post): 0.5838541984558105 0.9515625238418579\\n\",\n \"Inferred-state aligned acc (pre/post): 0.48750001192092896 0.9630208611488342\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"def confusion_matrix(true_states: jnp.ndarray, pred_states: jnp.ndarray, num_states: int):\\n\",\n \" cm = jnp.zeros((num_states, num_states))\\n\",\n \" t = true_states.reshape(-1)\\n\",\n \" p = pred_states.reshape(-1)\\n\",\n \" cm = cm.at[t, p].add(1)\\n\",\n \" cm = cm / jnp.clip(cm.sum(axis=1, keepdims=True), a_min=1.0)\\n\",\n \" return cm\\n\",\n \"\\n\",\n \"\\n\",\n \"val_batch_full = val_data\\n\",\n \"val_agent_full = build_agent(val_batch_full['x_seq'].shape[0])\\n\",\n \"\\n\",\n \"pre_metrics = evaluate_model(model_init, val_batch_full, val_agent_full)\\n\",\n \"post_metrics = evaluate_model(model, val_batch_full, val_agent_full)\\n\",\n \"\\n\",\n \"# Encoder-level discrete category assignment quality\\n\",\n \"flat_x = val_data['x_seq'].reshape(-1, D)\\n\",\n \"flat_s = val_data['s_seq'].reshape(-1)\\n\",\n \"\\n\",\n \"enc_pre = predict_obs_idx(model_init, flat_x)\\n\",\n \"enc_post = predict_obs_idx(model, flat_x)\\n\",\n \"enc_pre_aligned, enc_pre_perm = best_aligned_accuracy(flat_s, enc_pre)\\n\",\n \"enc_post_aligned, enc_post_perm = best_aligned_accuracy(flat_s, enc_post)\\n\",\n \"\\n\",\n \"print('Encoder aligned acc (pre/post):', enc_pre_aligned, enc_post_aligned)\\n\",\n \"print('Inferred-state aligned acc (pre/post):', pre_metrics['aligned_acc'], post_metrics['aligned_acc'])\\n\",\n \"\\n\",\n \"pre_pred_aligned = jnp.array(pre_metrics['best_perm'])[pre_metrics['pred_states']]\\n\",\n \"post_pred_aligned = jnp.array(post_metrics['best_perm'])[post_metrics['pred_states']]\\n\",\n \"cm_pre = confusion_matrix(val_data['s_seq'], pre_pred_aligned, K)\\n\",\n \"cm_post = confusion_matrix(val_data['s_seq'], post_pred_aligned, K)\\n\",\n \"\\n\",\n \"fig = plt.figure(figsize=(16, 4))\\n\",\n \"gs = fig.add_gridspec(1, 4, width_ratios=[1.35, 1.0, 0.06, 1.0], wspace=0.4)\\n\",\n \"\\n\",\n \"ax0 = fig.add_subplot(gs[0, 0])\\n\",\n \"ax1 = fig.add_subplot(gs[0, 1])\\n\",\n \"cax = fig.add_subplot(gs[0, 2])\\n\",\n \"ax2 = fig.add_subplot(gs[0, 3])\\n\",\n \"\\n\",\n \"ax0.plot(curve_steps, train_total_curve, label='train total')\\n\",\n \"ax0.plot(curve_steps, val_total_curve, label='val total')\\n\",\n \"ax0.plot(curve_steps, train_vfe_curve, '--', label='train VFE')\\n\",\n \"ax0.plot(curve_steps, train_temp_curve, '--', label='train temporal KL')\\n\",\n \"ax0.set_title('Training Curves')\\n\",\n \"ax0.set_xlabel('step')\\n\",\n \"ax0.legend()\\n\",\n \"\\n\",\n \"ax1.imshow(cm_pre, vmin=0.0, vmax=1.0)\\n\",\n \"ax1.set_title('State Confusion (Pre, aligned)')\\n\",\n \"ax1.set_xlabel('pred state')\\n\",\n \"ax1.set_ylabel('true state')\\n\",\n \"\\n\",\n \"im = ax2.imshow(cm_post, vmin=0.0, vmax=1.0)\\n\",\n \"ax2.set_title('State Confusion (Post, aligned)')\\n\",\n \"ax2.set_xlabel('pred state')\\n\",\n \"ax2.set_ylabel('true state')\\n\",\n \"\\n\",\n \"fig.colorbar(im, cax=cax)\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"17\",\n \"metadata\": {},\n \"source\": [\n \"## 9. Plan from Continuous Observations\\n\",\n \"\\n\",\n \"After training, we run a rollout starting from state 0.\\n\",\n \"\\n\",\n \"At each step, the agent receives a continuous sample, maps it through the encoder, infers state beliefs, selects an action from policy inference, and transitions under fixed `B`.\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"id\": \"18\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_16049/1731807479.py:39: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" return Agent(\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"rollout states: [0, 1, 2, 3, 4, 4, 4, 4, 4]\\n\",\n \"rollout actions: ['forward', 'forward', 'forward', 'forward', 'forward', 'forward', 'forward', 'forward']\\n\",\n \"reached target: True\\n\"\n ]\n }\n ],\n \"source\": [\n \"def rollout_from_state_zero(model_eval: FrontendModel, horizon: int = ROLLOUT_HORIZON, seed: int = 1):\\n\",\n \" agent = build_agent(batch_size=1)\\n\",\n \"\\n\",\n \" key = jr.PRNGKey(seed)\\n\",\n \" s_t = START_STATE\\n\",\n \" prior = [jax.nn.one_hot(jnp.array([s_t], dtype=jnp.int32), K)]\\n\",\n \"\\n\",\n \" states = [int(s_t)]\\n\",\n \" actions = []\\n\",\n \" obs_points = []\\n\",\n \" obs_probs_hist = []\\n\",\n \" qs_hist = []\\n\",\n \"\\n\",\n \" for _ in range(horizon):\\n\",\n \" key, key_obs = jr.split(key)\\n\",\n \"\\n\",\n \" x_t = GAUSSIAN_MEANS[s_t] + GAUSSIAN_SCALE * jr.normal(key_obs, (D,))\\n\",\n \" obs_t = model_obs_categorical(model_eval, x_t[None, :])\\n\",\n \"\\n\",\n \" qs_t_hist = agent.infer_states(obs_t, empirical_prior=prior)\\n\",\n \" qs_t = qs_t_hist[0][:, -1, :][0]\\n\",\n \"\\n\",\n \" q_pi_t, _ = agent.infer_policies(qs_t_hist)\\n\",\n \" a_t = agent.sample_action(q_pi_t)\\n\",\n \" a_int = int(a_t[0, 0])\\n\",\n \"\\n\",\n \" next_probs = B_TRUE[:, s_t, a_int]\\n\",\n \" s_next = int(jnp.argmax(next_probs))\\n\",\n \"\\n\",\n \" obs_points.append(x_t)\\n\",\n \" obs_probs_hist.append(obs_t[0][0])\\n\",\n \" qs_hist.append(qs_t)\\n\",\n \" actions.append(a_int)\\n\",\n \" states.append(s_next)\\n\",\n \"\\n\",\n \" prior = agent.update_empirical_prior(a_t, qs_t_hist)\\n\",\n \" s_t = s_next\\n\",\n \"\\n\",\n \" return {\\n\",\n \" 'states': jnp.array(states), # length horizon+1\\n\",\n \" 'actions': jnp.array(actions), # length horizon\\n\",\n \" 'obs_points': jnp.stack(obs_points), # (horizon, 2)\\n\",\n \" 'obs_probs': jnp.stack(obs_probs_hist),\\n\",\n \" 'qs': jnp.stack(qs_hist),\\n\",\n \" }\\n\",\n \"\\n\",\n \"\\n\",\n \"rollout = rollout_from_state_zero(model, horizon=ROLLOUT_HORIZON, seed=1)\\n\",\n \"action_names = ['back', 'stay', 'forward']\\n\",\n \"\\n\",\n \"print('rollout states:', rollout['states'].tolist())\\n\",\n \"print('rollout actions:', [action_names[int(a)] for a in rollout['actions']])\\n\",\n \"print('reached target:', int(rollout['states'][-1]) == TARGET_STATE)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"19\",\n \"metadata\": {},\n \"source\": [\n \"## 10. Animation: Continuous Density + Inference During Control\\n\",\n \"\\n\",\n \"The first GIF visualizes control over the continuous observation space:\\n\",\n \"\\n\",\n \"- left panel: state geometry, trajectory, and sampled observations over a Gaussian-density background\\n\",\n \"- right panel: inferred state posterior `q(s_t)` over time\\n\",\n \"- title: current inference summary plus the action taken at the previous timestep\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"id\": \"20\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"
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lo, 1e-12)\\n\",\n \"\\n\",\n \" return (capped - lo) / denom\\n\",\n \"\\n\",\n \"\\n\",\n \"def make_rollout_gif(rollout_data: dict):\\n\",\n \" states = rollout_data['states']\\n\",\n \" actions = rollout_data['actions']\\n\",\n \" obs_points = rollout_data['obs_points']\\n\",\n \" obs_probs = rollout_data['obs_probs']\\n\",\n \" qs = rollout_data['qs']\\n\",\n \"\\n\",\n \" horizon = actions.shape[0]\\n\",\n \"\\n\",\n \" fig, (ax_l, ax_r) = plt.subplots(1, 2, figsize=(12, 5))\\n\",\n \"\\n\",\n \" pad = 3 * GAUSSIAN_SCALE\\n\",\n \" x_min = float(jnp.min(GAUSSIAN_MEANS[:, 0])) - pad\\n\",\n \" x_max = float(jnp.max(GAUSSIAN_MEANS[:, 0])) + pad\\n\",\n \" y_min = float(jnp.min(GAUSSIAN_MEANS[:, 1])) - pad\\n\",\n \" y_max = float(jnp.max(GAUSSIAN_MEANS[:, 1])) + pad\\n\",\n \"\\n\",\n \" # Left: line-world geometry on top of summed Gaussian PDF background.\\n\",\n \" region_cmap = plt.get_cmap('tab10', K)\\n\",\n \" pdf_bg_sum, mode_peak = gaussian_pdf_sum_grid(GAUSSIAN_MEANS, GAUSSIAN_SCALE, x_min, x_max, y_min, y_max)\\n\",\n \" pdf_bg = normalize_density_for_display(pdf_bg_sum, mode_peak)\\n\",\n \"\\n\",\n \" ax_l.imshow(\\n\",\n \" pdf_bg,\\n\",\n \" extent=[x_min, x_max, y_min, y_max],\\n\",\n \" origin='lower',\\n\",\n \" cmap='seismic',\\n\",\n \" vmin=0.0,\\n\",\n \" vmax=1.0,\\n\",\n \" alpha=0.82,\\n\",\n \" aspect='auto',\\n\",\n \" zorder=0,\\n\",\n \" )\\n\",\n \"\\n\",\n \" ax_l.plot(GAUSSIAN_MEANS[:, 0], GAUSSIAN_MEANS[:, 1], 'k--', alpha=0.35, linewidth=1.0, zorder=2)\\n\",\n \" ax_l.scatter(GAUSSIAN_MEANS[:, 0], GAUSSIAN_MEANS[:, 1], s=180, c=jnp.arange(K), cmap=region_cmap, zorder=3, edgecolors='black')\\n\",\n \" for s in range(K):\\n\",\n \" ax_l.text(float(GAUSSIAN_MEANS[s, 0]) + 0.08, float(GAUSSIAN_MEANS[s, 1]) + 0.08, f's{s}', fontsize=10)\\n\",\n \"\\n\",\n \" path_line, = ax_l.plot([], [], '-o', color='tab:red', linewidth=2.0, markersize=6, zorder=4)\\n\",\n \" obs_dot = ax_l.scatter([], [], s=112, marker='x', color='green', linewidths=2.0, zorder=5)\\n\",\n \"\\n\",\n \" ax_l.set_title('State Path over Continuous Observation Density')\\n\",\n \" ax_l.set_xlabel('x1')\\n\",\n \" ax_l.set_ylabel('x2')\\n\",\n \" ax_l.set_aspect('equal', adjustable='box')\\n\",\n \" ax_l.set_xlim(x_min, x_max)\\n\",\n \" ax_l.set_ylim(y_min, y_max)\\n\",\n \"\\n\",\n \" # Right: inferred state posterior q(s_t) over time.\\n\",\n \" heat_init = jnp.full((K, horizon), jnp.nan)\\n\",\n \" heat = ax_r.imshow(heat_init, vmin=0.0, vmax=1.0, cmap='viridis', origin='lower', aspect='auto')\\n\",\n \" ax_r.set_title('Inference Result: q(s_t)')\\n\",\n \" ax_r.set_xlabel('timestep')\\n\",\n \" ax_r.set_ylabel('state index')\\n\",\n \" ax_r.set_xticks(range(horizon))\\n\",\n \" ax_r.set_yticks(range(K))\\n\",\n \" fig.colorbar(heat, ax=ax_r, fraction=0.046, pad=0.04)\\n\",\n \"\\n\",\n \" title = fig.suptitle('', fontsize=12)\\n\",\n \"\\n\",\n \" def update(frame):\\n\",\n \" # Show states only up to current time t (edge for a_t appears at frame t+1).\\n\",\n \" state_path = states[: frame + 1]\\n\",\n \" coords = GAUSSIAN_MEANS[state_path]\\n\",\n \" path_line.set_data(coords[:, 0], coords[:, 1])\\n\",\n \"\\n\",\n \" # Continuous observation sampled at current timestep t.\\n\",\n \" obs_dot.set_offsets(obs_points[: frame + 1])\\n\",\n \"\\n\",\n \" # Show inference results up to current frame.\\n\",\n \" heat_arr = jnp.full((K, horizon), jnp.nan)\\n\",\n \" heat_arr = heat_arr.at[:, : frame + 1].set(jnp.stack(qs[: frame + 1], axis=1))\\n\",\n \" heat.set_data(heat_arr)\\n\",\n \"\\n\",\n \" enc_idx = int(jnp.argmax(obs_probs[frame]))\\n\",\n \" q_idx = int(jnp.argmax(qs[frame]))\\n\",\n \" action_taken = 'None' if frame == 0 else action_names[int(actions[frame - 1])]\\n\",\n \"\\n\",\n \" title.set_text(\\n\",\n \" f't={frame} | true_state={int(states[frame])} | encoded_obs_idx={enc_idx} | inferred_state={q_idx} | action taken: {action_taken}'\\n\",\n \" )\\n\",\n \"\\n\",\n \" return path_line, obs_dot, heat\\n\",\n \"\\n\",\n \" ani = animation.FuncAnimation(fig, update, frames=horizon, interval=900, blit=False, repeat=True)\\n\",\n \" plt.close(fig)\\n\",\n \" return ani\\n\",\n \"\\n\",\n \"\\n\",\n \"make_rollout_gif_anim = make_rollout_gif(rollout)\\n\",\n \"make_rollout_gif_anim\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"21\",\n \"metadata\": {},\n \"source\": [\n \"## 11. Animation: Encoder Decision Regions + Control Trajectory\\n\",\n \"\\n\",\n \"The second GIF replaces the left-panel density background with encoder decision regions.\\n\",\n \"\\n\",\n \"Each region corresponds to the observation index predicted by the encoder, making the learned continuous-to-discrete partition explicit during rollout.\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"id\": \"22\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"
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pad\\n\",\n \" x_max = float(jnp.max(GAUSSIAN_MEANS[:, 0])) + pad\\n\",\n \" y_min = float(jnp.min(GAUSSIAN_MEANS[:, 1])) - pad\\n\",\n \" y_max = float(jnp.max(GAUSSIAN_MEANS[:, 1])) + pad\\n\",\n \"\\n\",\n \" xx, yy, pred_grid = encoder_decision_grid(model_eval, x_min, x_max, y_min, y_max, n=320)\\n\",\n \"\\n\",\n \" region_cmap = plt.get_cmap('tab10', K)\\n\",\n \" region_img = ax_l.imshow(\\n\",\n \" pred_grid,\\n\",\n \" extent=[x_min, x_max, y_min, y_max],\\n\",\n \" origin='lower',\\n\",\n \" cmap=region_cmap,\\n\",\n \" vmin=-0.5,\\n\",\n \" vmax=K - 0.5,\\n\",\n \" interpolation='nearest',\\n\",\n \" alpha=0.72,\\n\",\n \" aspect='auto',\\n\",\n \" zorder=0,\\n\",\n \" )\\n\",\n \"\\n\",\n \" ax_l.contour(\\n\",\n \" xx,\\n\",\n \" yy,\\n\",\n \" pred_grid,\\n\",\n \" levels=jnp.arange(0.5, K, 1.0),\\n\",\n \" colors='white',\\n\",\n \" linewidths=0.8,\\n\",\n \" alpha=0.9,\\n\",\n \" zorder=1,\\n\",\n \" )\\n\",\n \"\\n\",\n \" ax_l.plot(GAUSSIAN_MEANS[:, 0], GAUSSIAN_MEANS[:, 1], 'k--', alpha=0.35, linewidth=1.0, zorder=2)\\n\",\n \" ax_l.scatter(GAUSSIAN_MEANS[:, 0], GAUSSIAN_MEANS[:, 1], s=180, c=jnp.arange(K), cmap=region_cmap, zorder=3, edgecolors='black')\\n\",\n \" for s in range(K):\\n\",\n \" ax_l.text(float(GAUSSIAN_MEANS[s, 0]) + 0.08, float(GAUSSIAN_MEANS[s, 1]) + 0.08, f's{s}', fontsize=10)\\n\",\n \"\\n\",\n \" path_line, = ax_l.plot([], [], '-o', color='tab:red', linewidth=2.0, markersize=6, zorder=4)\\n\",\n \" obs_dot = ax_l.scatter([], [], s=112, marker='x', color='black', linewidths=2.0, zorder=5)\\n\",\n \"\\n\",\n \" ax_l.set_title('State Path over Encoder Decision Regions')\\n\",\n \" ax_l.set_xlabel('x1')\\n\",\n \" ax_l.set_ylabel('x2')\\n\",\n \" ax_l.set_aspect('equal', adjustable='box')\\n\",\n \" ax_l.set_xlim(x_min, x_max)\\n\",\n \" ax_l.set_ylim(y_min, y_max)\\n\",\n \"\\n\",\n \" cb_left = fig.colorbar(region_img, ax=ax_l, fraction=0.046, pad=0.03, ticks=jnp.arange(K))\\n\",\n \" cb_left.set_label('encoder class')\\n\",\n \"\\n\",\n \" heat_init = jnp.full((K, horizon), jnp.nan)\\n\",\n \" heat = ax_r.imshow(heat_init, vmin=0.0, vmax=1.0, cmap='viridis', origin='lower', aspect='auto')\\n\",\n \" ax_r.set_title('Inference Result: q(s_t)')\\n\",\n \" ax_r.set_xlabel('timestep')\\n\",\n \" ax_r.set_ylabel('state index')\\n\",\n \" ax_r.set_xticks(range(horizon))\\n\",\n \" ax_r.set_yticks(range(K))\\n\",\n \" fig.colorbar(heat, ax=ax_r, fraction=0.046, pad=0.04)\\n\",\n \"\\n\",\n \" title = fig.suptitle('', fontsize=12)\\n\",\n \"\\n\",\n \" def update(frame):\\n\",\n \" state_path = states[: frame + 1]\\n\",\n \" coords = GAUSSIAN_MEANS[state_path]\\n\",\n \" path_line.set_data(coords[:, 0], coords[:, 1])\\n\",\n \"\\n\",\n \" obs_dot.set_offsets(obs_points[: frame + 1])\\n\",\n \"\\n\",\n \" heat_arr = jnp.full((K, horizon), jnp.nan)\\n\",\n \" heat_arr = heat_arr.at[:, : frame + 1].set(jnp.stack(qs[: frame + 1], axis=1))\\n\",\n \" heat.set_data(heat_arr)\\n\",\n \"\\n\",\n \" enc_idx = int(jnp.argmax(obs_probs[frame]))\\n\",\n \" q_idx = int(jnp.argmax(qs[frame]))\\n\",\n \" action_taken = 'None' if frame == 0 else action_names[int(actions[frame - 1])]\\n\",\n \"\\n\",\n \" title.set_text(\\n\",\n \" f't={frame} | true_state={int(states[frame])} | encoded_obs_idx={enc_idx} | inferred_state={q_idx} | action taken: {action_taken}'\\n\",\n \" )\\n\",\n \"\\n\",\n \" return path_line, obs_dot, heat\\n\",\n \"\\n\",\n \" ani = animation.FuncAnimation(fig, update, frames=horizon, interval=900, blit=False, repeat=True)\\n\",\n \" plt.close(fig)\\n\",\n \" return ani\\n\",\n \"\\n\",\n \"\\n\",\n \"make_rollout_decision_gif_anim = make_rollout_decision_gif(model, rollout)\\n\",\n \"make_rollout_decision_gif_anim\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"23\",\n \"metadata\": {},\n \"source\": [\n \"## 12. Summary\\n\",\n \"\\n\",\n \"This notebook demonstrates a practical recipe for combining a differentiable layer with an structured `pymdp` generative model that can be trained with gradients & backpropagation, while the active inference agent performs variational inference and planning with explicit active inference style updates.\\n\",\n \"\\n\",\n \"One way of interpreting the differentiable front-end in this notebook, is as an _amortized inference module_ that learns how to execute inference in a Gaussian mixture model in its forward pass; specifically computing the latent assignment variable of a GMM (also known as the \\\"E-step\\\"). The analogy to amortized inference is not exact since the MLP layer is not guaranteed to provide calibrated probabilistic assignments; the decision-boundaries it creates in 2-D space are not the same as the soft decision-boundaries achieved by fitting a proper GMM via expectation maximization or variational Bayesian expectation maximization.\\n\",\n \"\\n\",\n \"In the current notebook, we fixed the generative model at the `pymdp` level; a natural next step would be to combine gradient-based learning with either gradient-based or explicitly Bayesian updates to the POMDP model parameters (A, B, and D).\"\n ]\n }\n ],\n \"metadata\": {},\n \"nbformat\": 4,\n \"nbformat_minor\": 5\n}\n" }, { "path": "examples/api/model_construction_tutorial.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Generative Model Construction with `Model` and `Distribution`\\n\",\n \"\\n\",\n \"This tutorial walks through usage of the `Model` and `Distribution` classes. The `Model` class wraps the `A`, `B`, `C`, and `D` arrays into a unified model object, whose structure can be generated automatically from a JSON-like configuration dict. The configuration dict, often labelled `model_description`, allows you to assign string-valued names to the random variables of the model (observations, hidden states, and control states), and to specify dependencies between these random variables (via the `\\\"depends_on\\\"` key within each variable-specific sub-dict). \\n\",\n \"\\n\",\n \"Within the `Model` object, each component distribution is an instance of the `Distribution` class. The `Distribution` class can use string- or integer-valued labels for both the axes and specific indices along those axes. The intention of these classes and their named dimensions/values, is to provide users a more user-friendly, interpretable entrypoint for building discrete generative models in `pymdp`.\\n\",\n \"\\n\",\n \"In the summary, the advantages of the `Model` and `Distribution` classes are:\\n\",\n \"- Reduce memory burden on the user (and the indexing errors that often ensue) by working with named axes and elements (e.g., \\\"left\\\", \\\"right\\\" instead of 0, 1)\\n\",\n \"- Increase interpretability (if applicable) and intuition in the generation and inspection of the POMDP model\\n\",\n \"- Flexible specification of dependencies between random variables via string labels\\n\",\n \"\\n\",\n \"## Tutorial Structure\\n\",\n \"\\n\",\n \"1. Basic Example: A simple grid navigation task built from a structured description using labels, in which the agent has to travel to a goal location.\\n\",\n \"2. A More Advanced Example: A simple foraging task built from a structured description using labels, in which the agent has to search for apples and eat them while they spawn at a set rate.\\n\",\n \"\\n\",\n \"---\\n\",\n \"\\n\",\n \"## Example 1: Grid World Navigation\\n\",\n \"\\n\",\n \"Let's start with the simple example: an agent moving horizontally in a 1D grid world. Our agent can be in one of four positions: \\\"left\\\", \\\"center_left\\\", \\\"center_right\\\", or \\\"right\\\", and can take actions \\\"move_right\\\" or \\\"move_left\\\". We give an example of setting up a single agent and then an example of running three agents in parallel by using the`batch_size` argument to the `Agent` constructor.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import jax.tree_util as jtu\\n\",\n \"from jax import numpy as jnp\\n\",\n \"from jax import random as jr\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp.distribution import compile_model\\n\",\n \"from pymdp.envs.env import Env\\n\",\n \"from pymdp.envs import rollout\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"positions = [\\\"left\\\", \\\"center_left\\\", \\\"center_right\\\", \\\"right\\\"]\\n\",\n \"actions = [\\\"move_left\\\", \\\"move_right\\\"]\\n\",\n \"\\n\",\n \"model_description = {\\n\",\n \" \\\"observations\\\": {\\n\",\n \" \\\"position_obs\\\": {\\n\",\n \" \\\"elements\\\": positions, \\n\",\n \" \\\"depends_on\\\": [\\\"position\\\"] # we specify that the observation depends on the \\\"position\\\" state factor\\n\",\n \" },\\n\",\n \" },\\n\",\n \" \\\"controls\\\": {\\n\",\n \" \\\"movement\\\": {\\\"elements\\\": actions} # we specify the available actions\\n\",\n \" },\\n\",\n \" \\\"states\\\": {\\n\",\n \" \\\"position\\\": {\\n\",\n \" \\\"elements\\\": positions, \\n\",\n \" \\\"depends_on\\\": [\\\"position\\\"], # our current position depends on previous position...\\n\",\n \" \\\"controlled_by\\\": [\\\"movement\\\"] # ...and the movement action taken\\n\",\n \" },\\n\",\n \" },\\n\",\n \"}\\n\",\n \"\\n\",\n \"# compile the model structure from the description\\n\",\n \"model = compile_model(model_description)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We have built a generative model structure using the model description, however the model's parameters are currently uninitialized arrays of zeros. So now, we can fill in the parameter tensors by using the axis and element labels we defined in the model description dict, to set values in particular indices of these arrays.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# fill in the likelihood (A) tensor\\n\",\n \"# the observations have an identical mapping to the states (i.e., the agent will perfectly observe its position)\\n\",\n \"model.A[\\\"position_obs\\\"][\\\"left\\\", \\\"left\\\"] = 1.0\\n\",\n \"model.A[\\\"position_obs\\\"][\\\"center_left\\\", \\\"center_left\\\"] = 1.0\\n\",\n \"model.A[\\\"position_obs\\\"][\\\"center_right\\\", \\\"center_right\\\"] = 1.0\\n\",\n \"model.A[\\\"position_obs\\\"][\\\"right\\\", \\\"right\\\"] = 1.0\\n\",\n \"# model.A[\\\"position_obs\\\"].data = jnp.eye(len(positions)) # you could also use the .data attribute to set the identity mapping directly\\n\",\n \"\\n\",\n \"# fill in the transition model (B) tensor\\n\",\n \"# note that it's specified as [\\\"to\\\", \\\"from\\\", \\\"action\\\"]\\n\",\n \"# moving right\\n\",\n \"model.B[\\\"position\\\"][\\\"center_left\\\", \\\"left\\\", \\\"move_right\\\"] = 1.0 \\n\",\n \"model.B[\\\"position\\\"][\\\"center_right\\\", \\\"center_left\\\", \\\"move_right\\\"] = 1.0 \\n\",\n \"model.B[\\\"position\\\"][\\\"right\\\", \\\"center_right\\\", \\\"move_right\\\"] = 1.0 \\n\",\n \"model.B[\\\"position\\\"][\\\"right\\\", \\\"right\\\", \\\"move_right\\\"] = 1.0 \\n\",\n \"\\n\",\n \"# moving left \\n\",\n \"model.B[\\\"position\\\"][\\\"left\\\", \\\"left\\\", \\\"move_left\\\"] = 1.0 \\n\",\n \"model.B[\\\"position\\\"][\\\"left\\\", \\\"center_left\\\", \\\"move_left\\\"] = 1.0 \\n\",\n \"model.B[\\\"position\\\"][\\\"center_left\\\", \\\"center_right\\\", \\\"move_left\\\"] = 1.0 \\n\",\n \"model.B[\\\"position\\\"][\\\"center_right\\\", \\\"right\\\", \\\"move_left\\\"] = 1.0 \\n\",\n \"\\n\",\n \"# set preferences (C) tensor - prefer to be at \\\"center_right\\\"\\n\",\n \"model.C[\\\"position_obs\\\"][\\\"center_left\\\"] = 1.0\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now, let's create the agent (via the Agent object) and have it infer which state it is in via an observation and select an action according to it's goal.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Current belief about position: left\\n\",\n \"Goal position: center_left\\n\",\n \"Action chosen: move_right\\n\"\n ]\n }\n ],\n \"source\": [\n \"gamma = 10 # deterministic behavior; make gamma smaller for stochastic behavior\\n\",\n \"\\n\",\n \"# create agent\\n\",\n \"agent = Agent(**model, gamma=gamma)\\n\",\n \"\\n\",\n \"# set up initial observation to be \\\"left\\\"\\n\",\n \"observation = jnp.zeros((agent.batch_size, 1)) # broadcast to agent's batch size (defaults to 1 agent) and add a time dimension\\n\",\n \"\\n\",\n \"# get the prior\\n\",\n \"qs_init = jtu.tree_map(lambda x: jnp.expand_dims(x, 1), agent.D) # qs needs a time dimension too\\n\",\n \"\\n\",\n \"# print initial beliefs, goal, and action chosen\\n\",\n \"qs = agent.infer_states([observation], qs_init)\\n\",\n \"print(f\\\"Current belief about position: {positions[jnp.argmax(qs[0][0])]}\\\")\\n\",\n \"qs = [jnp.squeeze(q, 1) for q in qs]\\n\",\n \"\\n\",\n \"print(f\\\"Goal position: {positions[jnp.argmax(agent.C[0])]}\\\")\\n\",\n \"\\n\",\n \"q_pi, G = agent.infer_policies(qs)\\n\",\n \"action_idx = agent.sample_action(q_pi)\\n\",\n \"print(f\\\"Action chosen: {actions[action_idx[0][0]]}\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can also run multiple agents or independent trials in parallel, each with a different initial observation (i.e., different initial position) by using the `batch_size` argument\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Agent 0's current belief about position: left\\n\",\n \"Agent 1's current belief about position: center_right\\n\",\n \"Agent 2's current belief about position: right\\n\",\n \"\\n\",\n \"Goal position for all agents: center_left\\n\",\n \"\\n\",\n \"Agent 0's action chosen: move_right\\n\",\n \"Agent 1's action chosen: move_left\\n\",\n \"Agent 2's action chosen: move_left\\n\"\n ]\n }\n ],\n \"source\": [\n \"batch_size = 3 # running 3 trials or agents in parallel\\n\",\n \"gamma = 10 # deterministic behavior; make gamma smaller for stochastic behavior\\n\",\n \"\\n\",\n \"# create agent\\n\",\n \"agent = Agent(**model, batch_size=batch_size, gamma=gamma)\\n\",\n \"\\n\",\n \"# set up different initial observations for each agent: \\\"left\\\", \\\"center_right\\\", and \\\"right\\\"\\n\",\n \"observation = [jnp.array([[0], [2], [3]])] # wrap in a list to indicate the single modality; observation[0].shape = (batch_size, 1)\\n\",\n \"\\n\",\n \"# get the prior\\n\",\n \"qs_init = jtu.tree_map(lambda x: jnp.expand_dims(x, 1), agent.D) # qs needs a time dimension too\\n\",\n \"\\n\",\n \"# print goal and initial beliefs\\n\",\n \"qs = agent.infer_states(observation, qs_init)\\n\",\n \"for a in range(batch_size): \\n\",\n \" print(f\\\"Agent {a}'s current belief about position: {positions[jnp.argmax(qs[0][a])]}\\\")\\n\",\n \"qs = [jnp.squeeze(q, 1) for q in qs]\\n\",\n \"\\n\",\n \"print(f\\\"\\\\nGoal position for all agents: {positions[jnp.argmax(agent.C[0])]}\\\\n\\\")\\n\",\n \"\\n\",\n \"q_pi, G = agent.infer_policies(qs)\\n\",\n \"action = agent.sample_action(q_pi)\\n\",\n \"for a in range(batch_size): \\n\",\n \" print(f\\\"Agent {a}'s action chosen: {actions[action[a][0]]}\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"---\\n\",\n \"\\n\",\n \"## Example 2: Apple Foraging Task\\n\",\n \"\\n\",\n \"Now let's look at a slightly more complex example: an apple foraging task. Here, we have a 1x3 grid, with a \\\"left\\\", \\\"center\\\", and \\\"right\\\" cell. These are orchard cells where an apple can grow at a set rate (1/3). The agent's objective is to find apples and eat them as they get a reward to eat apples. The agent can stay, move_left, move_right, or eat.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"num_locations = 3 # these correspond to \\\"left\\\", \\\"center\\\", and \\\"right\\\" and you can just specify [\\\"left\\\", \\\"center\\\", \\\"right\\\"] but we use numbers to show how to use the 'size' key instead of 'elements'\\n\",\n \"item_list = [\\\"orchard\\\", \\\"apple\\\"]\\n\",\n \"\\n\",\n \"model_description = {\\n\",\n \" \\\"observations\\\": {\\n\",\n \" \\\"location_obs\\\": {\\\"size\\\": num_locations, # if you want to use numbers instead of strings, you can use the 'size' key instead of 'elements'\\n\",\n \" \\\"depends_on\\\": [\\\"location_state\\\"],\\n\",\n \" },\\n\",\n \" \\\"item_obs\\\": {\\\"elements\\\": item_list, # \\\"elements\\\" key for strings\\n\",\n \" \\\"depends_on\\\": [\\\"location_state\\\", \\\"left_state\\\", \\\"center_state\\\", \\\"right_state\\\"],\\n\",\n \" },\\n\",\n \" \\\"reward_obs\\\": {\\\"elements\\\": [\\\"no_reward\\\", \\\"reward\\\"],\\n\",\n \" \\\"depends_on\\\": [\\\"reward_state\\\"],\\n\",\n \" },\\n\",\n \" },\\n\",\n \" \\\"controls\\\": {\\n\",\n \" \\\"move\\\": {\\\"elements\\\": [\\\"stay\\\", \\\"move_left\\\", \\\"move_right\\\"],\\n\",\n \" },\\n\",\n \" \\\"eat\\\": {\\\"elements\\\": [\\\"noop\\\", \\\"eat\\\"], # noop = no-operation\\n\",\n \" # note that if you cannot control a state, you still need to add \\n\",\n \" # an action for it (e.g., with elements: [\\\"null\\\"]) for the model to be initialized \\n\",\n \" # with the correct dimensions\\n\",\n \" },\\n\",\n \" },\\n\",\n \" \\\"states\\\": {\\n\",\n \" \\\"location_state\\\": {\\\"size\\\": num_locations,\\n\",\n \" \\\"depends_on\\\": [\\\"location_state\\\"],\\n\",\n \" \\\"controlled_by\\\": [\\\"move\\\"],\\n\",\n \" },\\n\",\n \" \\\"reward_state\\\": {\\\"elements\\\": [\\\"no_reward\\\", \\\"reward\\\"],\\n\",\n \" # if you have more than one dependency, the first dependency is its own state factor (at the previous timestep), \\n\",\n \" # then add the other dependencies in the order they are specified (you can skip over some state factors)\\n\",\n \" \\\"depends_on\\\": [\\\"reward_state\\\", \\\"location_state\\\", \\n\",\n \" \\\"left_state\\\", \\\"center_state\\\", \\\"right_state\\\"],\\n\",\n \" \\\"controlled_by\\\": [\\\"eat\\\"],\\n\",\n \" },\\n\",\n \" \\\"left_state\\\": {\\\"elements\\\": item_list,\\n\",\n \" \\\"depends_on\\\": [\\\"left_state\\\", \\\"location_state\\\"], \\n\",\n \" \\\"controlled_by\\\": [\\\"eat\\\"],\\n\",\n \" },\\n\",\n \" \\\"center_state\\\": {\\\"elements\\\": item_list,\\n\",\n \" \\\"depends_on\\\": [\\\"center_state\\\", \\\"location_state\\\"],\\n\",\n \" \\\"controlled_by\\\": [\\\"eat\\\"],\\n\",\n \" },\\n\",\n \" \\\"right_state\\\": {\\\"elements\\\": item_list,\\n\",\n \" \\\"depends_on\\\": [\\\"right_state\\\", \\\"location_state\\\"],\\n\",\n \" \\\"controlled_by\\\": [\\\"eat\\\"],\\n\",\n \" },\\n\",\n \" },\\n\",\n \"}\\n\",\n \"\\n\",\n \"model = compile_model(model_description)\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We have built a generative model structure using the model description, however the model's parameters are currently uninitialized arrays of zeros. So now, we can fill in the parameter tensors by using the axis and element labels we defined in the model description dict, to set values in particular indices of these arrays.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"'''\\n\",\n \"SPECIFY THE A TENSOR\\n\",\n \"'''\\n\",\n \"# identity mapping for the observations regarding location and reward\\n\",\n \"model.A[\\\"location_obs\\\"].data = jnp.eye(len(model.A[\\\"location_obs\\\"].data))\\n\",\n \"model.A[\\\"reward_obs\\\"].data = jnp.eye(len(model.A[\\\"reward_obs\\\"].data))\\n\",\n \"\\n\",\n \"# in any of the locations, the agent may observe apple or orchard\\n\",\n \"model.A[\\\"item_obs\\\"][\\\"apple\\\", 0, \\\"apple\\\", :, :] = 1.0\\n\",\n \"model.A[\\\"item_obs\\\"][\\\"apple\\\", 1, :, \\\"apple\\\", :] = 1.0\\n\",\n \"model.A[\\\"item_obs\\\"][\\\"apple\\\", 2, :, :, \\\"apple\\\"] = 1.0\\n\",\n \"model.A[\\\"item_obs\\\"][\\\"orchard\\\", 0, \\\"orchard\\\", :, :] = 1.0\\n\",\n \"model.A[\\\"item_obs\\\"][\\\"orchard\\\", 1, :, \\\"orchard\\\", :] = 1.0\\n\",\n \"model.A[\\\"item_obs\\\"][\\\"orchard\\\", 2, :, :, \\\"orchard\\\"] = 1.0\\n\",\n \"model.A[\\\"item_obs\\\"].data = model.A[\\\"item_obs\\\"].data + 1e-3 # add a small amount of noise to the observations\\n\",\n \"\\n\",\n \"'''\\n\",\n \"SPECIFY THE B TENSOR\\n\",\n \"'''\\n\",\n \"\\n\",\n \"# for moving between locations\\n\",\n \"# (to, from, action)\\n\",\n \"valid_transitions = [\\n\",\n \" # from 0 (left)\\n\",\n \" (0, 0, \\\"stay\\\"), # from left to left, stay\\n\",\n \" (1, 0, \\\"move_right\\\"), # from left to center, move right\\n\",\n \" (2, 0, \\\"move_left\\\"), # from left to right, move left\\n\",\n \"\\n\",\n \" # from 1 (center)\\n\",\n \" (0, 1, \\\"move_left\\\"), # from center to left, move left\\n\",\n \" (1, 1, \\\"stay\\\"), # from center to center, stay\\n\",\n \" (2, 1, \\\"move_right\\\"), # from center to right, move right\\n\",\n \"\\n\",\n \" # from 2 (right)\\n\",\n \" (0, 2, \\\"move_right\\\"), # from right to left, move right\\n\",\n \" (1, 2, \\\"move_left\\\"), # from right to cecenterntre, move left\\n\",\n \" (2, 2, \\\"stay\\\"), # from right to right, stay\\n\",\n \"]\\n\",\n \"\\n\",\n \"for to_state, from_state, action in valid_transitions:\\n\",\n \" model.B[\\\"location_state\\\"][to_state, from_state, action] = 1.0\\n\",\n \"\\n\",\n \"# again, remember the reward states will be set as [\\\"to\\\", \\\"from\\\", ...dependencies..., \\\"action\\\"]\\n\",\n \"# if the agent sees an apple and does not eat the apple (i.e., noop), it does not get a reward\\n\",\n \"model.B[\\\"reward_state\\\"][\\\"no_reward\\\", \\\"no_reward\\\", 0, \\\"apple\\\", :, :, \\\"noop\\\"] = 1.0\\n\",\n \"model.B[\\\"reward_state\\\"][\\\"no_reward\\\", \\\"no_reward\\\", 1, :, \\\"apple\\\", :, \\\"noop\\\"] = 1.0\\n\",\n \"model.B[\\\"reward_state\\\"][\\\"no_reward\\\", \\\"no_reward\\\", 2, :, :, \\\"apple\\\", \\\"noop\\\"] = 1.0\\n\",\n \"\\n\",\n \"# if the agent sees an orchard, it does not get a reward regardless of its actions\\n\",\n \"model.B[\\\"reward_state\\\"][\\\"no_reward\\\", \\\"no_reward\\\", 0, \\\"orchard\\\", :, :, :] = 1.0 \\n\",\n \"model.B[\\\"reward_state\\\"][\\\"no_reward\\\", \\\"no_reward\\\", 1, :, \\\"orchard\\\", :, :] = 1.0\\n\",\n \"model.B[\\\"reward_state\\\"][\\\"no_reward\\\", \\\"no_reward\\\", 2, :, :, \\\"orchard\\\", :] = 1.0\\n\",\n \"\\n\",\n \"# from a reward state, there will always be no reward in the next timestep regardless of the action\\n\",\n \"model.B[\\\"reward_state\\\"][\\\"no_reward\\\", \\\"reward\\\", 0, :, :, :, :] = 1.0\\n\",\n \"model.B[\\\"reward_state\\\"][\\\"no_reward\\\", \\\"reward\\\", 1, :, :, :, :] = 1.0\\n\",\n \"model.B[\\\"reward_state\\\"][\\\"no_reward\\\", \\\"reward\\\", 2, :, :, :, :] = 1.0\\n\",\n \"\\n\",\n \"# if the agent sees an orchard and eats, it will not get a reward\\n\",\n \"model.B[\\\"reward_state\\\"][\\\"reward\\\", \\\"no_reward\\\", 0, \\\"orchard\\\", :, :, \\\"eat\\\"] = 0.0\\n\",\n \"model.B[\\\"reward_state\\\"][\\\"reward\\\", \\\"no_reward\\\", 1, :, \\\"orchard\\\", :, \\\"eat\\\"] = 0.0\\n\",\n \"model.B[\\\"reward_state\\\"][\\\"reward\\\", \\\"no_reward\\\", 2, :, :, \\\"orchard\\\", \\\"eat\\\"] = 0.0\\n\",\n \"\\n\",\n \"# if the agent sees an apple and eats the apple, it gets a reward and never not get a reward\\n\",\n \"model.B[\\\"reward_state\\\"][\\\"no_reward\\\", \\\"no_reward\\\", 0, \\\"apple\\\", :, :, \\\"eat\\\"] = 0.0 \\n\",\n \"model.B[\\\"reward_state\\\"][\\\"no_reward\\\", \\\"no_reward\\\", 1, :, \\\"apple\\\", :, \\\"eat\\\"] = 0.0\\n\",\n \"model.B[\\\"reward_state\\\"][\\\"no_reward\\\", \\\"no_reward\\\", 2, :, :, \\\"apple\\\", \\\"eat\\\"] = 0.0\\n\",\n \"model.B[\\\"reward_state\\\"][\\\"reward\\\", \\\"no_reward\\\", 0, \\\"apple\\\", :, :, \\\"eat\\\"] = 1.0 \\n\",\n \"model.B[\\\"reward_state\\\"][\\\"reward\\\", \\\"no_reward\\\", 1, :, \\\"apple\\\", :, \\\"eat\\\"] = 1.0\\n\",\n \"model.B[\\\"reward_state\\\"][\\\"reward\\\", \\\"no_reward\\\", 2, :, :, \\\"apple\\\", \\\"eat\\\"] = 1.0\\n\",\n \"\\n\",\n \"apple_spawn_locations = [\\\"left_state\\\", \\\"center_state\\\", \\\"right_state\\\"]\\n\",\n \"apple_spawn_rate = 1/3\\n\",\n \"for i, state in enumerate(apple_spawn_locations):\\n\",\n \" model.B[state][\\\"orchard\\\", \\\"orchard\\\", :, :] = 1.0 - apple_spawn_rate # no spawn\\n\",\n \" model.B[state][\\\"apple\\\", \\\"orchard\\\", :, :] = apple_spawn_rate # spawn\\n\",\n \" for agent_location in range(num_locations):\\n\",\n \" if i == agent_location:\\n\",\n \" # if the agent does not eat the apple (noop), the apple will stay in the cell\\n\",\n \" model.B[state][\\\"apple\\\", \\\"apple\\\", agent_location, \\\"noop\\\"] = 1.0\\n\",\n \" # if the agent eats the apple, it will become an orchard cell\\n\",\n \" model.B[state][\\\"orchard\\\", \\\"apple\\\", agent_location, \\\"eat\\\"] = 1.0\\n\",\n \" model.B[state].data = model.B[state].data + 1e-3 # add a small amount of noise to the observations\\n\",\n \"\\n\",\n \"'''\\n\",\n \"SPECIFY THE C TENSOR. \\n\",\n \"'''\\n\",\n \"model.C[\\\"reward_obs\\\"][\\\"reward\\\"] = 1.0\\n\",\n \"\\n\",\n \"'''\\n\",\n \"NORMALISE THE TENSORS\\n\",\n \"'''\\n\",\n \"\\n\",\n \"model.A[\\\"location_obs\\\"].normalize()\\n\",\n \"model.A[\\\"item_obs\\\"].normalize()\\n\",\n \"model.A[\\\"reward_obs\\\"].normalize()\\n\",\n \"\\n\",\n \"model.B[\\\"location_state\\\"].normalize()\\n\",\n \"model.B[\\\"reward_state\\\"].normalize()\\n\",\n \"model.B[\\\"left_state\\\"].normalize()\\n\",\n \"model.B[\\\"center_state\\\"].normalize()\\n\",\n \"model.B[\\\"right_state\\\"].normalize()\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"gamma = 1.0\\n\",\n \"\\n\",\n \"agent = Agent(**model, learn_A=False, learn_B=False, gamma=gamma, sampling_mode=\\\"full\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can also turn the model description into an environment using `PymdpEnv`:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"from pymdp.envs import PymdpEnv\\n\",\n \"\\n\",\n \"env = PymdpEnv(**model)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"which can then be used to rollout the agent on the env.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"from pymdp.envs import rollout\\n\",\n \"\\n\",\n \"info, last = rollout(agent, env, num_timesteps=10, rng_key=jr.PRNGKey(0))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"There's also a `make` utility method that generates an `env` and `env_params` from the model description. You can decide whether to return `env_params` using the `make_env_params` argument\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"from pymdp.envs import make\\n\",\n \"\\n\",\n \"env, env_params = make(**model, make_env_params=False)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"info, last = rollout(agent, env, num_timesteps=10, rng_key=jr.PRNGKey(0))\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"info, last = rollout(agent, env, num_timesteps=10, rng_key=jr.PRNGKey(0), env_params=env_params)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If you provide `make_env_params = True` to the `make()` function, it will return out the environmental parameters as a separate dict of parameters (e.g., `A`, `B`, `D` as keys), with the batch size of these parameters matched to the batch size of the input tensors `A`, `B`, and `D`. \\n\",\n \"\\n\",\n \"Passing `env_params` as input arguments to `Env` functions like `reset()` and `step()`, rather than having them be stored internally as class attrbutes, enables the following:\\n\",\n \"* different environments per agent -- if you want to use a different environmental parameterization per agent (e.g., different transition probabilities per environment), then this can be differentiated in the leading dimensions of any array-valued leaves of the `env_params` pytree.\\n\",\n \"* custom changes to environmental parameters -- if you want to changing environmental paramters in a custom way (e.g. `env_params[\\\"B\\\"][factor_idx][batch_indices] = env_params[\\\"B\\\"][factor_idx].at[batch_indices][:,state_idx].set(new_transition_parameters)`) without having to construct a new `Env`. One can simply change the parameters (as long as as shapes align) and then pass them back into the same environment's `step` \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# here, just broadcast the compiled model's A, B, and D tensors across the batch dimension of the agent to show the point\\n\",\n \"A_env_batched = [jnp.broadcast_to(a.data, (agent.batch_size, ) + a.data.shape) for a in model.A]\\n\",\n \"B_env_batched = [jnp.broadcast_to(b.data, (agent.batch_size, ) + b.data.shape) for b in model.B]\\n\",\n \"D_env_batched = [jnp.broadcast_to(d.data, (agent.batch_size, ) + d.data.shape) for d in model.D]\\n\",\n \"\\n\",\n \"env, env_params = make(A_env_batched, B_env_batched, D_env_batched, agent.A_dependencies, agent.B_dependencies, make_env_params=True)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"In this case, also pass `env_params` to `rollout` for vmapping across both agents and environments in parallel. NOTE: This means that the `env_params` must have a matched batch size to the `Agent` class\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"info, last = rollout(agent, env, num_timesteps=10, rng_key=jr.PRNGKey(0), env_params=env_params)\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \".venv311\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.11.12\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/envs/chained_cue_navigation.py", "content": "\"\"\"Generate legacy-style chained-cue navigation GIFs with the JAX environment.\n\nThis script recreates:\n- `.github/chained_cue_navigation_v1.gif`\n- `.github/chained_cue_navigation_v2.gif`\n\nusing `CueChainingEnv`, `Agent`, and environment assets in `pymdp/envs/assets/`.\n\"\"\"\n\nfrom __future__ import annotations\n\nimport argparse\nfrom pathlib import Path\n\nimport jax.numpy as jnp\nimport jax.random as jr\nimport matplotlib.pyplot as plt\nimport matplotlib.patches as patches\nimport numpy as np\nimport scipy.ndimage as ndimage\nfrom matplotlib.animation import FuncAnimation, PillowWriter\nfrom matplotlib.offsetbox import AnnotationBbox, OffsetImage\n\nfrom pymdp.agent import Agent\nfrom pymdp.envs.cue_chaining import CueChainingEnv\nfrom pymdp.envs.rollout import rollout\n\n\ndef build_agent(env: CueChainingEnv, policy_len: int = 4) -> Agent:\n \"\"\"Construct an agent with known start location and uncertain latent context.\"\"\"\n C = [jnp.zeros((a.shape[0],), dtype=jnp.float32) for a in env.A]\n C[3] = C[3].at[1].set(2.0)\n C[3] = C[3].at[2].set(-4.0)\n\n D_agent = [\n env.D[0], # known initial location\n jnp.ones_like(env.D[1]) / env.D[1].shape[0], # uncertain cue2 latent\n jnp.ones_like(env.D[2]) / env.D[2].shape[0], # uncertain reward latent\n ]\n\n return Agent(\n A=env.A,\n B=env.B,\n C=C,\n D=D_agent,\n A_dependencies=env.A_dependencies,\n B_dependencies=env.B_dependencies,\n policy_len=policy_len,\n action_selection=\"deterministic\",\n batch_size=1,\n )\n\n\ndef rollout_locations(\n cue2_state: int,\n reward_condition: int,\n num_timesteps: int = 12,\n seed: int = 0,\n policy_len: int = 4,\n) -> tuple[list[tuple[int, int]], CueChainingEnv]:\n \"\"\"Run one rollout and return location trajectory and environment.\"\"\"\n env = CueChainingEnv(\n grid_shape=(5, 7),\n start_location=(0, 0),\n cue1_location=(2, 0),\n cue2_locations=((0, 2), (1, 3), (3, 3), (4, 2)),\n reward_locations=((1, 5), (3, 5)),\n cue2_state=cue2_state,\n reward_condition=reward_condition,\n )\n agent = build_agent(env, policy_len=policy_len)\n _, info = rollout(agent, env, num_timesteps=num_timesteps, rng_key=jr.PRNGKey(seed))\n locs = [env.index_to_coords(int(info[\"observation\"][0][0, t, 0])) for t in range(num_timesteps + 1)]\n return locs, env\n\n\ndef interpolate_locations(\n locations: list[tuple[int, int]],\n points_per_segment: int = 10,\n) -> np.ndarray:\n \"\"\"Linearly interpolate between discrete trajectory points for smoother animation.\"\"\"\n weights = np.linspace(0.0, 1.0, points_per_segment)\n segments = []\n for idx in range(len(locations) - 1):\n p0 = np.asarray(locations[idx], dtype=float)\n p1 = np.asarray(locations[idx + 1], dtype=float)\n inter = [(1.0 - w) * p0 + w * p1 for w in weights]\n segments.append(np.asarray(inter))\n return np.vstack(segments)\n\n\ndef load_assets(asset_dir: Path) -> dict[str, np.ndarray]:\n \"\"\"Load and orient image assets.\"\"\"\n mouse = plt.imread(asset_dir / \"mouse.png\")\n assets = {\n \"mouse_down\": mouse,\n \"mouse_right\": np.clip(ndimage.rotate(mouse, 90, reshape=True), 0.0, 1.0),\n \"mouse_left\": np.clip(ndimage.rotate(mouse, -90, reshape=True), 0.0, 1.0),\n \"mouse_up\": np.clip(ndimage.rotate(mouse, 180, reshape=True), 0.0, 1.0),\n \"cheese\": plt.imread(asset_dir / \"cheese.png\"),\n \"shock\": plt.imread(asset_dir / \"shock.png\"),\n }\n return assets\n\n\ndef make_animation(\n output_path: Path,\n env: CueChainingEnv,\n locations: list[tuple[int, int]],\n fps: int = 15,\n points_per_segment: int = 10,\n) -> None:\n \"\"\"Render one chained-cue navigation rollout to GIF.\"\"\"\n cue1_loc = env.cue1_location\n cue2_loc = env.cue2_locations[env.D[1].argmax().item()]\n reward_condition = env.D[2].argmax().item()\n reward_locs = env.reward_locations\n reward_loc = reward_locs[reward_condition]\n shock_loc = reward_locs[1 - reward_condition]\n\n points = interpolate_locations(locations, points_per_segment=points_per_segment)\n\n rows, cols = env.grid_shape\n fig, ax = plt.subplots(figsize=(16, 10))\n X, Y = np.meshgrid(np.arange(cols + 1), np.arange(rows + 1))\n cue_grid = np.ones((rows, cols))\n cue_grid[cue1_loc[0], cue1_loc[1]] = 15.0\n for r, c in env.cue2_locations:\n cue_grid[r, c] = 5.0\n mesh = ax.pcolormesh(\n X,\n Y,\n cue_grid,\n edgecolors=\"k\",\n linewidth=3,\n cmap=\"coolwarm\",\n vmin=0,\n vmax=30,\n )\n ax.invert_yaxis()\n\n reward_top = ax.add_patch(\n patches.Rectangle(\n (reward_locs[0][1], reward_locs[0][0]),\n 1.0,\n 1.0,\n linewidth=10,\n edgecolor=[0.5, 0.5, 0.5],\n facecolor=\"none\",\n )\n )\n reward_bottom = ax.add_patch(\n patches.Rectangle(\n (reward_locs[1][1], reward_locs[1][0]),\n 1.0,\n 1.0,\n linewidth=10,\n edgecolor=[0.5, 0.5, 0.5],\n facecolor=\"none\",\n )\n )\n\n cue1_rect = ax.add_patch(\n patches.Rectangle(\n (cue1_loc[1], cue1_loc[0]),\n 1.0,\n 1.0,\n linewidth=15,\n edgecolor=[0.2, 0.7, 0.6],\n facecolor=\"none\",\n )\n )\n cue2_rect = ax.add_patch(\n patches.Rectangle(\n (cue2_loc[1], cue2_loc[0]),\n 1.0,\n 1.0,\n linewidth=15,\n edgecolor=[0.2, 0.7, 0.6],\n facecolor=\"none\",\n )\n )\n cue2_rect.set_visible(False)\n\n qmark_offsets = (0.4, 0.6)\n cue_texts = {}\n for i, (r, c) in enumerate(env.cue2_locations):\n cue_texts[(r, c)] = ax.text(c + qmark_offsets[0], r + qmark_offsets[1], \"?\", fontsize=55, color=\"k\")\n if i == 0:\n pass\n\n ax.text(cue1_loc[1] + 0.3, cue1_loc[0] + 0.6, \"Cue 1\", fontsize=20)\n ax.set_xticklabels([])\n ax.set_yticklabels([])\n ax.grid(which=\"minor\", color=\"w\", linestyle=\"-\", linewidth=2)\n fig.tight_layout()\n\n assets = load_assets(Path(__file__).resolve().parents[2] / \"pymdp\" / \"envs\" / \"assets\")\n mouse_images = {\n \"down\": OffsetImage(assets[\"mouse_down\"], zoom=0.05),\n \"right\": OffsetImage(assets[\"mouse_right\"], zoom=0.05),\n \"left\": OffsetImage(assets[\"mouse_left\"], zoom=0.05),\n \"up\": OffsetImage(assets[\"mouse_up\"], zoom=0.05),\n }\n cheese_img = OffsetImage(assets[\"cheese\"], zoom=0.03)\n shock_img = OffsetImage(assets[\"shock\"], zoom=0.13)\n\n mouse_artists = {\n name: AnnotationBbox(img, (points[0, 1] + 0.5, points[0, 0] + 0.5), frameon=False)\n for name, img in mouse_images.items()\n }\n for name, artist in mouse_artists.items():\n ax.add_artist(artist)\n artist.set_visible(name == \"down\")\n\n revealed_cue1 = False\n revealed_cue2 = False\n cheese_artist = None\n shock_artist = None\n\n def _set_mouse_heading(prev_xy: np.ndarray, curr_xy: np.ndarray) -> None:\n dx = curr_xy[1] - prev_xy[1]\n dy = curr_xy[0] - prev_xy[0]\n if dx > 1e-6:\n heading = \"right\"\n elif dx < -1e-6:\n heading = \"left\"\n elif dy > 1e-6:\n heading = \"down\"\n elif dy < -1e-6:\n heading = \"up\"\n else:\n heading = next(name for name, artist in mouse_artists.items() if artist.get_visible())\n\n for name, artist in mouse_artists.items():\n artist.set_visible(name == heading)\n if name == heading:\n artist.xy = (curr_xy[1] + 0.5, curr_xy[0] + 0.5)\n artist.xybox = (curr_xy[1] + 0.5, curr_xy[0] + 0.5)\n artist.set_zorder(3)\n\n def init():\n return [mesh, *mouse_artists.values()]\n\n def update(frame_idx: int):\n nonlocal revealed_cue1, revealed_cue2, cheese_artist, shock_artist\n curr = points[frame_idx]\n prev = points[max(frame_idx - 1, 0)]\n curr_rc = (int(round(curr[0])), int(round(curr[1])))\n\n if (not revealed_cue1) and curr_rc == cue1_loc:\n revealed_cue1 = True\n cue1_rect.set_visible(False)\n cue2_rect.set_visible(True)\n cue_grid[cue2_loc[0], cue2_loc[1]] = 15.0\n mesh.set_array(cue_grid.ravel())\n for coord, text in cue_texts.items():\n if coord == cue2_loc:\n text.set_position((cue2_loc[1] + 0.3, cue2_loc[0] + 0.6))\n text.set_text(\"Cue 2\")\n text.set_fontsize(20)\n else:\n text.set_visible(False)\n\n if (not revealed_cue2) and curr_rc == cue2_loc:\n revealed_cue2 = True\n cue2_rect.set_visible(False)\n if reward_condition == 0:\n reward_top.set_edgecolor(\"g\")\n reward_top.set_facecolor(\"g\")\n reward_bottom.set_edgecolor([0.7, 0.2, 0.2])\n reward_bottom.set_facecolor([0.7, 0.2, 0.2])\n else:\n reward_bottom.set_edgecolor(\"g\")\n reward_bottom.set_facecolor(\"g\")\n reward_top.set_edgecolor([0.7, 0.2, 0.2])\n reward_top.set_facecolor([0.7, 0.2, 0.2])\n\n cheese_artist = AnnotationBbox(\n cheese_img,\n (reward_loc[1] + 0.5, reward_loc[0] + 0.5),\n frameon=False,\n )\n cheese_artist.set_zorder(2)\n ax.add_artist(cheese_artist)\n\n shock_artist = AnnotationBbox(\n shock_img,\n (shock_loc[1] + 0.5, shock_loc[0] + 0.5),\n frameon=False,\n )\n shock_artist.set_zorder(2)\n ax.add_artist(shock_artist)\n\n _set_mouse_heading(prev, curr)\n artists = [mesh, *mouse_artists.values()]\n if cheese_artist is not None:\n artists.append(cheese_artist)\n if shock_artist is not None:\n artists.append(shock_artist)\n return artists\n\n anim = FuncAnimation(\n fig,\n update,\n frames=len(points),\n init_func=init,\n blit=True,\n interval=1000 / max(fps, 1),\n )\n\n output_path.parent.mkdir(parents=True, exist_ok=True)\n anim.save(output_path, writer=PillowWriter(fps=fps))\n plt.close(fig)\n\n\ndef main():\n parser = argparse.ArgumentParser(description=\"Generate chained-cue navigation GIFs.\")\n parser.add_argument(\n \"--output-dir\",\n type=Path,\n default=Path(\".github\"),\n help=\"Directory to write GIFs into.\",\n )\n parser.add_argument(\"--fps\", type=int, default=15, help=\"GIF frames per second.\")\n parser.add_argument(\"--timesteps\", type=int, default=12, help=\"Rollout timesteps.\")\n parser.add_argument(\n \"--interp-points\",\n type=int,\n default=10,\n help=\"Interpolated points per step transition.\",\n )\n args = parser.parse_args()\n\n # Legacy-matching variants:\n # v1 -> cue2 state 0 (Cue 1), reward condition 0 (TOP)\n # v2 -> cue2 state 2 (Cue 3), reward condition 1 (BOTTOM)\n variants = [\n (\"chained_cue_navigation_v1.gif\", 0, 0),\n (\"chained_cue_navigation_v2.gif\", 2, 1),\n ]\n\n for filename, cue2_state, reward_condition in variants:\n locations, env = rollout_locations(\n cue2_state=cue2_state,\n reward_condition=reward_condition,\n num_timesteps=args.timesteps,\n seed=0,\n policy_len=4,\n )\n make_animation(\n output_path=args.output_dir / filename,\n env=env,\n locations=locations,\n fps=args.fps,\n points_per_segment=args.interp_points,\n )\n print(f\"Saved {(args.output_dir / filename).as_posix()}\")\n\n\nif __name__ == \"__main__\":\n main()\n" }, { "path": "examples/envs/cue_chaining_demo.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"id\": \"b803090f\",\n \"metadata\": {},\n \"source\": [\n \"# Active Inference Demo: Cue Chaining (JAX)\\n\",\n \"\\n\",\n \"This tutorial ports the legacy cue-chaining demo to modern JAX `pymdp` using:\\n\",\n \"\\n\",\n \"- `CueChainingEnv` (a reusable `PymdpEnv` subclass)\\n\",\n \"- `Agent` for inference + planning\\n\",\n \"- `rollout()` for a scanned active-inference loop\\n\",\n \"\\n\",\n \"The task is a two-stage epistemic chain:\\n\",\n \"\\n\",\n \"1. Visit **Cue 1** to learn which **Cue 2** location is informative.\\n\",\n \"2. Visit that **Cue 2** location to learn which reward location is correct.\\n\",\n \"3. Exploit by moving to the rewarding location.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"id\": \"b59618c1\",\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-02-17T16:40:06.154964Z\",\n \"iopub.status.busy\": \"2026-02-17T16:40:06.154873Z\",\n \"iopub.status.idle\": \"2026-02-17T16:40:16.988569Z\",\n \"shell.execute_reply\": \"2026-02-17T16:40:16.988276Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"import jax.numpy as jnp\\n\",\n \"import jax.random as jr\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import pandas as pd\\n\",\n \"\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp.envs.cue_chaining import CueChainingEnv\\n\",\n \"from pymdp.envs.rollout import rollout\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"4f715d31\",\n \"metadata\": {},\n \"source\": [\n \"## 1) Build the Cue-Chaining Environment\\n\",\n \"\\n\",\n \"We fix the hidden cue and reward condition for interpretability.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"id\": \"21de5c24\",\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-02-17T16:40:16.990191Z\",\n \"iopub.status.busy\": \"2026-02-17T16:40:16.989980Z\",\n \"iopub.status.idle\": \"2026-02-17T16:40:17.862819Z\",\n \"shell.execute_reply\": \"2026-02-17T16:40:17.862419Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"A shapes: [(35, 35), (5, 35, 4), (3, 35, 4, 2), (3, 35, 2)]\\n\",\n \"B shapes: [(35, 35, 5), (4, 4, 1), (2, 2, 1)]\\n\",\n \"D shapes: [(35,), (4,), (2,)]\\n\"\n ]\n }\n ],\n \"source\": [\n \"env = CueChainingEnv(\\n\",\n \" grid_shape=(5, 7),\\n\",\n \" start_location=(0, 0),\\n\",\n \" cue1_location=(2, 0),\\n\",\n \" cue2_locations=((0, 2), (1, 3), (3, 3), (4, 2)),\\n\",\n \" reward_locations=((1, 5), (3, 5)),\\n\",\n \" cue2_state=3, # active cue2 is L4\\n\",\n \" reward_condition=1, # reward at second reward location\\n\",\n \")\\n\",\n \"\\n\",\n \"print(\\\"A shapes:\\\", [a.shape for a in env.A])\\n\",\n \"print(\\\"B shapes:\\\", [b.shape for b in env.B])\\n\",\n \"print(\\\"D shapes:\\\", [d.shape for d in env.D])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"0785fbbc\",\n \"metadata\": {},\n \"source\": [\n \"## 2) Create the Agent (Generative Model)\\n\",\n \"\\n\",\n \"We keep the legacy cue-chaining prior structure:\\n\",\n \"\\n\",\n \"- The agent is certain about its **start location**.\\n\",\n \"- The agent is uncertain (uniform) over latent **cue2 state** and **reward condition**.\\n\",\n \"\\n\",\n \"This lets short-horizon planning (`policy_len=4`) still prioritize epistemic actions (visiting cue1, then cue2).\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"id\": \"203e2547\",\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-02-17T16:40:17.865208Z\",\n \"iopub.status.busy\": \"2026-02-17T16:40:17.865087Z\",\n \"iopub.status.idle\": \"2026-02-17T16:40:18.998759Z\",\n \"shell.execute_reply\": \"2026-02-17T16:40:18.997954Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"num_states: [35, 4, 2]\\n\",\n \"num_obs: [35, 5, 3, 3]\\n\",\n \"num_controls: [5, 1, 1]\\n\",\n \"agent D shapes: [(35,), (4,), (2,)]\\n\"\n ]\n },\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_92050/3369534931.py:12: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agent = Agent(\\n\"\n ]\n }\n ],\n \"source\": [\n \"C = [jnp.zeros((a.shape[0],), dtype=jnp.float32) for a in env.A]\\n\",\n \"C[3] = C[3].at[1].set(3.0)\\n\",\n \"C[3] = C[3].at[2].set(-6.0)\\n\",\n \"\\n\",\n \"# Legacy-style prior: known initial location, uncertain latent context.\\n\",\n \"D_agent = [\\n\",\n \" env.D[0],\\n\",\n \" jnp.ones_like(env.D[1]) / env.D[1].shape[0],\\n\",\n \" jnp.ones_like(env.D[2]) / env.D[2].shape[0],\\n\",\n \"]\\n\",\n \"\\n\",\n \"agent = Agent(\\n\",\n \" A=env.A,\\n\",\n \" B=env.B,\\n\",\n \" C=C,\\n\",\n \" D=D_agent,\\n\",\n \" A_dependencies=env.A_dependencies,\\n\",\n \" B_dependencies=env.B_dependencies,\\n\",\n \" policy_len=4,\\n\",\n \" action_selection='deterministic',\\n\",\n \" batch_size=1,\\n\",\n \")\\n\",\n \"\\n\",\n \"print(\\\"num_states:\\\", agent.num_states)\\n\",\n \"print(\\\"num_obs:\\\", agent.num_obs)\\n\",\n \"print(\\\"num_controls:\\\", agent.num_controls)\\n\",\n \"print(\\\"agent D shapes:\\\", [d.shape for d in D_agent])\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"92e9b6a5\",\n \"metadata\": {},\n \"source\": [\n \"## 3) Run `rollout()`\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"id\": \"ea613d7d\",\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-02-17T16:40:19.000570Z\",\n \"iopub.status.busy\": \"2026-02-17T16:40:19.000446Z\",\n \"iopub.status.idle\": \"2026-02-17T16:40:20.737451Z\",\n \"shell.execute_reply\": \"2026-02-17T16:40:20.736672Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"action shape: (1, 11, 3)\\n\",\n \"location observation shape: (1, 11, 1)\\n\",\n \"reward observation shape: (1, 11, 1)\\n\"\n ]\n }\n ],\n \"source\": [\n \"T = 10\\n\",\n \"_, info = rollout(agent, env, num_timesteps=T, rng_key=jr.PRNGKey(0))\\n\",\n \"\\n\",\n \"print(\\\"action shape:\\\", info[\\\"action\\\"].shape)\\n\",\n \"print(\\\"location observation shape:\\\", info[\\\"observation\\\"][0].shape)\\n\",\n \"print(\\\"reward observation shape:\\\", info[\\\"observation\\\"][3].shape)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"13dc607b\",\n \"metadata\": {},\n \"source\": [\n \"## 4) Decode Observations and Actions\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"id\": \"c6a9125f\",\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-02-17T16:40:20.738979Z\",\n \"iopub.status.busy\": \"2026-02-17T16:40:20.738871Z\",\n \"iopub.status.idle\": \"2026-02-17T16:40:20.790395Z\",\n \"shell.execute_reply\": \"2026-02-17T16:40:20.790080Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"
\\n\",\n \"\\n\",\n \"\\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \" \\n\",\n \"
tloccue1_obscue2_obsreward_obsaction
00(0, 0)NullNullNullDOWN
11(1, 0)NullNullNullDOWN
22(2, 0)L4NullNullDOWN
33(3, 0)NullNullNullDOWN
44(4, 0)NullNullNullRIGHT
55(4, 1)NullNullNullRIGHT
66(4, 2)Nullreward_on_bottomNullUP
77(3, 2)NullNullNullRIGHT
88(3, 3)NullNullNullRIGHT
99(3, 4)NullNullNullRIGHT
1010(3, 5)NullNullCheeseSTAY
\\n\",\n \"
\"\n ],\n \"text/plain\": [\n \" t loc cue1_obs cue2_obs reward_obs action\\n\",\n \"0 0 (0, 0) Null Null Null DOWN\\n\",\n \"1 1 (1, 0) Null Null Null DOWN\\n\",\n \"2 2 (2, 0) L4 Null Null DOWN\\n\",\n \"3 3 (3, 0) Null Null Null DOWN\\n\",\n \"4 4 (4, 0) Null Null Null RIGHT\\n\",\n \"5 5 (4, 1) Null Null Null RIGHT\\n\",\n \"6 6 (4, 2) Null reward_on_bottom Null UP\\n\",\n \"7 7 (3, 2) Null Null Null RIGHT\\n\",\n \"8 8 (3, 3) Null Null Null RIGHT\\n\",\n \"9 9 (3, 4) Null Null Null RIGHT\\n\",\n \"10 10 (3, 5) Null Null Cheese STAY\"\n ]\n },\n \"execution_count\": 5,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"records = []\\n\",\n \"for t in range(T + 1):\\n\",\n \" loc_obs = int(info[\\\"observation\\\"][0][0, t, 0])\\n\",\n \" cue1_obs = int(info[\\\"observation\\\"][1][0, t, 0])\\n\",\n \" cue2_obs = int(info[\\\"observation\\\"][2][0, t, 0])\\n\",\n \" rew_obs = int(info[\\\"observation\\\"][3][0, t, 0])\\n\",\n \" action_idx = int(info[\\\"action\\\"][0, t, 0])\\n\",\n \"\\n\",\n \" records.append(\\n\",\n \" {\\n\",\n \" \\\"t\\\": t,\\n\",\n \" \\\"loc\\\": env.index_to_coords(loc_obs),\\n\",\n \" \\\"cue1_obs\\\": env.cue1_obs_names[cue1_obs],\\n\",\n \" \\\"cue2_obs\\\": env.cue2_obs_names[cue2_obs],\\n\",\n \" \\\"reward_obs\\\": env.reward_obs_names[rew_obs],\\n\",\n \" \\\"action\\\": env.ACTION_LABELS[action_idx],\\n\",\n \" }\\n\",\n \" )\\n\",\n \"\\n\",\n \"trajectory_df = pd.DataFrame(records)\\n\",\n \"trajectory_df\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"e9b08794\",\n \"metadata\": {},\n \"source\": [\n \"## 5) Visualize the trajectory\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"id\": \"ee345b31\",\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-02-17T16:40:20.791550Z\",\n \"iopub.status.busy\": \"2026-02-17T16:40:20.791455Z\",\n \"iopub.status.idle\": \"2026-02-17T16:40:21.209469Z\",\n \"shell.execute_reply\": \"2026-02-17T16:40:21.209081Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig, ax = plt.subplots(figsize=(10, 5))\\n\",\n \"rows, cols = env.grid_shape\\n\",\n \"\\n\",\n \"for r in range(rows):\\n\",\n \" for c in range(cols):\\n\",\n \" ax.add_patch(plt.Rectangle((c, r), 1, 1, facecolor=\\\"white\\\", edgecolor=\\\"black\\\", linewidth=1))\\n\",\n \"\\n\",\n \"c1r, c1c = env.cue1_location\\n\",\n \"ax.add_patch(plt.Rectangle((c1c, c1r), 1, 1, facecolor=\\\"#d6bcfa\\\", edgecolor=\\\"#553c9a\\\", linewidth=2))\\n\",\n \"ax.text(c1c + 0.5, c1r + 0.5, \\\"Cue1\\\", ha=\\\"center\\\", va=\\\"center\\\", fontsize=9)\\n\",\n \"\\n\",\n \"active_cue_idx = int(info[\\\"env_state\\\"][1][0, 0])\\n\",\n \"for i, (r, c) in enumerate(env.cue2_locations):\\n\",\n \" color = \\\"#68d391\\\" if i == active_cue_idx else \\\"#e2e8f0\\\"\\n\",\n \" ax.add_patch(plt.Rectangle((c, r), 1, 1, facecolor=color, edgecolor=\\\"#2d3748\\\", linewidth=2))\\n\",\n \" ax.text(c + 0.5, r + 0.5, env.cue2_names[i], ha=\\\"center\\\", va=\\\"center\\\", fontsize=9)\\n\",\n \"\\n\",\n \"true_reward_state = int(info[\\\"env_state\\\"][2][0, 0])\\n\",\n \"for i, (r, c) in enumerate(env.reward_locations):\\n\",\n \" is_reward = i == true_reward_state\\n\",\n \" face = \\\"#9ae6b4\\\" if is_reward else \\\"#feb2b2\\\"\\n\",\n \" label = \\\"Cheese\\\" if is_reward else \\\"Shock\\\"\\n\",\n \" ax.add_patch(plt.Rectangle((c, r), 1, 1, facecolor=face, edgecolor=\\\"#1a202c\\\", linewidth=2))\\n\",\n \" ax.text(c + 0.5, r + 0.5, label, ha=\\\"center\\\", va=\\\"center\\\", fontsize=8)\\n\",\n \"\\n\",\n \"coords = [env.index_to_coords(int(info[\\\"observation\\\"][0][0, t, 0])) for t in range(T + 1)]\\n\",\n \"xs = [c + 0.5 for _, c in coords]\\n\",\n \"ys = [r + 0.5 for r, _ in coords]\\n\",\n \"ax.plot(xs, ys, color=\\\"#2b6cb0\\\", linewidth=2)\\n\",\n \"ax.scatter(xs, ys, c=range(T + 1), cmap=\\\"viridis\\\", s=50)\\n\",\n \"\\n\",\n \"for t, (x, y) in enumerate(zip(xs, ys)):\\n\",\n \" ax.text(x, y - 0.2, str(t), ha=\\\"center\\\", va=\\\"center\\\", fontsize=7)\\n\",\n \"\\n\",\n \"ax.set_xlim(0, cols)\\n\",\n \"ax.set_ylim(rows, 0)\\n\",\n \"ax.set_aspect(\\\"equal\\\")\\n\",\n \"ax.set_title(\\\"Cue-chaining rollout (time-coded trajectory)\\\")\\n\",\n \"ax.set_xticks(range(cols + 1))\\n\",\n \"ax.set_yticks(range(rows + 1))\\n\",\n \"plt.tight_layout()\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"f17c82fc\",\n \"metadata\": {},\n \"source\": [\n \"This reusable environment can now be used directly in future planning and docs demos.\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.11.12\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 5\n}\n" }, { "path": "examples/envs/generalized_tmaze_demo.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# T-Maze Task with Distractors\\n\",\n \"\\n\",\n \"In this tutorial, we set up a T-maze task where an agent navigates a grid to locate rewards. The agent can move in four directions: up, down, left, or right. \\n\",\n \"\\n\",\n \"The agent would navigate to the cues to obtain information about two potential reward locations. While these cues guide the agent's search, they do not guarantee the presence of a real reward. The agent must learn that some cues are distractors, so it may follow them initially but should recognize when a location does not contain a real reward and continue exploring.\\n\",\n \"\\n\",\n \"This is to test sophisticated inference. \\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Initial Setup\\n\",\n \"To run this notebook, it's recommended to use a virtual environment. You can refer to [this guide](https://packaging.python.org/en/latest/guides/installing-using-pip-and-virtual-environments/) to learn how to set up a virtual environment.\\n\",\n \"\\n\",\n \"Then, install the current repo as a package in editable mode by running the following command in your terminal:\\n\",\n \"```bash\\n\",\n \"pip install -e .\\n\",\n \"```\\n\",\n \"\\n\",\n \"And then, install mediapy by running the following command in your terminal:\\n\",\n \"```bash\\n\",\n \"pip install mediapy\\n\",\n \"```\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"%load_ext autoreload\\n\",\n \"%autoreload 2\\n\",\n \"\\n\",\n \"from jax import numpy as jnp, random as jr\\n\",\n \"\\n\",\n \"from pymdp.envs.generalized_tmaze import (\\n\",\n \" GeneralizedTMazeEnv, parse_maze, get_maze_matrix \\n\",\n \")\\n\",\n \"\\n\",\n \"from pymdp.envs.rollout import rollout\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp.utils import list_array_uniform\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Creating the Environment\\n\",\n \"\\n\",\n \"The environment consists of the following elements, which are represented in the figure:\\n\",\n \"\\n\",\n \"- **Agent (Green Square)**: The agent starts at a designated position and explores the grid to locate rewards.\\n\",\n \"- **Cues and Reward Sets**: Each colour represents a set that includes one cue (marked by a black cross) and two potential reward locations associated with that cue.\\n\",\n \" - **Green Set (True Reward Set)**: Contains real outcomes. Each reward location has a secondary dot to indicate the type of outcome:\\n\",\n \" - **Red Dot**: Indicates a reward.\\n\",\n \" - **Blue Dot**: Indicates a punishment.\\n\",\n \" - **Orange and Blue Sets (Distractor Sets)**: These are distractor sets that do not contain real rewards. The reward locations in these sets lack a secondary dot, indicating a false reward location. Although the cues point to these locations, they do not contain actual rewards.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"M = get_maze_matrix()\\n\",\n \"key = jr.PRNGKey(0)\\n\",\n \"\\n\",\n \"key, subkey = jr.split(key)\\n\",\n \"env_info_m = parse_maze(M, subkey)\\n\",\n \"\\n\",\n \"tmaze_env = GeneralizedTMazeEnv(env_info_m)\\n\",\n \"\\n\",\n \"init_obs, init_state = tmaze_env.reset(key)\\n\",\n \"tmaze_env.render(states=init_state, mode=\\\"human\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Creating the Agent\\n\",\n \"\\n\",\n \"State Factors: \\n\",\n \"- Position: however large the grid is\\n\",\n \"- Reward: location of the reward\\n\",\n \"\\n\",\n \"Observation Modalities:\\n\",\n \"- Position: however large the grid is\\n\",\n \"- Cued info: null, first location, second location\\n\",\n \"- Reward: null, no reward, reward\\n\",\n \"\\n\",\n \"The `PymdpEnv` class contains the environmental parameters as POMDP parameters (`A`, `B`, and `D`). We initialize our agent's generative model using the same parameters. This means that the agent has full knowledge about the environment transitions, and likelihoods. We initialize the agent with a flat prior, i.e. it does not know where it, or the reward is. Finally, we set the C vector to have a preference only over the rewarding observation of cue-reward pair 1 (i.e. C[1][1] = 1 and zero for other values). \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"A, B = tmaze_env.A, tmaze_env.B\\n\",\n \"A_dependencies, B_dependencies = tmaze_env.A_dependencies, tmaze_env.B_dependencies\\n\",\n \"\\n\",\n \"# [position], [cue], [reward]\\n\",\n \"C = [jnp.zeros(a.shape[0]) for a in A]\\n\",\n \"\\n\",\n \"rewarding_modality = -1\\n\",\n \"\\n\",\n \"C[rewarding_modality] = C[rewarding_modality].at[1].set(1.0)\\n\",\n \"C[rewarding_modality] = C[rewarding_modality].at[2].set(-3.0)\\n\",\n \"\\n\",\n \"D = list_array_uniform([b.shape[0] for b in B])\\n\",\n \"\\n\",\n \"# make 9 different agents to simulate in parallel\\n\",\n \"batch_size = 9\\n\",\n \"\\n\",\n \"\\n\",\n \"agent = Agent(\\n\",\n \" A, B, C, D, \\n\",\n \" E=None,\\n\",\n \" pA=None,\\n\",\n \" pB=None,\\n\",\n \" policy_len=5,\\n\",\n \" A_dependencies=A_dependencies, \\n\",\n \" B_dependencies=B_dependencies,\\n\",\n \" use_utility=True,\\n\",\n \" use_states_info_gain=True,\\n\",\n \" sampling_mode='full',\\n\",\n \" action_selection='stochastic',\\n\",\n \" gamma=4.0,\\n\",\n \" batch_size=batch_size,\\n\",\n \" learn_A=False,\\n\",\n \" learn_B=False\\n\",\n \")\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"A tensors\\n\",\n \"(9, 25, 25)\\n\",\n \"(9, 3, 25, 2)\\n\",\n \"(9, 3, 25, 2)\\n\",\n \"(9, 3, 25, 2)\\n\",\n \"(9, 3, 25, 2)\\n\",\n \"(9, 3, 25, 2)\\n\",\n \"(9, 3, 25, 2)\\n\",\n \"\\n\",\n \"B tensors\\n\",\n \"(9, 25, 25, 5)\\n\",\n \"(9, 2, 2, 1)\\n\",\n \"(9, 2, 2, 1)\\n\",\n \"(9, 2, 2, 1)\\n\",\n \"\\n\",\n \"C tensors\\n\",\n \"(9, 25)\\n\",\n \"(9, 3)\\n\",\n \"(9, 3)\\n\",\n \"(9, 3)\\n\",\n \"(9, 3)\\n\",\n \"(9, 3)\\n\",\n \"(9, 3)\\n\",\n \"\\n\",\n \"D tensors\\n\",\n \"(9, 25)\\n\",\n \"(9, 2)\\n\",\n \"(9, 2)\\n\",\n \"(9, 2)\\n\",\n \"\\n\",\n \"A and B dependencies\\n\",\n \"[[0], [0, 1], [0, 2], [0, 3], [0, 1], [0, 2], [0, 3]]\\n\",\n \"[[0], [1], [2], [3]]\\n\"\n ]\n }\n ],\n \"source\": [\n \"print(\\\"A tensors\\\")\\n\",\n \"print(agent.A[0].shape)\\n\",\n \"print(agent.A[1].shape)\\n\",\n \"print(agent.A[2].shape)\\n\",\n \"print(agent.A[3].shape)\\n\",\n \"print(agent.A[4].shape)\\n\",\n \"print(agent.A[5].shape)\\n\",\n \"print(agent.A[6].shape)\\n\",\n \"print()\\n\",\n \"print(\\\"B tensors\\\")\\n\",\n \"print(agent.B[0].shape)\\n\",\n \"print(agent.B[1].shape)\\n\",\n \"print(agent.B[2].shape)\\n\",\n \"print(agent.B[3].shape)\\n\",\n \"print()\\n\",\n \"print(\\\"C tensors\\\")\\n\",\n \"print(agent.C[0].shape)\\n\",\n \"print(agent.C[1].shape)\\n\",\n \"print(agent.C[2].shape)\\n\",\n \"print(agent.C[3].shape)\\n\",\n \"print(agent.C[4].shape)\\n\",\n \"print(agent.C[5].shape)\\n\",\n \"print(agent.C[6].shape)\\n\",\n \"print()\\n\",\n \"print(\\\"D tensors\\\")\\n\",\n \"print(agent.D[0].shape)\\n\",\n \"print(agent.D[1].shape)\\n\",\n \"print(agent.D[2].shape)\\n\",\n \"print(agent.D[3].shape)\\n\",\n \"print()\\n\",\n \"print(\\\"A and B dependencies\\\")\\n\",\n \"print(agent.A_dependencies)\\n\",\n \"print(agent.B_dependencies)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Rollout an agent episode \\n\",\n \"\\n\",\n \"Using the rollout function, we can run an active inference agent in this environment over a specified number of discrete timesteps using the parameters previously set. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"key = jr.PRNGKey(1)\\n\",\n \"T = 10\\n\",\n \"_, info = rollout(agent, tmaze_env, num_timesteps=T, rng_key=key)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"images = []\\n\",\n \"for t in range(T):\\n\",\n \" env_state_t = [s[:, t] for s in info['env_state']]\\n\",\n \" images.append(tmaze_env.render(states=env_state_t, mode=\\\"rgb_array\\\"))\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 12,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"# make animation\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import matplotlib.animation as animation\\n\",\n \"from IPython.display import HTML\\n\",\n \"\\n\",\n \"\\n\",\n \"def animate(images, savefile=None, interval=1000):\\n\",\n \" # Make a bigger figure (pick whatever looks good)\\n\",\n \" fig = plt.figure(figsize=(6, 6), dpi=150)\\n\",\n \"\\n\",\n \" # Axes that fills the entire figure\\n\",\n \" ax = fig.add_axes([0, 0, 1, 1])\\n\",\n \" ax.set_axis_off()\\n\",\n \"\\n\",\n \" im = ax.imshow(images[0], animated=True)\\n\",\n \"\\n\",\n \" def update(k):\\n\",\n \" im.set_data(images[k])\\n\",\n \" return (im,)\\n\",\n \"\\n\",\n \" ani = animation.FuncAnimation(\\n\",\n \" fig, update, frames=len(images), interval=interval, blit=True, repeat_delay=1000\\n\",\n \" )\\n\",\n \"\\n\",\n \" if savefile is not None:\\n\",\n \" ani.save(savefile)\\n\",\n \"\\n\",\n \" plt.close(fig)\\n\",\n \" return ani\\n\",\n \"\\n\",\n \"ani = animate(images)\\n\",\n \"HTML(ani.to_html5_video())\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"pymdp_dev_env\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/envs/graph_worlds_demo.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Graph worlds\\n\",\n \"\\n\",\n \"This environment demonstrates agents that can navigate a graph and find an object. Object is only visible when agent is at the same location as the object.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:18.683564Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:18.683447Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:22.673717Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:22.673356Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# a way to edit and run code and see the effects in the notebook without having to restart the kernel\\n\",\n \"%load_ext autoreload\\n\",\n \"%autoreload 2\\n\",\n \"\\n\",\n \"from jax import numpy as jnp, random as jr, jit\\n\",\n \"from jax import vmap\\n\",\n \"import networkx as nx\\n\",\n \"\\n\",\n \"from pymdp.envs import GraphEnv\\n\",\n \"from pymdp.envs.graph_worlds import generate_connected_clusters\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp.envs.rollout import rollout\\n\",\n \"from pymdp.utils import list_array_uniform, list_array_zeros\\n\",\n \"\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"\\n\",\n \"key = jr.PRNGKey(0)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Start by generating a graph of locations\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:22.675254Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:22.675132Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:22.711116Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:22.710815Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"graph, _ = generate_connected_clusters(cluster_size=3, connections=2)\\n\",\n \"nx.draw(graph, with_labels=True, font_weight=\\\"bold\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can create a GraphEnv given this graph. \\n\",\n \"\\n\",\n \"We then specify two object locations and two agent location, which using `env.generate_env_params(...)` can be used to generate two environments which differ in their initial state prior (their `D` vectors), which will encode precise priors over a particular initial object location and agent location.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:22.728168Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:22.728062Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:23.547234Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:23.546948Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"env = GraphEnv(graph)\\n\",\n \"\\n\",\n \"object_locations=[3, 5]\\n\",\n \"agent_locations=[0, 1]\\n\",\n \"\\n\",\n \"env_params = env.generate_env_params(key=key, graph=graph, object_locations=object_locations, agent_locations=agent_locations)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"To create an Agent, we reuse the environment's A and B tensors, but give the agent a uniform initial belief about the object location, and a preference to find (see) the object.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:23.548655Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:23.548575Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:24.284551Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:24.284270Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61026/831457487.py:9: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agent = Agent(A, B, C, D, A_dependencies=A_dependencies, B_dependencies=B_dependencies, policy_len=2, batch_size=2)\\n\"\n ]\n }\n ],\n \"source\": [\n \"A, B = env.A, env.B\\n\",\n \"A_dependencies, B_dependencies = env.A_dependencies, env.B_dependencies\\n\",\n \"\\n\",\n \"C = list_array_zeros([a.shape[0] for a in A])\\n\",\n \"C[1] = C[1].at[1].set(1.0)\\n\",\n \"\\n\",\n \"D = list_array_uniform([b.shape[0] for b in B])\\n\",\n \"\\n\",\n \"agent = Agent(A, B, C, D, A_dependencies=A_dependencies, B_dependencies=B_dependencies, policy_len=2, batch_size=2)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Using the `rollout` function, we can easily simulate two agents in parallel for 10 timesteps...\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:24.285830Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:24.285749Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:25.187202Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:25.186837Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"rollout_jitted = jit(rollout, static_argnums=[1,2])\\n\",\n \"last, result = rollout_jitted(agent, env, num_timesteps=10, rng_key=key, env_params=env_params)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"if you want to continue, call `rollout` again but with `initial_carry=last`\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:25.188717Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:25.188616Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:25.766341Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:25.766014Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"last, result2 = rollout_jitted(agent, env, num_timesteps=10, rng_key=key, env_params=env_params, initial_carry=last)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The result dict contains the expected free energy, executed actions, observations, environment state and beliefs over states and policies.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:25.768119Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:25.768003Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:25.777434Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:25.777195Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"dict_keys(['action', 'empirical_prior', 'env_state', 'neg_efe', 'observation', 'qpi', 'qs'])\"\n ]\n },\n \"execution_count\": 7,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"result.keys()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The beliefs result is an array for each state factor, and the shape is [batch_size x time x factor_size]\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:25.778621Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:25.778545Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:25.785706Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:25.785467Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"2\\n\",\n \"(2, 11, 7)\\n\"\n ]\n }\n ],\n \"source\": [\n \"print(len(result[\\\"qs\\\"]))\\n\",\n \"print(result[\\\"qs\\\"][0].shape)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can plot the agent's beliefs over time.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:25.786826Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:25.786748Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:26.031626Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:26.031042Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"def plot_results(result, agent_idx=0):\\n\",\n \" \\\"\\\"\\\"Plot the results of the agent's beliefs and actions.\\\"\\\"\\\"\\n\",\n \" fig, ax = plt.subplots()\\n\",\n \" ax.title.set_text(f\\\"Agent {agent_idx}\\\")\\n\",\n \"\\n\",\n \" # Plot the agent location belief as blue dots\\n\",\n \" T = result[\\\"qs\\\"][0].shape[1]\\n\",\n \" locations = [jnp.argmax(result[\\\"qs\\\"][0][agent_idx, t, :]) for t in range(T)]\\n\",\n \" ax.scatter(jnp.arange(T), locations, c=\\\"tab:blue\\\")\\n\",\n \"\\n\",\n \" # Plot object location beliefs as greyscale intensity\\n\",\n \" ax.imshow(result[\\\"qs\\\"][1][agent_idx, :, :].T, cmap=\\\"gray_r\\\", vmin=0.0, vmax=1.0)\\n\",\n \"\\n\",\n \"plot_results(result, agent_idx=0)\\n\",\n \"plot_results(result, agent_idx=1)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If you cannot use the `rollout` method, e.g., you are using a 3rd party environment that is not jax.jit compatible, you can construct your own loop using the `infer_and_plan` function.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:26.032916Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:26.032823Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:29.888893Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:29.888628Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Step 1: Action taken: [[1 0]\\n\",\n \" [0 0]], Observation: [Array([[1.],\\n\",\n \" [0.]], dtype=float32), Array([[0.],\\n\",\n \" [0.]], dtype=float32)]\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Step 2: Action taken: [[0 0]\\n\",\n \" [2 0]], Observation: [Array([[0.],\\n\",\n \" [2.]], dtype=float32), Array([[0.],\\n\",\n \" [0.]], dtype=float32)]\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Step 3: Action taken: [[2 0]\\n\",\n \" [0 0]], Observation: [Array([[2.],\\n\",\n \" [0.]], dtype=float32), Array([[0.],\\n\",\n \" [0.]], dtype=float32)]\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Step 4: Action taken: [[0 0]\\n\",\n \" [3 0]], Observation: [Array([[0.],\\n\",\n \" [3.]], dtype=float32), Array([[0.],\\n\",\n \" [0.]], dtype=float32)]\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Step 5: Action taken: [[3 0]\\n\",\n \" [4 0]], Observation: [Array([[3.],\\n\",\n \" [4.]], dtype=float32), Array([[1.],\\n\",\n \" [0.]], dtype=float32)]\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Step 6: Action taken: [[1 0]\\n\",\n \" [3 0]], Observation: [Array([[3.],\\n\",\n \" [3.]], dtype=float32), Array([[1.],\\n\",\n \" [0.]], dtype=float32)]\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Step 7: Action taken: [[1 0]\\n\",\n \" [5 0]], Observation: [Array([[3.],\\n\",\n \" [5.]], dtype=float32), Array([[1.],\\n\",\n \" [1.]], dtype=float32)]\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Step 8: Action taken: [[1 0]\\n\",\n \" [0 0]], Observation: [Array([[3.],\\n\",\n \" [5.]], dtype=float32), Array([[1.],\\n\",\n \" [1.]], dtype=float32)]\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Step 9: Action taken: [[1 0]\\n\",\n \" [0 0]], Observation: [Array([[3.],\\n\",\n \" [5.]], dtype=float32), Array([[1.],\\n\",\n \" [1.]], dtype=float32)]\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Step 10: Action taken: [[1 0]\\n\",\n \" [0 0]], Observation: [Array([[3.],\\n\",\n \" [5.]], dtype=float32), Array([[1.],\\n\",\n \" [1.]], dtype=float32)]\\n\"\n ]\n }\n ],\n \"source\": [\n \"from jax import vmap\\n\",\n \"import jax.tree_util as jtu\\n\",\n \"from pymdp.envs.rollout import infer_and_plan\\n\",\n \"\\n\",\n \"rng_key = jr.PRNGKey(0)\\n\",\n \"\\n\",\n \"# start with None action, and expand agent.D to add time dimension\\n\",\n \"action = -jnp.ones((agent.batch_size, len(agent.num_controls)), dtype=jnp.int32)\\n\",\n \"qs = jtu.tree_map(lambda x: jnp.expand_dims(x, -2), agent.D)\\n\",\n \"\\n\",\n \"# reset environment and get initial observation\\n\",\n \"keys = jr.split(rng_key, agent.batch_size + 1)\\n\",\n \"rng_key = keys[0]\\n\",\n \"observation, state = vmap(env.reset)(keys[1:], env_params=env_params)\\n\",\n \"\\n\",\n \"for i in range(10):\\n\",\n \" # random keys\\n\",\n \" keys = jr.split(rng_key, agent.batch_size + 2)\\n\",\n \" rng_key = keys[0]\\n\",\n \"\\n\",\n \" # infer and plan\\n\",\n \" agent, action, qs, _ = infer_and_plan(agent, qs, observation, action, keys[1])\\n\",\n \"\\n\",\n \" # step the environment\\n\",\n \" observation, state = vmap(env.step)(keys[2:], state, action, env_params=env_params)\\n\",\n \"\\n\",\n \" print(f\\\"Step {i+1}: Action taken: {action}, Observation: {observation}\\\")\"\n ]\n }\n ],\n \"metadata\": {\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.11.12\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/envs/knapsack_demo.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Demo: Knapsack Problem\\n\",\n \"\\n\",\n \"In this notebook, we demonstrate how to solve the knapsack problem, a classic Operations Research problem. In this problem, we have a knapsack with fixed weight capacity and a set of items each associated with a weight and a value. We want fit items into the knapsack in a way such as the total value of all fitted items is as high as possible, however, the sum of item weights cannot exceed the knapsack weight capacity. \\n\",\n \"\\n\",\n \"While is problem is traditionally solved with linear programming, we can convert it into a contextual bandit problem (a simplified 1-stage Markov decision problem) and solve it using pymdp.\\n\",\n \"\\n\",\n \"Let us define our actions `a_i` as whether to include an item or not for each item i. The state `s_i` of the system is defined as whether an item is included or not, i.e., copying the action variables over to the corresponding state variables. We also need another state variable `z` which represents whether the knapsack capacity is exceeded. If an item is included, i.e., `s_i = 1`, we get a reward `r_i`, otherwise, we get a reward of 0 when `s_i = 0`. We can thus define our preference of including valuable items to be proportional to the exponential of reward: `C[s_i] = softmax([0, r_i])`. Our preference on the capacity constraint variable `z` is to never violate it, i.e., `C[z] = [1, 0]`. Since the system is fully observable, we will set all the Categorical/Dirichlet parameters of the emission model (the `A` tensors) to be diagonal.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import numpy as np\\n\",\n \"from jax import numpy as jnp, random as jr\\n\",\n \"from jax import tree_util as jtu\\n\",\n \"import jax.nn as nn\\n\",\n \"import itertools\\n\",\n \"\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp import distribution\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Specify model structure\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"item rewards [0.00729382 0.02089119 0.5814265 0.36183798 0.22303772]\\n\",\n \"item weights [8.211571 4.9118934 5.1358905 4.603628 4.9590673]\\n\",\n \"item weight sum 27.822052\\n\"\n ]\n }\n ],\n \"source\": [\n \"# knapsack problem setup\\n\",\n \"num_items = 5\\n\",\n \"max_capacity = 20\\n\",\n \"key = jr.PRNGKey(0)\\n\",\n \"key_w, key_r = jr.split(key)\\n\",\n \"item_weights = max_capacity / num_items + jr.uniform(key_w, shape=(num_items,), minval=0.0, maxval=5.0)\\n\",\n \"rewards = jr.uniform(key_r, shape=(num_items,), minval=0.0, maxval=1.0)\\n\",\n \"\\n\",\n \"print(\\\"item rewards\\\", rewards)\\n\",\n \"print(\\\"item weights\\\", item_weights)\\n\",\n \"print(\\\"item weight sum\\\", item_weights.sum())\\n\",\n \"\\n\",\n \"# mdp config\\n\",\n \"state_config = {\\n\",\n \" f\\\"s_{i}\\\": {\\\"elements\\\": [\\\"not enclude\\\", \\\"include\\\"], \\\"depends_on\\\": [f\\\"s_{i}\\\"], \\\"controlled_by\\\": [f\\\"a_{i}\\\"]} \\n\",\n \" for i in range(num_items)\\n\",\n \"}\\n\",\n \"state_config[\\\"z\\\"] = {\\n\",\n \" \\\"elements\\\": [\\\"not violated\\\", \\\"violated\\\"], \\\"depends_on\\\": [\\\"z\\\"], \\\"controlled_by\\\": [f\\\"a_{i}\\\" for i in range(num_items)]\\n\",\n \"} \\n\",\n \"\\n\",\n \"obs_config = {\\n\",\n \" k: {\\\"elements\\\": v[\\\"elements\\\"], \\\"depends_on\\\": [k]} for k, v in state_config.items()\\n\",\n \"}\\n\",\n \"\\n\",\n \"act_config = {\\n\",\n \" f\\\"a_{i}\\\": {\\\"elements\\\": [\\\"not enclude\\\", \\\"include\\\"]} \\n\",\n \" for i in range(num_items)\\n\",\n \"}\\n\",\n \"\\n\",\n \"model_description = {\\n\",\n \" \\\"observations\\\": obs_config,\\n\",\n \" \\\"controls\\\": act_config,\\n\",\n \" \\\"states\\\": state_config,\\n\",\n \"}\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Specify model parameters\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"A shapes [(2, 2), (2, 2), (2, 2), (2, 2), (2, 2), (2, 2)]\\n\",\n \"B shapes [(2, 2, 2), (2, 2, 2), (2, 2, 2), (2, 2, 2), (2, 2, 2), (2, 2, 2, 2, 2, 2, 2)]\\n\"\n ]\n }\n ],\n \"source\": [\n \"model = distribution.compile_model(model_description)\\n\",\n \"\\n\",\n \"print(\\\"A shapes\\\", [a.data.shape for a in model.A])\\n\",\n \"print(\\\"B shapes\\\", [a.data.shape for a in model.B])\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"A shapes [(2, 2), (2, 2), (2, 2), (2, 2), (2, 2), (2, 2)]\\n\",\n \"B shapes [(2, 2, 2), (2, 2, 2), (2, 2, 2), (2, 2, 2), (2, 2, 2), (2, 2, 2, 2, 2, 2, 2)]\\n\",\n \"A normalized [True, True, True, True, True, True]\\n\",\n \"B normalized [True, True, True, True, True, True]\\n\",\n \"C normalized [True, True, True, True, True, True]\\n\"\n ]\n }\n ],\n \"source\": [\n \"def create_identity_transition_factor(mat):\\n\",\n \" for i in range(mat.shape[1]):\\n\",\n \" mat[:, i] = np.eye(len(mat))\\n\",\n \" return mat\\n\",\n \"\\n\",\n \"def create_constraint_factor_z_greater_than(act_dim, maximum, num_items, weights):\\n\",\n \" # Create an array of shape (2, act_dim, act_dim, ..., act_dim)\\n\",\n \" tensor_shape = (2,) + (act_dim,) * num_items\\n\",\n \" \\n\",\n \" # Create an array with indices from 0 to act_dim - 1 along each dimension\\n\",\n \" indices = np.indices(tensor_shape[1:])\\n\",\n \"\\n\",\n \" # Reshape weights to fit indices shape\\n\",\n \" weights_reshaped = np.array(weights).reshape((-1,) + (1,) * (indices.ndim - 1))\\n\",\n \" # Multiply weights with matrix that conforms to constraint\\n\",\n \" result = np.array(indices == (act_dim - 1)) * weights_reshaped\\n\",\n \"\\n\",\n \" # Calculate the total for each combination of actions\\n\",\n \" total = np.sum(result, axis=0)\\n\",\n \" \\n\",\n \" # Create the tensor based on the total hours condition\\n\",\n \" tensor = np.where(total > maximum, 1, 0)\\n\",\n \"\\n\",\n \" # Stack the tensor along the first axis to create the final tensor\\n\",\n \" tensor = np.stack((1 - tensor, tensor), axis=0)\\n\",\n \"\\n\",\n \" # make a copy for self state \\n\",\n \" tensor = np.stack([tensor, tensor], axis=1)\\n\",\n \" return tensor\\n\",\n \"\\n\",\n \"# update A tensor\\n\",\n \"for i in range(len(model.A)):\\n\",\n \" model.A[i].data = np.eye(len(model.A[i].data))\\n\",\n \"\\n\",\n \"# update B tensors\\n\",\n \"for i in range(num_items):\\n\",\n \" model.B[i].data = create_identity_transition_factor(model.B[i].data)\\n\",\n \"\\n\",\n \"model.B[-1].data = create_constraint_factor_z_greater_than(2, max_capacity, num_items, item_weights)\\n\",\n \"\\n\",\n \"# create C tensors\\n\",\n \"preferences = nn.softmax(np.stack([np.zeros_like(rewards), rewards], axis=-1), axis=-1)\\n\",\n \"Cs = [None for _ in range(len(model.A))]\\n\",\n \"for i in range(len(model.A)):\\n\",\n \" Cs[i] = preferences[i]\\n\",\n \" \\n\",\n \"Cs[-1] = np.array([1., 0]) # capacity constraint cannot be violated\\n\",\n \"\\n\",\n \"print(\\\"A shapes\\\", [a.data.shape for a in model.A])\\n\",\n \"print(\\\"B shapes\\\", [a.data.shape for a in model.B])\\n\",\n \"\\n\",\n \"print(\\\"A normalized\\\", [np.isclose(a.data.sum(0), 1.).all() for a in model.A])\\n\",\n \"print(\\\"B normalized\\\", [np.isclose(b.data.sum(0), 1.).all() for b in model.B])\\n\",\n \"print(\\\"C normalized\\\", [np.isclose(a.sum(0), 1.).all() for a in Cs])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Run agent\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"agent = Agent(\\n\",\n \" model.A, model.B, Cs,\\n\",\n \" B_action_dependencies=model.B_action_dependencies,\\n\",\n \" num_controls=model.num_controls,\\n\",\n \")\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"qs = jtu.tree_map(lambda x: jnp.expand_dims(x, axis=0), agent.D)\\n\",\n \"q_pi, G = agent.infer_policies(qs)\\n\",\n \"action = agent.sample_action(q_pi)\\n\",\n \"action_multi = agent.decode_multi_actions(action)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"best action [[ 0 1 1 1 1 15]]\\n\",\n \"best action multi [[0 1 1 1 1]]\\n\",\n \"item weights\\n\",\n \"[8.211571 4.9118934 5.1358905 4.603628 4.9590673]\\n\",\n \"item rewards\\n\",\n \"[0.00729382 0.02089119 0.5814265 0.36183798 0.22303772]\\n\"\n ]\n }\n ],\n \"source\": [\n \"print(\\\"best action\\\", action)\\n\",\n \"print(\\\"best action multi\\\", action_multi)\\n\",\n \"print(\\\"item weights\\\")\\n\",\n \"print(item_weights)\\n\",\n \"print(\\\"item rewards\\\")\\n\",\n \"print(rewards)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Verify that the solution chosen by the active inference agent is the best solution, as validated by brute force search\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Brute-force best bits: [0 1 1 1 1] reward: 1.1871933937072754\\n\",\n \"Agent best bits: [0 1 1 1 1] reward: 1.1871933937072754\\n\"\n ]\n }\n ],\n \"source\": [\n \"def brute_force_knapsack(weights, rewards, capacity):\\n\",\n \" best_r = -jnp.inf\\n\",\n \" best_bits = None\\n\",\n \" for bits in itertools.product([0,1], repeat=len(weights)):\\n\",\n \" w = jnp.dot(jnp.array(bits), weights)\\n\",\n \" if w <= capacity + 1e-9:\\n\",\n \" r = jnp.dot(jnp.array(bits), rewards)\\n\",\n \" if r > best_r:\\n\",\n \" best_r, best_bits = float(r), jnp.array(bits)\\n\",\n \" return best_bits, best_r\\n\",\n \"\\n\",\n \"bf_bits, bf_reward = brute_force_knapsack(item_weights, rewards, max_capacity)\\n\",\n \"print(\\\"Brute-force best bits:\\\", bf_bits, \\\"reward:\\\", bf_reward)\\n\",\n \"print(\\\"Agent best bits:\\\", action_multi[0], \\\"reward:\\\", float(jnp.dot(action_multi[0], rewards)))\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"\\n\",\n \"action [ 0 1 1 1 1 15]\\n\",\n \"action multi [0 1 1 1 1]\\n\",\n \"efe: -3.79, reward: 1.19\\n\",\n \"\\n\",\n \"action [0 0 1 1 1 7]\\n\",\n \"action multi [0 0 1 1 1]\\n\",\n \"efe: -3.78, reward: 1.17\\n\",\n \"\\n\",\n \"action [ 0 1 1 1 0 14]\\n\",\n \"action multi [0 1 1 1 0]\\n\",\n \"efe: -3.68, reward: 0.96\\n\",\n \"\\n\",\n \"action [ 1 0 1 1 0 22]\\n\",\n \"action multi [1 0 1 1 0]\\n\",\n \"efe: -3.67, reward: 0.95\\n\",\n \"\\n\",\n \"action [0 0 1 1 0 6]\\n\",\n \"action multi [0 0 1 1 0]\\n\",\n \"efe: -3.67, reward: 0.94\\n\",\n \"\\n\",\n \"action [ 0 1 1 0 1 13]\\n\",\n \"action multi [0 1 1 0 1]\\n\",\n \"efe: -3.61, reward: 0.83\\n\"\n ]\n }\n ],\n \"source\": [\n \"# print top actions, sorted in decreasing posterior probability (lowest EFE first)\\n\",\n \"from pymdp import utils\\n\",\n \"for i, idx in enumerate(np.argsort(q_pi[0])[::-1]):\\n\",\n \" action_multi_f = utils.index_to_combination(agent.policies[idx, 0][-1].tolist(), agent.num_controls_multi)\\n\",\n \" print(\\\"\\\\naction\\\", agent.policies[idx, 0])\\n\",\n \" print(\\\"action multi\\\", action_multi_f)\\n\",\n \" print(\\\"efe: -{:.2f}, reward: {:.2f}\\\".format(G[0, idx], np.sum(rewards * action_multi_f)))\\n\",\n \" if i == 5:\\n\",\n \" break\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"pymdp_dev_env\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.12.3\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/envs/tmaze_demo.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# T-Maze Demo\\n\",\n \"\\n\",\n \"In this notebook, we simulate an active inference agent solving the T-Maze task - a type of two-armed contextual bandit. Note that unlike in earlier demos in the legacy version of the [`pymdp` package](https://pymdp-rtd.readthedocs.io/en/latest/) which has a `NumPy` backend, this demo relies on `pymdp`'s new `jax` backend. The JAX backend accelerates `pymdp` by dispatching the core inference, learning and planning computations to CUDA-compatible GPU devices (if available). This, in combination with JAX's just-in-time (JIT) compilation features, enables pymdp to take advantage of batch processing (i.e., running many AIF processes in parallel) and increased memory-usage / speed, especially recurrent operations (e.g., iterative inference routines or processes that run over time).\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## The T-Maze Task\\n\",\n \"\\n\",\n \"The T-Maze task implemented in this notebook is adapted from [the sophisticated inference paper](https://discovery.ucl.ac.uk/id/eprint/10124606/), and was originally introduced in an active inference context in [\\\"Active Inference and Epistemic Value\\\"](https://pubmed.ncbi.nlm.nih.gov/25689102/). The T-maze is a two-armed contextual bandit: at any given time, the agent can choose between sampling a cue (context) or choosing between two reward arms (left vs. right).” This task represents a classic problem in sequential decision-making, where an agent (in this case, analogized to a rat) must navigate a T-shaped maze. The agent starts at the centre of the T-maze. Within either the left or right arm, there is either a preferred (i.e., rewarding; cheese) stimulus or an aversive (i.e., punishing; shock) stimulus, with these reward contingencies initially unknown to the agent. In the bottom part of the T-Maze, a cue provides information about the which arm the rewarding stimulus is in.\\n\",\n \"\\n\",\n \"The agent is faced with a dilemma: commit to one of the potentially rewarding arms or first seek information from the cue to identify the more rewarding option before taking action. We use the term \\\"cue validity\\\" to indicate the probability that the cue correctly indicates the reward's location. If the cue has information about which of the two arms is more rewarded (i.e., the cue validity is greater than 50%), then the optimal behavior entails first visiting the cue arm and then choosing one of the two reward arms. \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Outline of this notebook\\n\",\n \"### This notebook steps through the following variants of the T-Maze Demo:\\n\",\n \"\\n\",\n \"#### **1.** A deterministic generative process (environment), and a single agent solving the task with standard (non-sophisticated) active inference.\\n\",\n \"\\n\",\n \"#### **2.** A noisy generative process, and a single agent solving the task with standard active inference.\\n\",\n \"\\n\",\n \"#### **3.** A noisy generative model with A and B learning, with correct and incorrect prior structure of those parameters, and a single agent solving the task with standard active inference.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:30.989078Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:30.988960Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:34.892366Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:34.891996Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# a way to edit and run code and see the effects in the notebook without having to restart the kernel\\n\",\n \"%load_ext autoreload\\n\",\n \"%autoreload 2\\n\",\n \"\\n\",\n \"# importing necessary libraries\\n\",\n \"import jax.numpy as jnp\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import numpy as np\\n\",\n \"import mediapy\\n\",\n \"\\n\",\n \"from jax import random as jr\\n\",\n \"from pymdp.envs import TMaze, rollout\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp.maths import dirichlet_expected_value\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Creating the T-Maze Task (Generative Process)\\n\",\n \"\\n\",\n \"- The `reward_condition` parameter determines the reward location: `0` for the left arm, `1` for the right arm, or `None` for random allocation.\\n\",\n \"- The `reward_probability` parameter sets the chance of receiving a reward in the correct arm. For example, if set at 0.80, there would be an 80% chance of reward and 20% chance of no outcome in the rewarding arm.\\n\",\n \"- The `punishment_probability` parameter specifies the likelihood of punishment in the other arm. For example, if set at 0.80, there would be an 80% chance of punishment and 20% chance of no outcome in the non-rewarding arm.\\n\",\n \"- The `cue_validity` parameter represents the accuracy of the cues as a probability between 0 and 1.\\n\",\n \"\\n\",\n \"
\\n\",\n \" Click here to see how the generative process is set up. \\n\",\n \"\\n\",\n \"#### States and Observations\\n\",\n \"\\n\",\n \"**State Factors:**\\n\",\n \"1. Location (5 states):\\n\",\n \" - 0: centre (start location)\\n\",\n \" - 1: left arm\\n\",\n \" - 2: right arm\\n\",\n \" - 3: cue location (bottom)\\n\",\n \" - 4: middle of arms (between left and right arm)\\n\",\n \"2. Reward Location (2 states):\\n\",\n \" - 0: reward in left arm \\n\",\n \" - 1: reward in right arm\\n\",\n \"\\n\",\n \"**Observation Modalities:**\\n\",\n \"1. Location (5 observations):\\n\",\n \" - Matches the location states exactly\\n\",\n \"2. Outcome (3 observations):\\n\",\n \" - 0: no outcome\\n\",\n \" - 1: reward (cheese)\\n\",\n \" - 2: punishment (shock)\\n\",\n \"3. Cue (3 observations):\\n\",\n \" - 0: no cue\\n\",\n \" - 1: left arm cued\\n\",\n \" - 2: right arm cued\\n\",\n \"\\n\",\n \"#### Environment Parameters\\n\",\n \"\\n\",\n \"**Observation Likelihood Model (A):**\\n\",\n \"- A[0]: Location observations (5x5 tensor)\\n\",\n \" - Perfect mapping between true and observed location.\\n\",\n \"- A[1]: Outcome observations (3x5x2 tensor)\\n\",\n \" - In the more rewarding arm, reward is presented with a likelihood determined by the `reward_probability` parameter.\\n\",\n \" - In the less rewarding arm, punishment is presented with a likelihood determined by the `punishment_probability` parameter.\\n\",\n \" - No outcomes are observed in the centre/start location, cue location, or middle of the two arms.\\n\",\n \"- A[2]: Cue observations (3x5x2 tensor)\\n\",\n \" - Indicating the reward location, at the cue location (bottom), with accuracy set by the `cue_validity` parameter.\\n\",\n \" - No cues visible elsewhere.\\n\",\n \"\\n\",\n \"**Transition Model (B):**\\n\",\n \"- B[0]: Location transitions (5x5x5 tensor)\\n\",\n \" - Agent can move between adjacent maze cells or stay in the same cell.\\n\",\n \"- B[1]: Reward location (2x2x1 tensor)\\n\",\n \" - Reward location remains fixed throughout trial.\\n\",\n \"\\n\",\n \"**Initial Conditions (D):**\\n\",\n \"- D[0]: Starting location (5x1 tensor)\\n\",\n \" - Agent always begins in centre location\\n\",\n \"- D[1]: Reward placement (2x1 tensor)\\n\",\n \" - Default: Equal chance (50/50) of reward in either arm (`reward_condition=None`)\\n\",\n \" - Optional: Can fix reward to specific arm, by setting `reward_condition` to `0` (for left arm) or `1` (for right arm)\\n\",\n \"\\n\",\n \"
\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:34.893886Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:34.893745Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:35.262412Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:35.262092Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# setting the parameters for the environment\\n\",\n \"reward_condition = None # 0 is reward in left arm, 1 is reward in right arm, None is random allocation\\n\",\n \"reward_probability = 1.0 # 100% chance of reward in the correct arm\\n\",\n \"punishment_probability = 1.0 # 100% chance of punishment in the other arm\\n\",\n \"cue_validity = 1.0 # 100% valid cues\\n\",\n \"dependent_outcomes = False # if True, punishment occurs as a function of reward probability (i.e., if reward probability is 0.8, then 20% punishment). If False, punishment occurs with set probability (i.e., 20% no outcome and punishment will only occur in the other (non-rewarding) arm)\\n\",\n \"\\n\",\n \"# initialising the environment. see tmaze.py in pymdp/envs for the implementation details.\\n\",\n \"env = TMaze( \\n\",\n \" reward_probability=reward_probability, \\n\",\n \" punishment_probability=punishment_probability, \\n\",\n \" cue_validity=cue_validity, \\n\",\n \" reward_condition=reward_condition,\\n\",\n \" dependent_outcomes=dependent_outcomes\\n\",\n \")\\n\",\n \"\\n\",\n \"# you may print the environment parameters to see the shapes of the tensors and the values by editing and uncommenting the following lines and running the code: \\n\",\n \"\\n\",\n \"# print([a.shape for a in env.params[\\\"A\\\"]]) # shape of all A tensors; the shape should start with the batch_size, then the rows, columns, and additional dimensions for the dependencies\\n\",\n \"# print(env.params[\\\"A\\\"][1][0][:,:,1]) # likelihood of observing no outcome, reward, or punishment (rows), in each location (columns), when the reward condition is 1 (right arm)\\n\",\n \"# print(env.params[\\\"A\\\"][2][0][:,:,0]) # likelihood of observing no cue, left arm cued, or right arm cued (rows), in each location (columns), when the reward condition is 0 (left arm)\\n\",\n \"\\n\",\n \"# print([b.shape for b in env.params[\\\"B\\\"]]) # shape of all B tensors\\n\",\n \"# print(env.params[\\\"B\\\"][0][0][:,:,4]) # probability of transitioning to each location (rows), from each location (columns), when the agent wants to move to the middle of the arms (location 4)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# 1. A deterministic generative process (environment), and a single agent solving the task with standard active inference.\\n\",\n \"\\n\",\n \"### Creating the Agent (Generative Model)\\n\",\n \"\\n\",\n \"We will create the agent's generative model based off the true observation and transition models (encoded by tensors `A` and `B`, respectively) of the environment. In other words, we assume the agent knows how the environment works - i.e., it knows that the likelihood of observing a reward in the left arm is 1.0 (`reward_probability=1.0`) if the reward is actually in the left arm (`reward_condition=0`), and it knows the cues are 100% accurate (`cue_validity=1.0`), and it knows that the reward location will be fixed throughout the trial (non-volatile environment). We can of course change these assumptions to create a more complex agent, and we will do that in the next sections where the environment will be more stochastic and we will also add uncertainty to the agent's generative model so it will have to learn that the environment is deterministic or not.\\n\",\n \"\\n\",\n \"The preference tensors (`C`) are set using the known dimensions of the outcome modalities, which we can infer from the A tensor's shape. We fix the agent's preferences *a priori* to prefer reward and avoid punishment. The agent is set to not have any preference to observe certain locations and cues. \\n\",\n \"\\n\",\n \"The initial beliefs tensors (D; i.e., state priors) are set using the known dimensions of the hidden state factors, which we can infer from the B tensor's shape. The agent has the prior belief that it starts in the center location and it has no prior about the reward location - i.e., the prior for the reward location is uniformly distributed. \\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:35.263798Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:35.263720Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:36.072631Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:36.072248Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Number of generated agents: 1\\n\",\n \"\\n\",\n \"[(1, 5, 5), (1, 3, 5, 2), (1, 3, 5, 2)]\\n\",\n \"[[1. 0. 0. 1. 1.]\\n\",\n \" [0. 0. 1. 0. 0.]\\n\",\n \" [0. 1. 0. 0. 0.]]\\n\",\n \"[[ 0. 2. -3.]]\\n\"\n ]\n },\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61033/343300159.py:29: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agent = Agent(\\n\"\n ]\n }\n ],\n \"source\": [\n \"# setting A tensors from the environment parameters\\n\",\n \"A = env.A\\n\",\n \"A_dependencies = env.A_dependencies # dependencies allow you to specify which state factors each observation modality depends on, so you dont have to store all the conditional dependencies between all state factors and each modality\\n\",\n \"\\n\",\n \"# setting B tensors from the environment parameters\\n\",\n \"B = env.B\\n\",\n \"B_dependencies = env.B_dependencies\\n\",\n \"\\n\",\n \"# creating C tensors filled with zeros for [location], [reward], [cue] based on A shapes\\n\",\n \"C = [jnp.zeros(a.shape[0], dtype=jnp.float32) for a in A] \\n\",\n \"# setting preferences for outcomes only\\n\",\n \"C[1] = C[1].at[1].set(2.0) # prefer reward\\n\",\n \"C[1] = C[1].at[2].set(-3.0) # avoid punishment\\n\",\n \"\\n\",\n \"# creating D tensors [location], [reward] based on B shapes\\n\",\n \"D = []\\n\",\n \"# D[0]: location - all zeros except location 0 (centre) because the agent always starts in the centre\\n\",\n \"D_loc = jnp.zeros(B[0].shape[0], dtype=jnp.float32) \\n\",\n \"D_loc = D_loc.at[0].set(1.0) # set centre location to 1.0\\n\",\n \"D.append(D_loc)\\n\",\n \"\\n\",\n \"# D[1]: reward location - uniform distribution\\n\",\n \"D_reward = jnp.ones(B[1].shape[0], dtype=jnp.float32) \\n\",\n \"D_reward = D_reward / jnp.sum(D_reward, axis=0, keepdims=True) # normalise to get uniform distribution\\n\",\n \"D.append(D_reward)\\n\",\n \"\\n\",\n \"\\n\",\n \"# initialising the agent\\n\",\n \"agent = Agent(\\n\",\n \" A, B, C, D, \\n\",\n \" policy_len=2, # how long the action sequence is that the agent is evaluating\\n\",\n \" A_dependencies=A_dependencies, \\n\",\n \" B_dependencies=B_dependencies,\\n\",\n \" learn_A=False,\\n\",\n \" learn_B=False\\n\",\n \")\\n\",\n \"\\n\",\n \"# you may print the agent's generative model parameters to see the shapes of the tensors and the values by editing and uncommenting the following lines and running the code: \\n\",\n \"\\n\",\n \"print(f'Number of generated agents: {agent.batch_size}\\\\n')\\n\",\n \"print([a.shape for a in agent.A]) # shape of all A tensors\\n\",\n \"print(agent.A[1][0][:,:,1]) # likelihood of observing no outcome, reward, or punishment (rows), in each location (columns), when the reward condition is 1 (right arm)\\n\",\n \"print(agent.C[1]) # preferences for outcomes\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Running the active inference agent\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:36.074529Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:36.074406Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:37.066512Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:37.066101Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"key = jr.PRNGKey(0) # random key for seeding reproducible stochasticity in the AIF loop (e.g., for sampling any random processes in the TMaze, and for sampling actions from the agent's chosen policy).\\n\",\n \"T = 10 # number of timesteps to rollout the aif loop for\\n\",\n \"_, info = rollout(agent, env, num_timesteps=T, rng_key=key) # running the aif loop\\n\",\n \"\\n\",\n \"# you may print the info dictionary to see the numerical results of the aif agent completing the T-maze task by editing and uncommenting the following lines and running the code: \\n\",\n \"\\n\",\n \"# print(info.keys()) # keys in the info dictionary\\n\",\n \"# print(info[\\\"action\\\"][:,0,:]) # actions taken by the agent (locations throughout the maze) \\n\",\n \"# print(info[\\\"observation\\\"][0]) # observations of the locations for each batch\\n\",\n \"# print(info[\\\"observation\\\"][2]) # observations of the cues for each batch\\n\",\n \"# print(jnp.around(info[\\\"qs\\\"][1], decimals=2)) # posterior beliefs about the reward location\\n\",\n \"# print(info[\\\"qpi\\\"][0].shape) # shape of the policy tensor\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Rendering the Task to Visualise the Agent's Behaviour\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:37.067936Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:37.067856Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:39.106070Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:39.105739Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"
\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"frames = []\\n\",\n \"for t in range(info[\\\"observation\\\"][0].shape[1]): # iterate over timesteps\\n\",\n \" # get observations for this timestep\\n\",\n \" observations_t = [\\n\",\n \" info[\\\"observation\\\"][0][:, t, :],\\n\",\n \" info[\\\"observation\\\"][1][:, t, :], \\n\",\n \" info[\\\"observation\\\"][2][:, t, :] \\n\",\n \" ]\\n\",\n \" \\n\",\n \" frame = env.render(mode=\\\"rgb_array\\\", observations=observations_t) # render the environment using the observations for this timestep\\n\",\n \" frame = np.asarray(frame, dtype=np.uint8)\\n\",\n \" plt.close() # close the figure to prevent memory leak\\n\",\n \" frames.append(frame)\\n\",\n \"\\n\",\n \"frames = np.array(frames, dtype=np.uint8)\\n\",\n \"mediapy.show_video(frames, fps=1)\\n\",\n \"\\n\",\n \"# # uncomment the following lines to save the video as a gif\\n\",\n \"# os.makedirs(\\\"figures\\\", exist_ok=True)\\n\",\n \"# pil_frames = [Image.fromarray(frame) for frame in frames]\\n\",\n \"# reward_location = \\\"random\\\" if reward_condition is None else (\\\"left\\\" if reward_condition == 0 else \\\"right\\\")\\n\",\n \"# filename = os.path.join(\\\"figures\\\", f\\\"tmaze_{batch_size}_{reward_location}.gif\\\")\\n\",\n \"# pil_frames[0].save(\\n\",\n \"# filename,\\n\",\n \"# save_all=True,\\n\",\n \"# append_images=pil_frames[1:],\\n\",\n \"# duration=1000, # 1000ms per frame\\n\",\n \"# loop=0\\n\",\n \"# )\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Running multiple agents in parallel using the `batch_size` parameter\\n\",\n \"The active inference computations taking place within the the `Agent` methods (inference, planning/action selection, and learning) interally expect most arrays to have an additional leading dimension, with length `batch_size`. This extra dimension can be used to generate and run multiple agents in parallel, each with their own generative model, observation and action history, and posterior beliefs. For instance, if `batch_size = 10`, then each `A`, `B`, `C`, ... array will represent the corresponding generative model parameters for 10 different agents, and each agent will receive its own history of observations / emit its own actions. The single agent (default) case is therefore the case of `batch_size = 1`. If you pass in generative model arrays to the `Agent` constructor without a `(batch_size,)`-sized leading dimension (as we did in the previous example), they will be expanded internally to have this dimension, creating `batch_size` identical copies of the provided model parameters.\\n\",\n \"\\n\",\n \"One can also run multiple _environments_ in parallel by passing a separate, stateful `env_params` pytree which stores `batch_size` different `A`, `B`, and `D` arrays, but for now we are using a single fixed environment. This is the default case where the environmental attributes `env.A`, `env.B`, and `env.D` arrays have no leading `(batch_size,)` dimension, even while the `Agent` class _does_ have it.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:39.107336Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:39.107255Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:57.520123Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:57.519692Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61033/1007283590.py:32: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agent = Agent(\\n\"\n ]\n },\n {\n \"data\": {\n \"text/html\": [\n \"
\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"batch_size = 9 # number of agents to run in parallel\\n\",\n \"\\n\",\n \"# setting A tensors from the environment parameters\\n\",\n \"A, B = env.A, env.B\\n\",\n \"A_dependencies, B_dependencies = env.A_dependencies, env.B_dependencies # dependencies allow you to specify the state factors the observation modality depends on so you dont have to compute the full tensor using all state factors\\n\",\n \"\\n\",\n \"# now expand A and B to have a new batch_size-length leading dimension\\n\",\n \"A = [jnp.broadcast_to(a, (batch_size,) + a.shape) for a in A]\\n\",\n \"B = [jnp.broadcast_to(b, (batch_size,) + b.shape) for b in B]\\n\",\n \"\\n\",\n \"# creating C tensors filled with zeros for [location], [reward], [cue] based on A shapes\\n\",\n \"C = [jnp.zeros((batch_size, a.shape[1]), dtype=jnp.float32) for a in A] \\n\",\n \"# setting preferences for outcomes only\\n\",\n \"C[1] = C[1].at[:,1].set(2.0) # prefer reward\\n\",\n \"C[1] = C[1].at[:,2].set(-3.0) # avoid punishment\\n\",\n \"\\n\",\n \"\\n\",\n \"# creating D tensors [location], [reward] based on B shapes\\n\",\n \"D = []\\n\",\n \"# D[0]: location - all zeros except location 0 (centre) because the agent always starts in the centre\\n\",\n \"D_loc = jnp.zeros((batch_size, B[0].shape[1]), dtype=jnp.float32) \\n\",\n \"D_loc = D_loc.at[0,0].set(1.0) # set centre location to 1.0\\n\",\n \"D.append(D_loc)\\n\",\n \"\\n\",\n \"# D[1]: reward location - uniform distribution\\n\",\n \"D_reward = jnp.ones((batch_size, B[1].shape[1]), dtype=jnp.float32) \\n\",\n \"D_reward = D_reward / jnp.sum(D_reward, axis=1, keepdims=True) # normalise to get uniform distribution\\n\",\n \"D.append(D_reward)\\n\",\n \"\\n\",\n \"\\n\",\n \"# initialising the agent\\n\",\n \"agent = Agent(\\n\",\n \" A, B, C, D, \\n\",\n \" policy_len=2,\\n\",\n \" A_dependencies=A_dependencies, \\n\",\n \" B_dependencies=B_dependencies,\\n\",\n \" batch_size=batch_size, # note we have to pass in this batch_size parameter so the class knows to treat the first dimension as the batch size\\n\",\n \" learn_A=False,\\n\",\n \" learn_B=False\\n\",\n \")\\n\",\n \"\\n\",\n \"_, info = rollout(agent, env, num_timesteps=T, rng_key=key) # running the aif loop\\n\",\n \"\\n\",\n \"# rendering the task to visualise the agent's behaviour \\n\",\n \"frames = []\\n\",\n \"for t in range(info[\\\"observation\\\"][0].shape[1]): # iterate over timesteps\\n\",\n \" # get observations for this timestep\\n\",\n \" observations_t = [\\n\",\n \" info[\\\"observation\\\"][0][:, t, :],\\n\",\n \" info[\\\"observation\\\"][1][:, t, :], \\n\",\n \" info[\\\"observation\\\"][2][:, t, :] \\n\",\n \" ]\\n\",\n \" \\n\",\n \" frame = env.render(mode=\\\"rgb_array\\\", observations=observations_t) # render the environment using the observations for this timestep\\n\",\n \" frame = np.asarray(frame, dtype=np.uint8)\\n\",\n \" plt.close() # close the figure to prevent memory leak\\n\",\n \" frames.append(frame)\\n\",\n \"\\n\",\n \"frames = np.array(frames, dtype=np.uint8)\\n\",\n \"mediapy.show_video(frames, fps=1)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# 2. A noisy generative process, and a single agent solving the task with standard active inference.\\n\",\n \"\\n\",\n \"### Making the world more stochastic\\n\",\n \"\\n\",\n \"In this variant, we will once again give the agent true knowledge of the parameters of the generative process (by fixing the `A` and `B` tensors of the agent to those of the true generative process), but now we will add stochasticity to the true generative process parameters, such that the agent is not guaranteed to get reward in the rewarded-arm every time, but only more likely to get reward than punishment there. This stochasticity can be modulated using the `reward_probability` argument to the `TMaze()` environment. We can likewise modulate the probability of seeing punishment in the punishment arm, by changing the `punishment_probability` argument to the `TMaze` environment. Finally, another source of uncertainty is the cue reliability or validity, which encodes the likelihood that the signal observed in the cue location of the TMaze, accurately identifies which arm is the more-rewarding vs. more-punishing arm. This probability (of the cue signalling the 'correct arm') can be modulated using the `cue_validity` argument to the `TMaze` constructor.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:57.523036Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:57.522878Z\",\n \"iopub.status.idle\": \"2026-03-06T15:30:57.552414Z\",\n \"shell.execute_reply\": \"2026-03-06T15:30:57.552056Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# THE GENERATIVE PROCESS (NOISY)\\n\",\n \"# setting the parameters for the environment\\n\",\n \"batch_size = 4 # number of environments/agents to run in parallel\\n\",\n \"reward_condition = None # 0 is reward in left arm, 1 is reward in right arm, None is random allocation\\n\",\n \"reward_probability = 0.7 # 70% chance of reward in the correct arm\\n\",\n \"punishment_probability = 0.6 # 60% chance of punishment in the other arm\\n\",\n \"cue_validity = 0.95 # 90% valid cues\\n\",\n \"dependent_outcomes = False # if True, punishment occurs as a function of reward probability (i.e., if reward probability is 0.8, then 20% punishment). If False, punishment occurs with set probability (i.e., 20% no outcome and punishment will only occur in the other (non-rewarding) arm)\\n\",\n \"\\n\",\n \"# initialising the environment. see tmaze.py in pymdp/envs for the implementation details.\\n\",\n \"env = TMaze( \\n\",\n \" reward_probability=reward_probability, \\n\",\n \" punishment_probability=punishment_probability, \\n\",\n \" cue_validity=cue_validity, \\n\",\n \" reward_condition=reward_condition,\\n\",\n \" dependent_outcomes=dependent_outcomes\\n\",\n \")\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:30:57.553800Z\",\n \"iopub.status.busy\": \"2026-03-06T15:30:57.553715Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:00.132559Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:00.132150Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61033/34467052.py:32: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agent = Agent(\\n\"\n ]\n }\n ],\n \"source\": [\n \"# THE GENERATIVE MODEL\\n\",\n \"\\n\",\n \"# Get A, B, and dependencies from the environment\\n\",\n \"A, B = env.A, env.B\\n\",\n \"A_dependencies, B_dependencies = env.A_dependencies, env.B_dependencies # dependencies allow you to specify\\n\",\n \"\\n\",\n \"# now expand A and B to have a new batch_size-length leading dimension\\n\",\n \"A = [jnp.broadcast_to(a, (batch_size,) + a.shape) for a in A]\\n\",\n \"B = [jnp.broadcast_to(b, (batch_size,) + b.shape) for b in B]\\n\",\n \"\\n\",\n \"# creating C tensors filled with zeros for [location], [reward], [cue] based on A shapes\\n\",\n \"C = [jnp.zeros((batch_size, a.shape[1]), dtype=jnp.float32) for a in A] \\n\",\n \"# setting preferences for outcomes only\\n\",\n \"C[1] = C[1].at[:,1].set(3.0) # prefer reward\\n\",\n \"C[1] = C[1].at[:,2].set(-4.0) # avoid punishment\\n\",\n \"\\n\",\n \"\\n\",\n \"# creating D tensors [location], [reward] based on B shapes\\n\",\n \"D = []\\n\",\n \"# D[0]: location - all zeros except location 0 (centre) because the agent always starts in the centre\\n\",\n \"D_loc = jnp.zeros((batch_size, B[0].shape[1]), dtype=jnp.float32) \\n\",\n \"D_loc = D_loc.at[0,0].set(1.0) # set centre location to 1.0\\n\",\n \"D.append(D_loc)\\n\",\n \"\\n\",\n \"# D[1]: reward location - uniform distribution\\n\",\n \"D_reward = jnp.ones((batch_size, B[1].shape[1]), dtype=jnp.float32) \\n\",\n \"D_reward = D_reward / jnp.sum(D_reward, axis=1, keepdims=True) # normalise to get uniform distribution\\n\",\n \"D.append(D_reward)\\n\",\n \"\\n\",\n \"\\n\",\n \"# initialising the agent\\n\",\n \"agent = Agent(\\n\",\n \" A, B, C, D, \\n\",\n \" policy_len=3, # how long the action sequence is that the agent is evaluating\\n\",\n \" A_dependencies=A_dependencies, \\n\",\n \" B_dependencies=B_dependencies,\\n\",\n \" batch_size=batch_size,\\n\",\n \" learn_A=False,\\n\",\n \" learn_B=False\\n\",\n \")\\n\",\n \"\\n\",\n \"key = jr.PRNGKey(0) # random key for the aif loop\\n\",\n \"T = 20 # number of timesteps to rollout the aif loop for\\n\",\n \"_, info = rollout(agent, env, num_timesteps=T, rng_key=key) # running the aif loop\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:00.134138Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:00.134056Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:13.111259Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:13.110818Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"
\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"frames = []\\n\",\n \"for t in range(info[\\\"observation\\\"][0].shape[1]): # iterate over timesteps\\n\",\n \" # get observations for this timestep\\n\",\n \" observations_t = [\\n\",\n \" info[\\\"observation\\\"][0][:, t, :],\\n\",\n \" info[\\\"observation\\\"][1][:, t, :], \\n\",\n \" info[\\\"observation\\\"][2][:, t, :] \\n\",\n \" ]\\n\",\n \" \\n\",\n \" frame = env.render(mode=\\\"rgb_array\\\", observations=observations_t) # render the environment using the observations for this timestep\\n\",\n \" frame = np.asarray(frame, dtype=np.uint8)\\n\",\n \" plt.close() # close the figure to prevent memory leak\\n\",\n \" frames.append(frame)\\n\",\n \"\\n\",\n \"frames = np.array(frames, dtype=np.uint8)\\n\",\n \"mediapy.show_video(frames, fps=1)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# 3. Agent is equipped with a partially-uncertain model of the true generative process, and can also perform parameter learning to update its beliefs about outcome and transition contingencies over time.\\n\",\n \"\\n\",\n \"You can tweak the following arguments to the `Agent` constructor: `learn_A` and `learn_B` between True and False -- this selectively turns on/off the ability to update the parameters of the Dirichlet posterior over the `A` and `B` tensors, respectively. These functionalities should be used when your agent does not have a correct or confident model of the world, and you want the agent to *learn* its model over time.\\n\",\n \"\\n\",\n \"As an example, we will do the following two variants in this section:\\n\",\n \"\\n\",\n \"**1** We initialize the agent to have partially-uncertain beliefs about the A and B parameters, but the mode of their beliefs (i.e. the value with the highest probability) is still based on the true generative process.\\n\",\n \"\\n\",\n \"**2** We will equip the agent with incorrect beliefs about the generative process.\\n\",\n \"\\n\",\n \"### Correct Prior Structure\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:13.114299Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:13.114183Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:13.165763Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:13.165478Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# setting the parameters for the environment\\n\",\n \"reward_condition = 0 # 0 is reward in left arm, 1 is reward in right arm, None is random allocation\\n\",\n \"reward_probability = 1.0 # 100% chance of reward in the correct arm\\n\",\n \"punishment_probability = 1.0 # 100% chance of punishment in the other arm\\n\",\n \"cue_validity = 1.0 # 100% valid cues\\n\",\n \"dependent_outcomes = False\\n\",\n \"\\n\",\n \"# initialising the environment. see tmaze.py in pymdp/envs for the implementation details.\\n\",\n \"env = TMaze( \\n\",\n \" reward_probability=reward_probability, \\n\",\n \" punishment_probability=punishment_probability, \\n\",\n \" cue_validity=cue_validity, \\n\",\n \" reward_condition=reward_condition, \\n\",\n \" dependent_outcomes=dependent_outcomes\\n\",\n \")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### We can encode uncertainty in the agent's prior knowledge about the state-outcome contingencies by adding non-zero parameter values to the `pA` tensor (the prior Dirichlet parameters **over** the Categorical parameters of the A tensor). In practice, we still put 'true knowledge' into this prior, in the sense that the mode of the likelihood distribution aligned with the true generative process parameters, but we add some uncertainty by adding non-zero values into the parts of the Dirichlet prior tensor where they don't exist in the true generative process parameters; this encodes the agent's uncertainty about whether certain relationships between hidden states (e.g., location states or reward-condition states) and outcomes (cue signals or reward outcomes) exist.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:13.167263Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:13.167167Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:13.735458Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:13.735184Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61033/1366977802.py:37: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agent = Agent(\\n\"\n ]\n }\n ],\n \"source\": [\n \"# initializing the prior over the A tensors (pA) based on the environment parameters\\n\",\n \"num_obs = [a.shape[0] for a in env.A] # number of observations for each modality\\n\",\n \"num_states = [b.shape[0] for b in env.B] # number of states for each factor\\n\",\n \"\\n\",\n \"# initializing pA, pB to be identical to the environmental parameters\\n\",\n \"pA, pB = [jnp.copy(a) for a in env.A], [jnp.copy(b) for b in env.B] # have to copy them here because we will be modifying pA below\\n\",\n \"\\n\",\n \"# adding non-zero Dirichlet parameter values to pA flatten the expected value of the A tensor (make more uncertain) \\n\",\n \"alpha_scale_pA = 0.3 \\n\",\n \"for m in [1, 2]: # only modifying the outcome (m=1) and cue (m=2) observation likelihood mappings\\n\",\n \" pA[m] = pA[m] + (alpha_scale_pA * jnp.ones_like(pA[m]))\\n\",\n \"\\n\",\n \"expected_A = [dirichlet_expected_value(pa_m, event_dim=0) for pa_m in pA]# compute the expected value of the Dirichlet parameters in pA \\n\",\n \"expected_B = [dirichlet_expected_value(pb_f, event_dim=0) for pb_f in pB]# compute the expected value of the Dirichlet parameters in pB \\n\",\n \"\\n\",\n \"# creating C tensors filled with zeros for [location], [reward], [cue] based on modality shapes\\n\",\n \"C = [jnp.zeros(no, dtype=jnp.float32) for no in num_obs] \\n\",\n \"# setting preferences for outcomes only\\n\",\n \"C[1] = C[1].at[1].set(2.0) # prefer reward\\n\",\n \"C[1] = C[1].at[2].set(-3.0) # avoid punishment\\n\",\n \"\\n\",\n \"# creating D tensors [location], [reward] based on B shapes\\n\",\n \"D = [jnp.zeros(ns, dtype=jnp.float32) for ns in num_states] # creating D tensors filled with zeros for [location], [reward] based on B shapes\\n\",\n \"# D[0]: location - all zeros except location 0 (centre) because the agent always starts in the centre\\n\",\n \"D_loc = jnp.zeros(num_states[0], dtype=jnp.float32) \\n\",\n \"D_loc = D_loc.at[0].set(1.0) # set centre location to 1.0\\n\",\n \"D[0] = D_loc\\n\",\n \"\\n\",\n \"# D[1]: reward location - uniform distribution\\n\",\n \"D_reward = jnp.ones(num_states[1], dtype=jnp.float32) \\n\",\n \"D_reward = D_reward / jnp.sum(D_reward, axis=0, keepdims=True) # normalise to get uniform distribution\\n\",\n \"D[1] = D_reward\\n\",\n \"\\n\",\n \"\\n\",\n \"# initialising the agent\\n\",\n \"# NOTE: We initialize the first value of A and B based on the expected values of the Dirichlet parameters in pA and pB, respectively.\\n\",\n \"agent = Agent(\\n\",\n \" expected_A, expected_B, C, D, \\n\",\n \" pA=pA,\\n\",\n \" pB=pB, \\n\",\n \" policy_len=5, # how long the action sequence is that the agent is evaluating\\n\",\n \" A_dependencies=env.A_dependencies, \\n\",\n \" B_dependencies=env.B_dependencies,\\n\",\n \" learn_A=True,\\n\",\n \" learn_B=False,\\n\",\n \" gamma=1.0,\\n\",\n \" action_selection=\\\"stochastic\\\"\\n\",\n \")\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:13.736663Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:13.736571Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:14.973093Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:14.972575Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"key = jr.PRNGKey(0) # random key for the aif loop\\n\",\n \"T = 10 # number of timesteps to rollout the aif loop for\\n\",\n \"_, info = rollout(agent, env, num_timesteps=T, rng_key=key) # running the aif loop\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can print out the A tensors over time to see how the agent updates its beliefs about the state-outocome contingencies based on the data its collecting through active inference.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:14.974645Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:14.974520Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:15.009425Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:15.009143Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"the environment's A tensor\\n\",\n \"[[1. 0. 0. 1. 1.]\\n\",\n \" [0. 0. 1. 0. 0.]\\n\",\n \" [0. 1. 0. 0. 0.]]\\n\",\n \"\\n\",\n \"the agent's A tensor at t=0\\n\",\n \"[[0.68421054 0.15789475 0.15789476 0.68421054 0.68421054]\\n\",\n \" [0.15789476 0.15789475 0.68421054 0.15789476 0.15789476]\\n\",\n \" [0.15789476 0.68421054 0.15789476 0.15789476 0.15789476]]\\n\",\n \"\\n\",\n \"the agent's A tensor at t=10\\n\",\n \"[[0.86867255 0.15789475 0.15789476 0.72054607 0.6926888 ]\\n\",\n \" [0.06566371 0.15789475 0.68421054 0.13972697 0.15365562]\\n\",\n \" [0.06566371 0.68421054 0.15789476 0.13972697 0.15365562]]\\n\"\n ]\n }\n ],\n \"source\": [\n \"print(\\\"the environment's A tensor\\\")\\n\",\n \"print(env.A[1][:,:,1])\\n\",\n \"print()\\n\",\n \"print(\\\"the agent's A tensor at t=0\\\")\\n\",\n \"print(agent.A[1][0][:,:,1])\\n\",\n \"print()\\n\",\n \"print(f\\\"the agent's A tensor at t={T}\\\")\\n\",\n \"print(info[\\\"A\\\"][1][0,-1,:,:,1])\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:15.010576Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:15.010492Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:16.051568Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:16.051201Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"
\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"frames = []\\n\",\n \"for t in range(info[\\\"observation\\\"][0].shape[1]): # iterate over timesteps\\n\",\n \" # get observations for this timestep\\n\",\n \" observations_t = [\\n\",\n \" info[\\\"observation\\\"][0][:, t, :],\\n\",\n \" info[\\\"observation\\\"][1][:, t, :], \\n\",\n \" info[\\\"observation\\\"][2][:, t, :] \\n\",\n \" ]\\n\",\n \" \\n\",\n \" frame = env.render(mode=\\\"rgb_array\\\", observations=observations_t) # render the environment using the observations for this timestep\\n\",\n \" frame = np.asarray(frame, dtype=np.uint8)\\n\",\n \" plt.close() # close the figure to prevent memory leak\\n\",\n \" frames.append(frame)\\n\",\n \"\\n\",\n \"frames = np.array(frames, dtype=np.uint8)\\n\",\n \"mediapy.show_video(frames, fps=1)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:16.053250Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:16.053154Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:18.010715Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:18.010367Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61033/3157206125.py:16: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agent = Agent(\\n\"\n ]\n }\n ],\n \"source\": [\n \"# Random initialization test\\n\",\n \"key = jr.PRNGKey(24)\\n\",\n \"\\n\",\n \"# setting A tensors from the environment parameters, but randomize the prior over the transitions\\n\",\n \"pA, pB = [jnp.copy(a) for a in env.A], [jr.uniform(subkey, shape=b.shape) for subkey, b in zip(jr.split(key, num=2), env.B)]\\n\",\n \"\\n\",\n \"# adding noise to outcome and cue modalities to make priors more uncertain\\n\",\n \"key1, key2 = jr.split(key, num=2)\\n\",\n \"for(key_m, modality) in zip([key1, key2], [1, 2]): # only modifying the outcome (m=1) and cue (m=2) observation likelihood mappings\\n\",\n \" pA[modality] = jr.uniform(key_m, shape=pA[modality].shape) # generating random values between 0 and 1\\n\",\n \"\\n\",\n \"expected_A = [dirichlet_expected_value(pa_m, event_dim=0) for pa_m in pA] # compute the expected value of the Dirichlet parameters in pA\\n\",\n \"expected_B = [dirichlet_expected_value(pb_f, event_dim=0) for pb_f in pB]# compute the expected value of the Dirichlet parameters in pB\\n\",\n \"\\n\",\n \"# initialising the agent\\n\",\n \"agent = Agent(\\n\",\n \" expected_A, expected_B, C, D, \\n\",\n \" pA=pA,\\n\",\n \" pB=pB, \\n\",\n \" policy_len=5, # how long the action sequence is that the agent is evaluating\\n\",\n \" A_dependencies=env.A_dependencies, \\n\",\n \" B_dependencies=env.B_dependencies,\\n\",\n \" batch_size=batch_size, \\n\",\n \" learn_A=True,\\n\",\n \" learn_B=True,\\n\",\n \" gamma=0.1,\\n\",\n \" action_selection=\\\"stochastic\\\"\\n\",\n \")\\n\",\n \"\\n\",\n \"# running the active inference simulation\\n\",\n \"key = jr.PRNGKey(0) # random key for the aif loop\\n\",\n \"T = 50 # number of timesteps to rollout the aif loop for\\n\",\n \"_, info = rollout(agent, env, num_timesteps=T, rng_key=key) # running the aif loop\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:18.012533Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:18.012394Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:18.062683Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:18.062343Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"the environment's A tensor\\n\",\n \"[[1. 0. 0. 1. 1.]\\n\",\n \" [0. 0. 1. 0. 0.]\\n\",\n \" [0. 1. 0. 0. 0.]]\\n\",\n \"\\n\",\n \"the agent's A tensor at t=0\\n\",\n \"[[0.00308274 0.07115752 0.55618274 0.42624453 0.36277273]\\n\",\n \" [0.02319651 0.4746476 0.31333998 0.5615474 0.43671665]\\n\",\n \" [0.9737207 0.45419487 0.13047728 0.01220808 0.20051058]]\\n\",\n \"\\n\",\n \"the agent's A tensor at t=50\\n\",\n \"[[0.01081832 0.06939295 0.55391985 0.4478869 0.3744181 ]\\n\",\n \" [0.02301651 0.48767537 0.31206512 0.5403655 0.4287357 ]\\n\",\n \" [0.9661652 0.4429317 0.134015 0.01174758 0.19684626]]\\n\"\n ]\n }\n ],\n \"source\": [\n \"print(\\\"the environment's A tensor\\\")\\n\",\n \"print(env.A[1][:,:,1])\\n\",\n \"print()\\n\",\n \"print(\\\"the agent's A tensor at t=0\\\")\\n\",\n \"print(agent.A[1][0][:,:,1])\\n\",\n \"print()\\n\",\n \"print(f\\\"the agent's A tensor at t={T}\\\")\\n\",\n \"print(info[\\\"A\\\"][1][0,-1,:,:,1])\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 17,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:18.063914Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:18.063837Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:18.194246Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:18.193802Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"the environment's B tensor\\n\",\n \"[[1. 0.]\\n\",\n \" [0. 1.]]\\n\",\n \"\\n\",\n \"the agent's B tensor at t=0\\n\",\n \"[[0.8990159 0.44466075]\\n\",\n \" [0.10098408 0.5553392 ]]\\n\",\n \"\\n\",\n \"the agent's B tensor at t=50\\n\",\n \"[[0.9954207 0.6131649 ]\\n\",\n \" [0.0045793 0.38683507]]\\n\"\n ]\n }\n ],\n \"source\": [\n \"print(\\\"the environment's B tensor\\\")\\n\",\n \"print(env.B[1][:,:,1])\\n\",\n \"print()\\n\",\n \"print(\\\"the agent's B tensor at t=0\\\")\\n\",\n \"print(agent.B[1][0][:,:,1])\\n\",\n \"print()\\n\",\n \"print(f\\\"the agent's B tensor at t={T}\\\")\\n\",\n \"print(info[\\\"B\\\"][1][0,-1,:,:,1])\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 18,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:18.195581Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:18.195478Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:40.817883Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:40.816585Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"
\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"frames = []\\n\",\n \"for t in range(info[\\\"observation\\\"][0].shape[1]): # iterate over timesteps\\n\",\n \" # get observations for this timestep\\n\",\n \" observations_t = [\\n\",\n \" info[\\\"observation\\\"][0][:, t, :],\\n\",\n \" info[\\\"observation\\\"][1][:, t, :], \\n\",\n \" info[\\\"observation\\\"][2][:, t, :] \\n\",\n \" ]\\n\",\n \" \\n\",\n \" frame = env.render(mode=\\\"rgb_array\\\", observations=observations_t) # render the environment using the observations for this timestep\\n\",\n \" frame = np.asarray(frame, dtype=np.uint8)\\n\",\n \" plt.close() # close the figure to prevent memory leak\\n\",\n \" frames.append(frame)\\n\",\n \"\\n\",\n \"frames = np.array(frames, dtype=np.uint8)\\n\",\n \"mediapy.show_video(frames, fps=1)\"\n ]\n }\n ],\n \"metadata\": {\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.11.12\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/experimental/sophisticated_inference/mcts_generalized_tmaze.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Sophisticated inference with Monte Carlo Tree Search\\n\",\n \"\\n\",\n \"This notebook demonstrates how you can implement Sophisticated inference with a Monte Carlo tree search algorithm, to mitigate the combinatorial explosion of exploring all branches. \\n\",\n \"\\n\",\n \"### Sophisticated inference\\n\",\n \"\\n\",\n \"In sophisticated inference the choice probability is computed in an iteartive way, using the following recursive relation for expected free energy \\n\",\n \"\\n\",\n \"\\\\begin{equation}\\n\",\n \"\\\\begin{split}\\n\",\n \" G(u_\\\\tau| o_{\\\\leq\\\\tau}, u_{<\\\\tau}) &= - \\\\ln p(u_{\\\\tau}|u_{<\\\\tau}) + E_{Q(o_{\\\\tau+1}, s_{\\\\tau+1}|u_{\\\\leq\\\\tau}. o_{<\\\\tau})} \\\\left[ \\\\ln \\\\frac{Q(s_{\\\\tau+1}|u_{\\\\leq\\\\tau}, o_{<\\\\tau})}{P(o_{\\\\tau+1}, s_{\\\\tau+1})} \\\\right] \\\\\\\\ \\n\",\n \" &\\\\:\\\\:\\\\: + E_{Q(o_{\\\\tau+1}|u_{\\\\leq\\\\tau}, o_{\\\\leq\\\\tau}) Q(u_{\\\\tau+1}|u_{< \\\\tau + 1}, o_{\\\\leq\\\\tau+1})}\\\\left[G(u_{\\\\tau + 1}|o_{\\\\leq \\\\tau+1}, u_{<\\\\tau+1} ) \\\\right]\\\\\\\\ \\n\",\n \" Q(u_{\\\\tau}|o_{\\\\leq\\\\tau}, u_{<\\\\tau}) &= \\\\text{softmax}(- G(u_{\\\\tau}|o_{\\\\leq\\\\tau}, u_{<\\\\tau})) \\\\\\\\ \\n\",\n \" G(u_T|o_{\\\\leq T}, u_{< T}) &= - \\\\ln p(u_{T}|u_{< T}) + E_{Q(o_{T+1}, s_{T+1}|u_{\\\\leq T}, o_{< T})} \\\\left[ \\\\ln \\\\frac{Q(s_{T+1}|u_{\\\\leq T}, o_{< T})}{P(o_{T + 1}, s_{T + 1})} \\\\right]\\n\",\n \"\\\\end{split}\\n\",\n \"\\\\end{equation}\\n\",\n \"\\n\",\n \"where we use subscript $\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"M = get_maze_matrix()\\n\",\n \"key = jr.PRNGKey(0)\\n\",\n \"\\n\",\n \"key, subkey = jr.split(key)\\n\",\n \"env_info_m = parse_maze(M, subkey)\\n\",\n \"\\n\",\n \"tmaze_env = GeneralizedTMazeEnv(env_info_m)\\n\",\n \"\\n\",\n \"init_obs, init_state = tmaze_env.reset(key)\\n\",\n \"tmaze_env.render(states=init_state, mode=\\\"human\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### Create the agent. \\n\",\n \"\\n\",\n \"The PyMDPEnv class consists of a params dict that contains the A, B, and D vectors of the environment. We initialize our agent using the same parameters. This means that the agent has full knowledge about the environment transitions, and likelihoods. We initialize the agent with a flat prior, i.e. it does not know where it, or the reward is. Finally, we set the C vector to have a preference only over the rewarding observation of cue-reward pair 1 (i.e. C[-1] = [0, 1, -2] and zero for all other modalities). \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"def make_aif_agent(tmaze_env, batch_size=5):\\n\",\n \" A, B = tmaze_env.A, tmaze_env.B\\n\",\n \" A_dependencies, B_dependencies = tmaze_env.A_dependencies, tmaze_env.B_dependencies\\n\",\n \"\\n\",\n \" # [position], [cue], [reward]\\n\",\n \" C = list_array_zeros([a.shape[0] for a in A])\\n\",\n \"\\n\",\n \" rewarding_modality = -1\\n\",\n \"\\n\",\n \" C[rewarding_modality] = C[rewarding_modality].at[1].set(1.0)\\n\",\n \" C[rewarding_modality] = C[rewarding_modality].at[2].set(-2.0)\\n\",\n \"\\n\",\n \" D = list_array_uniform([b.shape[0] for b in B])\\n\",\n \"\\n\",\n \" agent = Agent(\\n\",\n \" A, B, C, D, \\n\",\n \" E=None,\\n\",\n \" pA=None,\\n\",\n \" pB=None,\\n\",\n \" policy_len=1,\\n\",\n \" A_dependencies=A_dependencies, \\n\",\n \" B_dependencies=B_dependencies,\\n\",\n \" use_utility=True,\\n\",\n \" use_states_info_gain=True,\\n\",\n \" sampling_mode='full',\\n\",\n \" action_selection='stochastic',\\n\",\n \" gamma=4.0,\\n\",\n \" batch_size=batch_size,\\n\",\n \" learn_A=False,\\n\",\n \" learn_B=False\\n\",\n \" )\\n\",\n \"\\n\",\n \" return agent\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### MCTS based policy search\\n\",\n \"\\n\",\n \"Here we defined the sofisticated active inference monte-carlo tree search policies using the [mctx](https://github.com/google-deepmind/mctx) package for google deep mind. Although other algorithms are provided in mctx package here we will use only Gumbel based planning algorithm intoroduced in [Policy improvement by planning with Gumbel](https://openreview.net/forum?id=bERaNdoegnO).\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Run active inference\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"timesteps, batch_size = 6, 9\\n\",\n \"agent = make_aif_agent(tmaze_env, batch_size=batch_size)\\n\",\n \"_, info = rollout(agent, tmaze_env, num_timesteps=timesteps, rng_key=key, policy_search=mcts_policy_search(search_algo=mctx.gumbel_muzero_policy, max_depth=3, num_simulations=1024))\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"dict_keys(['action', 'action_weights', 'empirical_prior', 'env_state', 'observation', 'qpi', 'qs', 'search_tree'])\"\n ]\n },\n \"execution_count\": 15,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"info.keys()\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Info keys: ['action', 'action_weights', 'empirical_prior', 'env_state', 'observation', 'qpi', 'qs', 'search_tree']\\n\",\n \"Env state shape: [(9, 7), (9, 7), (9, 7), (9, 7)]\\n\"\n ]\n }\n ],\n \"source\": [\n \"print(\\\"Info keys:\\\", list(info.keys()))\\n\",\n \"print(\\\"Env state shape:\\\", [s.shape for s in info[\\\"env_state\\\"]])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"When we plot the resulting data, we see all agents prefer the correct cue that is actually yielding reward, and avoid the distracting cues. Depending on the amount of samples though, some agents might still get distracted the first timestep.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"images = []\\n\",\n \"for t in range(timesteps):\\n\",\n \" env_state_t = [s[:, t] for s in info['env_state']]\\n\",\n \" images.append(tmaze_env.render(states=env_state_t, mode=\\\"rgb_array\\\"))\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 12,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"ani = animate(images)\\n\",\n \"HTML(ani.to_html5_video())\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \".venv311\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.11.12\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/experimental/sophisticated_inference/mcts_graph_world.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:43.007199Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:43.006910Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:43.763955Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:43.763519Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp.utils import list_array_zeros, list_array_norm_dist\\n\",\n \"from typing import Sequence, Optional\\n\",\n \"\\n\",\n \"import mctx\\n\",\n \"\\n\",\n \"import jax.numpy as jnp\\n\",\n \"import jax.random as jr\\n\",\n \"import jax.nn as nn\\n\",\n \"\\n\",\n \"import chex\\n\",\n \"import pygraphviz\\n\",\n \"\\n\",\n \"from IPython.display import SVG\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Utility function to convert and display the MCTX output to an SVG visualization of the search tree.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:43.765921Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:43.765742Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:43.769987Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:43.769739Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"def convert_tree_to_graph(\\n\",\n \" tree: mctx.Tree,\\n\",\n \" action_labels: Optional[Sequence[str]] = None,\\n\",\n \" batch_index: int = 0\\n\",\n \") -> pygraphviz.AGraph:\\n\",\n \" \\\"\\\"\\\"Converts a search tree into a Graphviz graph.\\n\",\n \"\\n\",\n \" Args:\\n\",\n \" tree: A `Tree` containing a batch of search data.\\n\",\n \" action_labels: Optional labels for edges, defaults to the action index.\\n\",\n \" batch_index: Index of the batch element to plot.\\n\",\n \"\\n\",\n \" Returns:\\n\",\n \" A Graphviz graph representation of `tree`.\\n\",\n \" \\\"\\\"\\\"\\n\",\n \" chex.assert_rank(tree.node_values, 2)\\n\",\n \" batch_size = tree.node_values.shape[0]\\n\",\n \" if action_labels is None:\\n\",\n \" action_labels = range(tree.num_actions)\\n\",\n \" elif len(action_labels) != tree.num_actions:\\n\",\n \" raise ValueError(\\n\",\n \" f\\\"action_labels {action_labels} has the wrong number of actions \\\"\\n\",\n \" f\\\"({len(action_labels)}). \\\"\\n\",\n \" f\\\"Expecting {tree.num_actions}.\\\")\\n\",\n \"\\n\",\n \" def node_to_str(node_i, reward=0, discount=1):\\n\",\n \" return (f\\\"{node_i}\\\\n\\\"\\n\",\n \" f\\\"Reward: {reward:.2f}\\\\n\\\"\\n\",\n \" f\\\"Discount: {discount:.2f}\\\\n\\\"\\n\",\n \" f\\\"Value: {tree.node_values[batch_index, node_i]:.2f}\\\\n\\\"\\n\",\n \" f\\\"Visits: {tree.node_visits[batch_index, node_i]}\\\\n\\\")\\n\",\n \"\\n\",\n \" def edge_to_str(node_i, a_i):\\n\",\n \" node_index = jnp.full([batch_size], node_i)\\n\",\n \" probs = nn.softmax(tree.children_prior_logits[batch_index, node_i])\\n\",\n \" return (f\\\"{action_labels[a_i]}\\\\n\\\"\\n\",\n \" f\\\"Q: {tree.qvalues(node_index)[batch_index, a_i]:.2f}\\\\n\\\" # pytype: disable=unsupported-operands # always-use-return-annotations\\n\",\n \" f\\\"p: {probs[a_i]:.2f}\\\\n\\\")\\n\",\n \"\\n\",\n \" graph = pygraphviz.AGraph(directed=True)\\n\",\n \"\\n\",\n \" # Add root\\n\",\n \" graph.add_node(0, label=node_to_str(node_i=0), color=\\\"green\\\")\\n\",\n \" # Add all other nodes and connect them up.\\n\",\n \" for node_i in range(tree.num_simulations):\\n\",\n \" for a_i in range(tree.num_actions):\\n\",\n \" # Index of children, or -1 if not expanded\\n\",\n \" children_i = tree.children_index[batch_index, node_i, a_i]\\n\",\n \" if children_i >= 0:\\n\",\n \" graph.add_node(\\n\",\n \" children_i,\\n\",\n \" label=node_to_str(\\n\",\n \" node_i=children_i,\\n\",\n \" reward=tree.children_rewards[batch_index, node_i, a_i],\\n\",\n \" discount=tree.children_discounts[batch_index, node_i, a_i]),\\n\",\n \" color=\\\"red\\\")\\n\",\n \" graph.add_edge(node_i, children_i, label=edge_to_str(node_i, a_i))\\n\",\n \"\\n\",\n \" return graph\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's test it on the graph world example as well.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:43.771113Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:43.771033Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:47.657184Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:47.656936Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"import networkx as nx\\n\",\n \"from pymdp.envs import GraphEnv\\n\",\n \"from pymdp.envs.graph_worlds import generate_connected_clusters\\n\",\n \"\\n\",\n \"graph, _ = generate_connected_clusters(cluster_size=3, connections=2)\\n\",\n \"env = GraphEnv(graph, object_location=4, agent_location=0)\\n\",\n \"\\n\",\n \"nx.draw(graph, with_labels=True)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We set the initial location of the agent at node 1, and prior belief that the object is at node 4. Therefore, the expected rewarding path is 1 -> 0 -> 3 -> 4.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:47.658379Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:47.658247Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:48.370082Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:48.369784Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61044/329308290.py:12: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agent = Agent(\\n\"\n ]\n }\n ],\n \"source\": [\n \"A, B= env.A, env.B\\n\",\n \"A_dependencies, B_dependencies = env.A_dependencies, env.B_dependencies\\n\",\n \"\\n\",\n \"C = list_array_zeros([a.shape[0] for a in A])\\n\",\n \"C[1] = C[1].at[1].set(1.0)\\n\",\n \"\\n\",\n \"D = [jnp.ones(d.shape[0]) for d in env.D]\\n\",\n \"D[0] = D[0].at[0].set(100.0)\\n\",\n \"D[1] = D[1].at[4].set(10.0)\\n\",\n \"D = list_array_norm_dist(D)\\n\",\n \"\\n\",\n \"agent = Agent(\\n\",\n \" A=A,\\n\",\n \" B=B,\\n\",\n \" C=C,\\n\",\n \" D=D,\\n\",\n \" A_dependencies=A_dependencies,\\n\",\n \" B_dependencies=B_dependencies,\\n\",\n \" categorical_obs=False,\\n\",\n \")\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:48.371274Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:48.371191Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:48.389603Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:48.389313Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"import mctx\\n\",\n \"from pymdp.planning.mcts import make_aif_recurrent_fn\\n\",\n \"\\n\",\n \"recurrent_fn = make_aif_recurrent_fn()\\n\",\n \"rng_key = jr.PRNGKey(111)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:48.390928Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:48.390851Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:51.874739Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:51.874453Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[[1.5554491e-16 6.9548679e-11 1.7227886e-17 1.3283233e-13 1.9635755e-14\\n\",\n \" 1.0000000e+00 1.0319131e-14]]\\n\"\n ]\n },\n {\n \"data\": {\n \"image/svg+xml\": [\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"0\\n\",\n 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],\n \"source\": [\n \"# %%timeit\\n\",\n \"root = mctx.RootFnOutput(\\n\",\n \" prior_logits=jnp.log(agent.E),\\n\",\n \" value=jnp.zeros((agent.batch_size)),\\n\",\n \" embedding=agent.D,\\n\",\n \")\\n\",\n \"\\n\",\n \"policy_output = mctx.gumbel_muzero_policy(\\n\",\n \" agent,\\n\",\n \" rng_key,\\n\",\n \" root,\\n\",\n \" recurrent_fn,\\n\",\n \" num_simulations=1024,\\n\",\n \" max_depth=3\\n\",\n \")\\n\",\n \"\\n\",\n \"tree_gumbel = policy_output.search_tree\\n\",\n \"print(policy_output.action_weights)\\n\",\n \"\\n\",\n \"graph = convert_tree_to_graph(tree_gumbel)\\n\",\n \"svg = graph.draw(format='svg', prog='dot').decode(graph.encoding)\\n\",\n \"SVG(svg)\"\n ]\n }\n ],\n \"metadata\": {\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.11.12\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/experimental/sophisticated_inference/si_generalized_tmaze.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Sophisticated inference on a Generalized T-Maze\\n\",\n \"\\n\",\n \"This notebook demonstrates the effect of sophisticated inference on a generalized T-maze which has multiple cues, out of which only one leads to reward. Sophisticated inference correctly focuses on the cue that yields reward, whereas vanilla AIF will be distracted by the prospect of information gain of the other cues. However, due to the long planning horizon this takes a long time to compute doing the full tree search. See the mcts_generalized_tmaze example to see how to combat this using MCMC sampling.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"%load_ext autoreload\\n\",\n \"%autoreload 2\\n\",\n \"\\n\",\n \"from pymdp.envs.generalized_tmaze import (\\n\",\n \" GeneralizedTMazeEnv, get_maze_matrix, parse_maze \\n\",\n \")\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp.utils import list_array_zeros, list_array_uniform\\n\",\n \"\\n\",\n \"from jax import random as jr, numpy as jnp\\n\",\n \"from jax import tree_util as jtu\\n\",\n \"\\n\",\n \"key = jr.PRNGKey(0)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"key, subkey = jr.split(key)\\n\",\n \"M = get_maze_matrix(small=True)\\n\",\n \"env_info = parse_maze(M, subkey)\\n\",\n \"tmaze_env = GeneralizedTMazeEnv(env_info)\\n\",\n \"\\n\",\n \"init_obs, init_state = tmaze_env.reset(key)\\n\",\n \"tmaze_env.render(states=init_state, mode=\\\"human\\\")\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"A, B = tmaze_env.A, tmaze_env.B\\n\",\n \"A_dependencies, B_dependencies = tmaze_env.A_dependencies, tmaze_env.B_dependencies\\n\",\n \"\\n\",\n \"# [position], [cue], [reward]\\n\",\n \"C = list_array_zeros([a.shape[0] for a in A])\\n\",\n \"\\n\",\n \"rewarding_modality = 2 + env_info[\\\"num_cues\\\"]\\n\",\n \"\\n\",\n \"C[rewarding_modality] = C[rewarding_modality].at[1].set(2.0)\\n\",\n \"C[rewarding_modality] = C[rewarding_modality].at[2].set(-3.0)\\n\",\n \"\\n\",\n \"D = list_array_uniform([b.shape[0] for b in B])\\n\",\n \"D[0] = tmaze_env.D[0].copy()\\n\",\n \"\\n\",\n \"agent = Agent(\\n\",\n \" A, B, C, D, \\n\",\n \" None, None, None, \\n\",\n \" policy_len=1,\\n\",\n \" A_dependencies=A_dependencies, \\n\",\n \" B_dependencies=B_dependencies\\n\",\n \" )\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"qs = agent.infer_states(\\n\",\n \" observations=jtu.tree_map(lambda x: jnp.broadcast_to(x, (agent.batch_size,) + x.shape), init_obs),\\n\",\n \" past_actions=None,\\n\",\n \" empirical_prior=agent.D,\\n\",\n \" qs_hist=None,\\n\",\n \")\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"from pymdp.planning.si import si_policy_search\\n\",\n \"\\n\",\n \"key = jr.PRNGKey(0)\\n\",\n \"policy_search = si_policy_search(horizon=3, entropy_stop_threshold=0.0, gamma=5)\\n\",\n \"qpi, info = policy_search(agent, qs, key) \\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"When plotting the plan tree, the preferred plan is indeed to go to the right cue, and then fetch the reward.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"from pymdp.planning.visualize import visualize_plan_tree\\n\",\n \"\\n\",\n \"\\n\",\n \"def generalized_tmaze_observation_description(observation, model=None, env_info=env_info):\\n\",\n \" obs = observation[0]\\n\",\n \" maze_shape = env_info[\\\"maze\\\"].shape\\n\",\n \" num_cues = env_info[\\\"num_cues\\\"]\\n\",\n \"\\n\",\n \" pos_idx = int(obs[0])\\n\",\n \" row, col = divmod(pos_idx, maze_shape[1])\\n\",\n \"\\n\",\n \" cue_vals = [int(v) for v in obs[1 : 1 + num_cues]]\\n\",\n \" reward_vals = [int(v) for v in obs[1 + num_cues : 1 + (2 * num_cues)]]\\n\",\n \"\\n\",\n \" cue_map = {0: \\\"none\\\", 1: \\\"r1\\\", 2: \\\"r2\\\"}\\n\",\n \" reward_map = {0: \\\"none\\\", 1: \\\"reward\\\", 2: \\\"punish\\\"}\\n\",\n \"\\n\",\n \" cues_str = \\\", \\\".join(\\n\",\n \" f\\\"c{i + 1}:{cue_map.get(v, v)}\\\" for i, v in enumerate(cue_vals)\\n\",\n \" )\\n\",\n \" rewards_str = \\\", \\\".join(\\n\",\n \" f\\\"r{i + 1}:{reward_map.get(v, v)}\\\" for i, v in enumerate(reward_vals)\\n\",\n \" )\\n\",\n \"\\n\",\n \" return (\\n\",\n \" f\\\"pos: {pos_idx} ({row},{col})\\\\n\\\"\\n\",\n \" f\\\"cues: {cues_str}\\\\n\\\"\\n\",\n \" f\\\"rewards: {rewards_str}\\\"\\n\",\n \" )\\n\",\n \"\\n\",\n \"\\n\",\n \"def generalized_tmaze_action_description(action, model=None):\\n\",\n \" action_idx = int(action[0])\\n\",\n \" actions = [\\\"down\\\", \\\"up\\\", \\\"left\\\", \\\"right\\\", \\\"stay\\\"]\\n\",\n \"\\n\",\n \" if 0 <= action_idx < len(actions):\\n\",\n \" return actions[action_idx]\\n\",\n \" return str(action_idx)\\n\",\n \"\\n\",\n \"\\n\",\n \"visualize_plan_tree(\\n\",\n \" info,\\n\",\n \" time_idx=None,\\n\",\n \" observation_description=generalized_tmaze_observation_description,\\n\",\n \" action_description=generalized_tmaze_action_description,\\n\",\n \")\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"If we limit the planning horizon to a single step, we can see that indeed it renders both cues equally attractive.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"policy_search = si_policy_search(horizon=1, entropy_stop_threshold=0.0, gamma=5)\\n\",\n \"qpi, info = policy_search(agent, qs, key) \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"visualize_plan_tree(\\n\",\n \" info,\\n\",\n \" time_idx=None,\\n\",\n \" observation_description=generalized_tmaze_observation_description,\\n\",\n \" action_description=generalized_tmaze_action_description,\\n\",\n \")\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": []\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \".venv\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.11.11\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/experimental/sophisticated_inference/si_graph_world.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Sophisticated inference on Graph Worlds\\n\",\n \"\\n\",\n \"This notebook demonstrates tree searching policies with sophisticated active inference.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We create a `GraphEnv`, where an agent can move between locations on a graph, and see objects at the location it is at.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"from jax import numpy as jnp, random as jr\\n\",\n \"from jax import vmap\\n\",\n \"import jax.tree_util as jtu\\n\",\n \"from pymdp.utils import list_array_zeros, list_array_norm_dist\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import networkx as nx\\n\",\n \"from pymdp.envs import GraphEnv\\n\",\n \"from pymdp.envs.graph_worlds import generate_connected_clusters\\n\",\n \"\\n\",\n \"graph, _ = generate_connected_clusters(cluster_size=3, connections=2)\\n\",\n \"env = GraphEnv(graph, object_location=4, agent_location=0)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"nx.draw(graph, with_labels=True, font_weight=\\\"bold\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's create an agent, we give the agent a prior on the object location to showcase the planning depth and pruning. We let the agent start at location 0, and give it a prior about where the object is (location 4).\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"from pymdp.agent import Agent\\n\",\n \"\\n\",\n \"A, B = env.A, env.B\\n\",\n \"A_dependencies, B_dependencies = env.A_dependencies, env.B_dependencies\\n\",\n \"\\n\",\n \"C = list_array_zeros([a.shape[0] for a in A])\\n\",\n \"C[1] = C[1].at[1].set(10.0)\\n\",\n \"\\n\",\n \"D = [jnp.ones(d.shape[0]) for d in env.D]\\n\",\n \"D[0] = D[0].at[0].set(100.0)\\n\",\n \"D[1] = D[1].at[4].set(100.0)\\n\",\n \"D = list_array_norm_dist(D)\\n\",\n \"\\n\",\n \"agent = Agent(A, B, C, D, A_dependencies=A_dependencies, B_dependencies=B_dependencies, policy_len=1)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can call the `si_policy_search` method and visualize the planning tree.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"from pymdp.planning.si import si_policy_search\\n\",\n \"from pymdp.envs import rollout\\n\",\n \"\\n\",\n \"key = jr.PRNGKey(0)\\n\",\n \"last, info = rollout(agent, env, 5, key, policy_search=si_policy_search(horizon=3))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Given the agent prior, it should commit to going to location 4, expecting to see the object there.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"from pymdp.planning.visualize import visualize_plan_tree\\n\",\n \"\\n\",\n \"def graph_world_observation_description(observation, model=None, graph=graph):\\n\",\n \" obs = observation[0]\\n\",\n \" loc_idx = int(obs[0])\\n\",\n \" obj_val = int(obs[1])\\n\",\n \"\\n\",\n \" obj_str = \\\"object\\\" if obj_val == 1 else \\\"no object\\\"\\n\",\n \" return f\\\"loc: {loc_idx}\\\\nobj: {obj_str}\\\"\\n\",\n \"\\n\",\n \"\\n\",\n \"def graph_world_action_description(action, model=None, graph=graph):\\n\",\n \" action_idx = int(action[0])\\n\",\n \" if action_idx in graph.nodes:\\n\",\n \" return f\\\"go to node {action_idx}\\\"\\n\",\n \" return str(action_idx)\\n\",\n \"\\n\",\n \"\\n\",\n \"visualize_plan_tree(\\n\",\n \" info,\\n\",\n \" observation_description=graph_world_observation_description,\\n\",\n \" action_description=graph_world_action_description,\\n\",\n \")\\n\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \".venv\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.11.11\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/experimental/sophisticated_inference/si_tmaze_SIvalidation.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Validating Sophisticated Inference (SI) Planning Algorithm using the T-Maze Task\\n\",\n \"\\n\",\n \"### Overview\\n\",\n \"\\n\",\n \"This notebook provides a comparative test of two planning algorithms within the active inference framework:\\n\",\n \"1. Vanilla Active Inference Planning: Standard and default planning approach in `pymdp.control.infer_policies()` that computes the expected free energy of policies in parallel, and the log probability of each policy is proportional to its expected free energy. The expected free energy of each policy is computed by propagating beliefs about hidden states forward in time under each policy (a typical 'posterior predictive rollout'), without updating those beliefs with counterfactual observations, expected under those future states. This means the belief over hidden states at timestep `t` in a given rollout, only depends on:\\n\",\n \"- the previous belief over hidden states at time `t` and\\n\",\n \"- the action entailed by the policy in question at time `t`.\\n\",\n \"\\n\",\n \"2. Sophisticated Inference (SI) Planning: A more complex but thorough planning approach that evaluates policies using recursive expected free energy calculations, where the agent considers how its beliefs would change under counterfactual observations encountered in the future. This algorithm has higher complexity since it branches on both observations and actions in the future, but it more accurately captures how uncertainty over hidden states changes in the future, as a function of (possibly-encountered) observations.\\n\",\n \"\\n\",\n \"This notebook uses a simplified version of the T-Maze environment `TMazeSimplified` as described in the [sophisticated inference paper](https://discovery.ucl.ac.uk.id/eprint/10124606/) to validate the SI implementation. \\n\",\n \"\\n\",\n \"### The T-Maze Task\\n\",\n \"\\n\",\n \"The T-maze is a classic sequential decision-making problem where the agent (analogized to a rat) faces a fundamental exploration vs. exploitation dilemma. The agent begins at the center of a T-shaped maze, where there is also a left arm, right arm, and cue location (bottom arm). One arm contains reward (cheese), the other punishment (shock), but the agent does not know which arm contains what. A cue at the bottom provides information about reward location with a given accuracy. This version of the T-Maze differs from that described in the [T-Maze Demo](https://github.com/infer-actively/pymdp/blob/main/examples/envs/tmaze_demo.ipynb) because there is no \\\"middle\\\" location between the left and right arms, and because every location is reachable from every other location. Additionally, location and cue observations are embedded into a single modality, rather than separated out into two separate modalities.\\n\",\n \"\\n\",\n \"The agent must choose between immediate but risky exploitation by directly committing to one of the reward arms (50% chance of success) or gather information (explore) first by visiting the cue location at the expense of time, then make an informed choice. When cue validity > 50%, the optimal strategy is to first gather information at the cue location, then select the indicated rewarding arm. This notebook tests whether both planning algorithms can discover this optimal policy and how.\\n\",\n \"\\n\",\n \"### Notebook Structure\\n\",\n \"1. Environment Setup: Set up the generative process for the T-Maze environment\\n\",\n \"2. Agent Setup: Set up the generative model for the agent\\n\",\n \"3. Active Inference Rollout: Run active inference rollouts with vanilla and sophisticated inference planning algorithms, with optional visualizations of the agents' behavior\\n\",\n \"4. Results Analysis: Compare actions selected and policy evaluations \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:52.929478Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:52.929410Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:56.831792Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:56.831372Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"%load_ext autoreload\\n\",\n \"%autoreload 2\\n\",\n \"\\n\",\n \"import jax.numpy as jnp\\n\",\n \"import jax.random as jr\\n\",\n \"\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import numpy as np\\n\",\n \"import mediapy\\n\",\n \"\\n\",\n \"from pymdp.envs import SimplifiedTMaze, rollout\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp.planning.si import si_policy_search\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Setting up the T-Maze environment (Generative Process)\\n\",\n \"\\n\",\n \"- The `reward_condition` parameter determines the reward location: `0` for the left arm, `1` for the right arm, or `None` for random allocation.\\n\",\n \"- The `cue_validity` parameter (default 0.95) represents the accuracy of the cues as a probability.\\n\",\n \"- The `reward_probability` parameter sets the probability `a` of receiving a reward in the correct arm. \\n\",\n \"- With `dependent_outcomes=True`, the remaining probability (`1-a`) becomes punishment in the correct arm (and reward in the incorrect arm). With `dependent_outcomes=False`, the remaining probability in the correct arm is no-outcome, and punishment in the incorrect arm is set by `punishment_probability` (with no-outcome as the remainder).\\n\",\n \"\\n\",\n \"
\\n\",\n \" Click here to see how the generative process is set up. \\n\",\n \"\\n\",\n \"#### States and Observations\\n\",\n \"\\n\",\n \"**State Factors:**\\n\",\n \"1. Location (4 states): \\n\",\n \" - 0: center (start location)\\n\",\n \" - 1: left arm\\n\",\n \" - 2: right arm\\n\",\n \" - 3: cue location (bottom arm)\\n\",\n \"2. Reward Location (2 states):\\n\",\n \" - 0: reward in left arm \\n\",\n \" - 1: reward in right arm\\n\",\n \"\\n\",\n \"**Control State Factors:**\\n\",\n \"1. Location (4 actions): \\n\",\n \" - 0: move to center (start location)\\n\",\n \" - 1: move to left arm\\n\",\n \" - 2: move to right arm\\n\",\n \" - 3: move to cue location (bottom arm)\\n\",\n \"\\n\",\n \"**Observation Modalities:**\\n\",\n \"1. Location (5 observations):\\n\",\n \" - 0: center (start location)\\n\",\n \" - 1: left arm\\n\",\n \" - 2: right arm\\n\",\n \" - 3: cued left arm (bottom arm)\\n\",\n \" - 4: cued right arm (bottom arm)\\n\",\n \"2. Outcome (3 observations):\\n\",\n \" - 0: no outcome\\n\",\n \" - 1: reward (cheese)\\n\",\n \" - 2: punishment (shock)\\n\",\n \"\\n\",\n \"#### Environment Parameters\\n\",\n \"\\n\",\n \"**Observation Likelihood Model (A):**\\n\",\n \"- A[0]: Location observations (5x4x2 tensor)\\n\",\n \" - Perfect mapping between true and observed locations.\\n\",\n \" - At the cue location (bottom), the rewarding arm is cued with accuracy set by the `cue_validity` parameter.\\n\",\n \"- A[1]: Outcome observations (3x4x2 tensor)\\n\",\n \" - In the rewarding arm (set by `reward_condition`), reward is presented with a likelihood determined by the `reward_probability` parameter.\\n\",\n \" - Punishment and/or no-outcome are presented with a likelihood determined depending on if `dependent_outcome` is True or False and consequently by the `punishment_probability` parameter.\\n\",\n \" - No-outcome is observed in the center/start location and cue location.\\n\",\n \"\\n\",\n \"**Transition Model (B):**\\n\",\n \"- B[0]: Location transitions (4x4x4 tensor)\\n\",\n \" - Agent can move to any one of the four locations from any location regardless of adjacency.\\n\",\n \"- B[1]: Reward location (2x2x1 tensor)\\n\",\n \" - Reward location remains fixed throughout trial.\\n\",\n \"\\n\",\n \"**Initial Conditions (D):**\\n\",\n \"- D[0]: Starting location (4x1 tensor)\\n\",\n \" - Agent always begins in center location\\n\",\n \"- D[1]: Reward placement (2x1 tensor)\\n\",\n \" - Default: Equal chance (50/50) of reward in either arm (`reward_condition=None`)\\n\",\n \" - Optional: Can fix reward to specific arm, by setting `reward_condition` to `0` (for left arm) or `1` (for right arm)\\n\",\n \"\\n\",\n \"
\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:56.833504Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:56.833257Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:56.847073Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:56.846835Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# setting the parameters for the environment\\n\",\n \"reward_condition = 0 # 0 is reward in left arm, 1 is reward in right arm, None is random allocation\\n\",\n \"cue_validity = 0.95 # 95% valid cues\\n\",\n \"\\n\",\n \"reward_probability = 1.0 # 100% chance of reward in the correct arm\\n\",\n \"dependent_outcomes = True # if True, punishment occurs as a function of reward probability (i.e., if reward probability is 0.8, then 20% punishment). If False, punishment occurs with set probability (i.e., 20% no outcome and punishment will only occur in the other (non-rewarding) arm depending on the punishment_probability parameter)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:56.848285Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:56.848208Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:57.167276Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:57.166854Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# initializing the environment. see si_tmaze.py in pymdp/envs for the implementation details\\n\",\n \"env = SimplifiedTMaze(\\n\",\n \" reward_condition=reward_condition,\\n\",\n \" cue_validity=cue_validity, \\n\",\n \" reward_probability=reward_probability, \\n\",\n \" dependent_outcomes=dependent_outcomes,\\n\",\n \")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Setting up the Agents\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:57.168745Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:57.168662Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:57.218343Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:57.218066Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# creating C tensors filled with zeros for [location], [reward], [cue] based on A shapes for the Agent\\n\",\n \"C = [jnp.zeros(a.shape[0], dtype=jnp.float32) for a in env.A] \\n\",\n \"\\n\",\n \"# setting preferences for outcomes only\\n\",\n \"C[1] = C[1].at[1].set(2.0) # prefer reward\\n\",\n \"C[1] = C[1].at[2].set(-6.0) # avoid punishment\\n\",\n \"\\n\",\n \"# slight cost of observing a cue\\n\",\n \"# C[0] = C[0].at[3].set(-1.0).at[4].set(-1.0)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:57.219677Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:57.219596Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:57.256084Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:57.255633Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# flat D tensors [location], [reward] based on B shapes for the agent\\n\",\n \"D = [jnp.ones(b.shape[0], dtype=jnp.float32) / b.shape[0] for b in env.B]\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:57.257395Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:57.257311Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:57.878736Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:57.878428Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61048/282069077.py:8: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agent_vanilla = Agent(\\n\",\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61048/282069077.py:20: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agent_si = Agent(\\n\"\n ]\n }\n ],\n \"source\": [\n \"# note that we initialize agents with different policy lengths for the vanilla vs sophisticated inference planning algorithms\\n\",\n \"# even though both will eventually end up planning with a horizon of 2. The sophisticated inference planning algorithm requires\\n\",\n \"# a policy length of 1 in the Agent as we specify horizon length of 2 when initializing the planning algorithm in the `rollout`.\\n\",\n \"\\n\",\n \"# action_selection=\\\"deterministic\\\" means selecting an action from the policy probability distribution (q_pi) by arg-maxxing\\n\",\n \"# sampling_mode=\\\"full\\\" means evaluating the whole action sequence in each policy and executing the first action (as opposed to marginal where the agent evaluates each action type)\\n\",\n \"policy_len = 2\\n\",\n \"agent_vanilla = Agent(\\n\",\n \" env.A, env.B, C, D, \\n\",\n \" A_dependencies=env.A_dependencies, \\n\",\n \" B_dependencies=env.B_dependencies,\\n\",\n \" policy_len=policy_len,\\n\",\n \" learn_A=False,\\n\",\n \" learn_B=False,\\n\",\n \" action_selection=\\\"deterministic\\\",\\n\",\n \" sampling_mode=\\\"full\\\",\\n\",\n \" gamma=3.0\\n\",\n \")\\n\",\n \"\\n\",\n \"agent_si = Agent(\\n\",\n \" env.A, env.B, C, D, \\n\",\n \" A_dependencies=env.A_dependencies, \\n\",\n \" B_dependencies=env.B_dependencies,\\n\",\n \" policy_len=1,\\n\",\n \" learn_A=False,\\n\",\n \" learn_B=False,\\n\",\n \" action_selection=\\\"deterministic\\\",\\n\",\n \" sampling_mode=\\\"full\\\",\\n\",\n \" gamma=3.0\\n\",\n \")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Running the active inference rollouts\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:57.879961Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:57.879884Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:57.903963Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:57.903562Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"key = jr.PRNGKey(0) \\n\",\n \"T = 3\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:57.905455Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:57.905365Z\",\n \"iopub.status.idle\": \"2026-03-06T15:31:57.914559Z\",\n \"shell.execute_reply\": \"2026-03-06T15:31:57.914227Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"si_search = si_policy_search(\\n\",\n \" horizon=policy_len, # plans 2 timesteps ahead\\n\",\n \" max_nodes=5000, # maximum number of nodes allowed in the tree\\n\",\n \" max_branching=10, # maximum number of children allowed per node (moderating the branching factor)\\n\",\n \" policy_prune_threshold=0.0, # no pruning of unlikely policies\\n\",\n \" observation_prune_threshold=0.0, # no pruning of unlikely observations\\n\",\n \" entropy_stop_threshold=0.0, # disabling halting of expansion if agent is certain enough\\n\",\n \" neg_efe_stop_threshold=1e10, # disabling efe value based halting of expansion\\n\",\n \" kl_threshold=-1, # disabling node reuse if agent is in similar states after an action\\n\",\n \" prune_penalty=512, # default value for prune penalty\\n\",\n \" gamma=3, # temperature parameter; lower value (--> 1) prunes policies less aggressively as probabilities are flattened while higher value (--> 16) prunes more aggressively\\n\",\n \" topk_obsspace=10000, # max number of top observation combinations - this default value just means we want to consider all the observation combinations\\n\",\n \")\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:31:57.915721Z\",\n \"iopub.status.busy\": \"2026-03-06T15:31:57.915633Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:00.062125Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:00.061837Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"_, info_vanilla = rollout(agent_vanilla, env, num_timesteps=T, rng_key=key) # default policy search is vanilla\\n\",\n \"_, info_si = rollout(agent_si, env, num_timesteps=T, rng_key=key, policy_search=si_search)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:00.063840Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:00.063750Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:00.072935Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:00.072623Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"def make_gif(info):\\n\",\n \" frames = []\\n\",\n \" for t in range(info[\\\"observation\\\"][0].shape[1]): # iterate over timesteps\\n\",\n \" # get observations for this timestep\\n\",\n \" observations_t = [\\n\",\n \" info[\\\"observation\\\"][0][:, t, :],\\n\",\n \" info[\\\"observation\\\"][1][:, t, :], \\n\",\n \" ]\\n\",\n \" \\n\",\n \" frame = env.render(mode=\\\"rgb_array\\\", observations=observations_t) # render the environment using the observations for this timestep\\n\",\n \" frame = np.asarray(frame, dtype=np.uint8)\\n\",\n \" plt.close() # close the figure to prevent memory leak\\n\",\n \" frames.append(frame)\\n\",\n \"\\n\",\n \" frames = np.array(frames, dtype=np.uint8)\\n\",\n \" mediapy.show_video(frames, fps=1)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:00.074536Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:00.074457Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:00.798079Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:00.797742Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"
\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"make_gif(info_vanilla)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:00.799469Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:00.799378Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:01.460002Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:01.459679Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"
\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"make_gif(info_si)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Result analysis\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:01.461295Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:01.461200Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:01.474045Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:01.473684Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# qpi is a posterior over whole policies (action sequences).\\n\",\n \"# To get the probability of the *current* action, we marginalize over policies\\n\",\n \"# that share the same first action and sum their qpi values.\\n\",\n \"# helper functions for:\\n\",\n \"# - printing out policies and respective probabilities of selecting those policies\\n\",\n \"# - printing out action and observation info for each timestep\\n\",\n \"\\n\",\n \"np.set_printoptions(precision=2, suppress=True)\\n\",\n \"\\n\",\n \"def print_qpi(agent, info, print_t1=False):\\n\",\n \" qpi_values = info[\\\"qpi\\\"]\\n\",\n \"\\n\",\n \" action_names = {\\n\",\n \" 0: \\\"move to center\\\",\\n\",\n \" 1: \\\"move to left arm\\\",\\n\",\n \" 2: \\\"move to right arm\\\",\\n\",\n \" 3: \\\"move to cue\\\",\\n\",\n \" }\\n\",\n \" max_timesteps = 1 if print_t1 else qpi_values.shape[1]\\n\",\n \"\\n\",\n \" # unique_multiactions returns the unique first-step actions across policies\\n\",\n \" # for a single control factor, this is just a list of action indices\\n\",\n \" unique_actions = agent.unique_multiactions[:, 0]\\n\",\n \"\\n\",\n \" for t in range(max_timesteps):\\n\",\n \" print(f\\\"Timestep {t}:\\\")\\n\",\n \" action_probs = agent.multiaction_probabilities(qpi_values[:, t, :])[0]\\n\",\n \"\\n\",\n \" for action_idx, total_prob in zip(unique_actions.tolist(), action_probs.tolist()):\\n\",\n \" if action_idx < 0:\\n\",\n \" continue\\n\",\n \" action_name = action_names.get(action_idx, f\\\"action_{action_idx}\\\")\\n\",\n \" print(f\\\" {action_name}: {total_prob:.3f}\\\")\\n\",\n \" print()\\n\",\n \"\\n\",\n \"def print_agent_behavior(info):\\n\",\n \"\\n\",\n \" action_names = {0: \\\"move to center\\\", 1: \\\"move to left arm\\\", 2: \\\"move to right arm\\\", 3: \\\"move to cue\\\"}\\n\",\n \"\\n\",\n \" location_obs = {0: \\\"center loc\\\", 1: \\\"left arm loc\\\", 2: \\\"right arm loc\\\", 3: \\\"cue-left-arm\\\", 4: \\\"cue-right-arm\\\"}\\n\",\n \" outcome_obs = {0: \\\"no_outcome\\\", 1: \\\"reward\\\", 2: \\\"punishment\\\"}\\n\",\n \"\\n\",\n \" actions = info[\\\"action\\\"]\\n\",\n \" observations = info[\\\"observation\\\"]\\n\",\n \"\\n\",\n \" num_timesteps = actions.shape[1]\\n\",\n \"\\n\",\n \" for t in range(num_timesteps):\\n\",\n \" action_idx = int(actions[0, t, 0]) # [batch, timestep, action_dim]\\n\",\n \" action_name = action_names.get(action_idx, f\\\"action_{action_idx}\\\")\\n\",\n \"\\n\",\n \" location_obs_idx = int(observations[0][0, t, 0]) # [modality][batch, timestep, obs_dim]\\n\",\n \" outcome_obs_idx = int(observations[1][0, t, 0])\\n\",\n \"\\n\",\n \" location_name = location_obs.get(location_obs_idx)\\n\",\n \" outcome_name = outcome_obs.get(outcome_obs_idx)\\n\",\n \"\\n\",\n \" print(f\\\"t={t}: observed=({location_name}, {outcome_name}) -> action={action_name}\\\")\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can see both agents select the optimal actions to go to the cue first and then go to the left arm to get a reward. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:01.475190Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:01.475112Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:01.512705Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:01.512455Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"t=0: observed=(center loc, no_outcome) -> action=move to cue\\n\",\n \"t=1: observed=(cue-left-arm, no_outcome) -> action=move to left arm\\n\",\n \"t=2: observed=(left arm loc, reward) -> action=move to left arm\\n\",\n \"t=3: observed=(left arm loc, reward) -> action=move to left arm\\n\"\n ]\n }\n ],\n \"source\": [\n \"print_agent_behavior(info_vanilla)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:01.514071Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:01.513970Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:01.522916Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:01.522628Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"t=0: observed=(center loc, no_outcome) -> action=move to cue\\n\",\n \"t=1: observed=(cue-left-arm, no_outcome) -> action=move to left arm\\n\",\n \"t=2: observed=(left arm loc, reward) -> action=move to left arm\\n\",\n \"t=3: observed=(left arm loc, reward) -> action=move to left arm\\n\"\n ]\n }\n ],\n \"source\": [\n \"print_agent_behavior(info_si)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now, to see how the two planning algorithms differ, let's examine how they evaluate policies... \\n\",\n \"\\n\",\n \"While both agents select the optimal strategy (information gathering first), they differ significantly in their confidence, with the SI agent shows much stronger preference for the information-gathering strategy.\\n\",\n \"- Vanilla Agent: 81% probability for cue-seeking, 18% for staying at center\\n\",\n \"- SI Agent: 98% probability for cue-seeking, <1% for staying at center\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:01.524335Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:01.524244Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:02.045804Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:02.045524Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Timestep 0:\\n\",\n \" move to center: 0.183\\n\",\n \" move to left arm: 0.004\\n\",\n \" move to right arm: 0.004\\n\",\n \" move to cue: 0.809\\n\",\n \"\\n\"\n ]\n }\n ],\n \"source\": [\n \"print_qpi(agent_vanilla, info_vanilla, print_t1=True)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 17,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:02.047026Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:02.046935Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:02.257558Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:02.257293Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Timestep 0:\\n\",\n \" move to center: 0.003\\n\",\n \" move to left arm: 0.008\\n\",\n \" move to right arm: 0.008\\n\",\n \" move to cue: 0.980\\n\",\n \"\\n\"\n ]\n }\n ],\n \"source\": [\n \"print_qpi(agent_si, info_si, print_t1=True)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Doing the same experiment but with the extended`TMaze` environment used in other demos\\n\",\n \"\\n\",\n \"This section mirrors the preceding section, but uses `pymdp`'s default T-Maze environment as used in the [T-Maze Demo](https://github.com/infer-actively/pymdp/blob/main/examples/envs/tmaze_demo.ipynb). It differs from the `SimplifiedTMaze` environment used before due to the restricted spatial geometry (middle connector that the agent must pass through to reach the two arms) and the fact that the cue and location modalities are split out into separate modalities. We set cue validity (cue probability) to 1.0, use `policy_len = 4` (to account for the additional planning depth required for navigating the T-Maze), and `observation_prune_threshold = 1e-4` for the SI search.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 18,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:02.258821Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:02.258747Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:02.267207Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:02.266928Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"from pymdp.envs import TMaze\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Setting up the T-Maze environment (Generative Process)\\n\",\n \"\\n\",\n \"The rules/hyperparameters of the T-Maze are identical to the TMaze above, except that the generative process parameters (states and observations) are slightly different due to the factorization of the joint cue+location modality (embedded together in `SimplifiedTMaze`) into two separate modalities. \\n\",\n \"\\n\",\n \"
\\n\",\n \" Click here to see how the generative process for the `TMaze` env (non-simplified) is set up. \\n\",\n \"\\n\",\n \"#### States and Observations\\n\",\n \"\\n\",\n \"**State Factors:**\\n\",\n \"1. Location (5 states): \\n\",\n \" - 0: center (start location)\\n\",\n \" - 1: left arm\\n\",\n \" - 2: right arm\\n\",\n \" - 3: cue location (bottom arm)\\n\",\n \" - 4: middle (junction between center and arms)\\n\",\n \"2. Reward Location (2 states):\\n\",\n \" - 0: reward in left arm \\n\",\n \" - 1: reward in right arm\\n\",\n \"\\n\",\n \"**Control State Factors:**\\n\",\n \"1. Location (5 actions): \\n\",\n \" - 0: move to center (start location)\\n\",\n \" - 1: move to left arm\\n\",\n \" - 2: move to right arm\\n\",\n \" - 3: move to cue location (bottom arm)\\n\",\n \" - 4: move to middle (junction)\\n\",\n \"\\n\",\n \"**Observation Modalities:**\\n\",\n \"1. Location (5 observations):\\n\",\n \" - 0: center (start location)\\n\",\n \" - 1: left arm\\n\",\n \" - 2: right arm\\n\",\n \" - 3: cue location (bottom arm)\\n\",\n \" - 4: middle (junction)\\n\",\n \"2. Outcome (3 observations):\\n\",\n \" - 0: no outcome\\n\",\n \" - 1: reward (cheese)\\n\",\n \" - 2: punishment (shock)\\n\",\n \"3. Cue (3 observations):\\n\",\n \" - 0: no cue\\n\",\n \" - 1: cue indicates left arm\\n\",\n \" - 2: cue indicates right arm\\n\",\n \"\\n\",\n \"#### Environment Parameters\\n\",\n \"\\n\",\n \"**Observation Likelihood Model (A):**\\n\",\n \"- A[0]: Location observations (5x5 tensor)\\n\",\n \" - Perfect mapping between true and observed locations.\\n\",\n \"- A[1]: Outcome observations (3x5x2 tensor)\\n\",\n \" - In the rewarding arm (set by `reward_condition`), reward is presented with a likelihood determined by the `reward_probability` parameter.\\n\",\n \" - Punishment and/or no-outcome are presented with a likelihood determined depending on if `dependent_outcomes` is True or False and consequently by the `punishment_probability` parameter.\\n\",\n \" - No-outcome is observed in the center/start location, cue location, and middle.\\n\",\n \"- A[2]: Cue observations (3x5x2 tensor)\\n\",\n \" - The cue is only observed at the cue location, with accuracy set by `cue_validity`.\\n\",\n \" - No cue is observed at all other locations.\\n\",\n \"\\n\",\n \"**Transition Model (B):**\\n\",\n \"- B[0]: Location transitions (5x5x5 tensor)\\n\",\n \" - Agent can move between adjacent locations in the T-maze; invalid moves leave the agent in place.\\n\",\n \"- B[1]: Reward location (2x2x1 tensor)\\n\",\n \" - Reward location remains fixed throughout trial.\\n\",\n \"\\n\",\n \"**Initial Conditions (D):**\\n\",\n \"- D[0]: Starting location (5x1 tensor)\\n\",\n \" - Agent always begins in center location\\n\",\n \"- D[1]: Reward placement (2x1 tensor)\\n\",\n \" - Default: Equal chance (50/50) of reward in either arm (`reward_condition=None`)\\n\",\n \" - Optional: Can fix reward to specific arm, by setting `reward_condition` to `0` (for left arm) or `1` (for right arm)\\n\",\n \"\\n\",\n \"
\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 19,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:02.268359Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:02.268289Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:02.275050Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:02.274830Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# setting the parameters for the environment\\n\",\n \"reward_condition = 0 # 0 is reward in left arm, 1 is reward in right arm, None is random allocation\\n\",\n \"cue_validity = 1.0 # 100% valid cues (cue probability)\\n\",\n \"\\n\",\n \"reward_probability = 1.0 # 100% chance of reward in the correct arm\\n\",\n \"dependent_outcomes = True # if True, punishment occurs as a function of reward probability (i.e., if reward probability is 0.8, then 20% punishment). If False, punishment occurs with set probability (i.e., 20% no outcome and punishment will only occur in the other (non-rewarding) arm depending on the punishment_probability parameter)\\n\",\n \"punishment_probability = 1.0 # 100% chance of punishment in the other arm\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 20,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:02.276198Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:02.276130Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:02.468939Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:02.468537Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# initializing the environment. see tmaze.py in pymdp/envs for the implementation details\\n\",\n \"env = TMaze(\\n\",\n \" reward_condition=reward_condition,\\n\",\n \" cue_validity=cue_validity, \\n\",\n \" reward_probability=reward_probability,\\n\",\n \" punishment_probability=punishment_probability, \\n\",\n \" dependent_outcomes=dependent_outcomes,\\n\",\n \")\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Setting up the Agents\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 21,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:02.470266Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:02.470180Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:02.480041Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:02.479797Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# creating C tensors filled with zeros for [location], [reward], [cue] based on A shapes for the Agent\\n\",\n \"C = [jnp.zeros(a.shape[0], dtype=jnp.float32) for a in env.A] \\n\",\n \"\\n\",\n \"# setting preferences for outcomes only\\n\",\n \"C[1] = C[1].at[1].set(2.0) # prefer reward\\n\",\n \"C[1] = C[1].at[2].set(-6.0) # avoid punishment\\n\",\n \"\\n\",\n \"# slight cost of observing a cue\\n\",\n \"C[2] = C[2].at[1].set(-0.5) \\n\",\n \"C[2] = C[2].at[2].set(-0.5)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 22,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:02.481139Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:02.481067Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:02.515618Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:02.515309Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# D tensors [location], [reward] based on B shapes for the agent\\n\",\n \"# - agent starts in the center location\\n\",\n \"# - reward location prior is uniform\\n\",\n \"D_loc = jnp.zeros(env.B[0].shape[0], dtype=jnp.float32)\\n\",\n \"D_loc = D_loc.at[0].set(1.0)\\n\",\n \"\\n\",\n \"D_reward = jnp.ones(env.B[1].shape[0], dtype=jnp.float32)\\n\",\n \"D_reward = D_reward / jnp.sum(D_reward, axis=0, keepdims=True)\\n\",\n \"\\n\",\n \"D = [D_loc, D_reward]\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 23,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:02.516898Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:02.516821Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:03.124129Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:03.123813Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61048/2056066623.py:10: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agent_vanilla = Agent(\\n\",\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61048/2056066623.py:22: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agent_si = Agent(\\n\"\n ]\n }\n ],\n \"source\": [\n \"# note that we initialize agents with different policy lengths for the vanilla vs sophisticated inference planning algorithms\\n\",\n \"# even though both will eventually end up planning with a horizon of 4. The sophisticated inference planning algorithm requires\\n\",\n \"# a policy length of 1 in the Agent as we specify horizon length of 4 when initializing the planning algorithm in the `rollout`.\\n\",\n \"\\n\",\n \"# action_selection=\\\"deterministic\\\" means selecting an action from the policy probability distribution (q_pi) by arg-maxxing\\n\",\n \"# sampling_mode=\\\"full\\\" means evaluating the whole action sequence in each policy and executing the first action (as opposed to marginal where the agent evaluates each action type)\\n\",\n \"\\n\",\n \"gamma = 3.0\\n\",\n \"policy_len = 4 \\n\",\n \"agent_vanilla = Agent(\\n\",\n \" env.A, env.B, C, D, \\n\",\n \" A_dependencies=env.A_dependencies, \\n\",\n \" B_dependencies=env.B_dependencies,\\n\",\n \" policy_len=policy_len,\\n\",\n \" learn_A=False,\\n\",\n \" learn_B=False,\\n\",\n \" action_selection=\\\"deterministic\\\",\\n\",\n \" sampling_mode=\\\"full\\\",\\n\",\n \" gamma=gamma,\\n\",\n \")\\n\",\n \"\\n\",\n \"agent_si = Agent(\\n\",\n \" env.A, env.B, C, D, \\n\",\n \" A_dependencies=env.A_dependencies, \\n\",\n \" B_dependencies=env.B_dependencies,\\n\",\n \" policy_len=1,\\n\",\n \" learn_A=False,\\n\",\n \" learn_B=False,\\n\",\n \" action_selection=\\\"deterministic\\\",\\n\",\n \" sampling_mode=\\\"full\\\",\\n\",\n \" gamma=gamma,\\n\",\n \")\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Running the active inference rollouts\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 24,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:03.125390Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:03.125293Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:03.134006Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:03.133672Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"key = jr.PRNGKey(0) \\n\",\n \"T = 5\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 25,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:03.135256Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:03.135176Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:03.142772Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:03.142315Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"si_search = si_policy_search(\\n\",\n \" horizon=policy_len, # plans 4 timesteps ahead\\n\",\n \" max_nodes=5000, # maximum number of nodes allowed in the tree\\n\",\n \" max_branching=45, # maximum number of children allowed per node (moderating the branching factor)\\n\",\n \" policy_prune_threshold=0.0, # no pruning of unlikely policies\\n\",\n \" observation_prune_threshold=1e-4, # no pruning of unlikely observations\\n\",\n \" entropy_stop_threshold=0.0, # disabling halting of expansion if agent is certain enough\\n\",\n \" neg_efe_stop_threshold=1e10, # disabling efe value based halting of expansion\\n\",\n \" kl_threshold=-1, # disabling node reuse if agent is in similar states after an action\\n\",\n \" prune_penalty=512, # default value for prune penalty\\n\",\n \" gamma=gamma, # temperature parameter; lower value (---> 1) prunes policies less aggressively as probabilities are flattened while higher value (---> 16) prunes more aggressively\\n\",\n \" topk_obsspace=10000, # max number of top observation combinations - this default value just means we want to consider all the observation combinations\\n\",\n \")\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 26,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:03.143984Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:03.143902Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:06.213280Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:06.212996Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"_, info_vanilla = rollout(agent_vanilla, env, num_timesteps=T, rng_key=key) # default policy search is vanilla\\n\",\n \"_, info_si = rollout(agent_si, env, num_timesteps=T, rng_key=key, policy_search=si_search)\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 27,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:06.215016Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:06.214922Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:06.224643Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:06.224077Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"def make_gif(info):\\n\",\n \" frames = []\\n\",\n \" for t in range(info[\\\"observation\\\"][0].shape[1]): # iterate over timesteps\\n\",\n \" # get observations for this timestep\\n\",\n \" observations_t = [\\n\",\n \" info[\\\"observation\\\"][0][:, t, :],\\n\",\n \" info[\\\"observation\\\"][1][:, t, :], \\n\",\n \" info[\\\"observation\\\"][2][:, t, :],\\n\",\n \" ]\\n\",\n \" \\n\",\n \" frame = env.render(mode=\\\"rgb_array\\\", observations=observations_t) # render the environment using the observations for this timestep\\n\",\n \" frame = np.asarray(frame, dtype=np.uint8)\\n\",\n \" plt.close() # close the figure to prevent memory leak\\n\",\n \" frames.append(frame)\\n\",\n \"\\n\",\n \" frames = np.array(frames, dtype=np.uint8)\\n\",\n \" mediapy.show_video(frames, fps=1)\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 28,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:06.226122Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:06.226036Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:07.084714Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:07.084232Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"
\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"make_gif(info_vanilla)\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 29,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:07.086134Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:07.086057Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:07.907502Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:07.907193Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/html\": [\n \"
\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"make_gif(info_si)\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Result analysis\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 30,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:07.908846Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:07.908757Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:07.921807Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:07.921532Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# qpi is a posterior over whole policies (action sequences).\\n\",\n \"# To get the probability of the *current* action, we marginalize over policies\\n\",\n \"# that share the same first action and sum their qpi values.\\n\",\n \"# helper functions for:\\n\",\n \"# - printing out policies and respective probabilities of selecting those policies\\n\",\n \"# - printing out action and observation info for each timestep\\n\",\n \"\\n\",\n \"np.set_printoptions(precision=2, suppress=True)\\n\",\n \"\\n\",\n \"def print_qpi(agent, info, print_t1=False):\\n\",\n \" qpi_values = info[\\\"qpi\\\"]\\n\",\n \"\\n\",\n \" action_names = {\\n\",\n \" 0: \\\"move to center\\\",\\n\",\n \" 1: \\\"move to left arm\\\",\\n\",\n \" 2: \\\"move to right arm\\\",\\n\",\n \" 3: \\\"move to cue\\\",\\n\",\n \" 4: \\\"move to middle\\\",\\n\",\n \" }\\n\",\n \" max_timesteps = 1 if print_t1 else qpi_values.shape[1]\\n\",\n \"\\n\",\n \" # unique_multiactions returns the unique first-step actions across policies\\n\",\n \" # for a single control factor, this is just a list of action indices\\n\",\n \" unique_actions = agent.unique_multiactions[:, 0]\\n\",\n \"\\n\",\n \" for t in range(max_timesteps):\\n\",\n \" print(f\\\"Timestep {t}:\\\")\\n\",\n \" action_probs = agent.multiaction_probabilities(qpi_values[:, t, :])[0]\\n\",\n \"\\n\",\n \" for action_idx, total_prob in zip(unique_actions.tolist(), action_probs.tolist()):\\n\",\n \" if action_idx < 0:\\n\",\n \" continue\\n\",\n \" action_name = action_names.get(action_idx, f\\\"action_{action_idx}\\\")\\n\",\n \" print(f\\\" {action_name}: {total_prob:.3f}\\\")\\n\",\n \" print()\\n\",\n \"\\n\",\n \"def print_agent_behavior(info):\\n\",\n \"\\n\",\n \" action_names = {\\n\",\n \" 0: \\\"move to center\\\",\\n\",\n \" 1: \\\"move to left arm\\\",\\n\",\n \" 2: \\\"move to right arm\\\",\\n\",\n \" 3: \\\"move to cue\\\",\\n\",\n \" 4: \\\"move to middle\\\",\\n\",\n \" }\\n\",\n \" \\n\",\n \" location_obs = {\\n\",\n \" 0: \\\"center loc\\\",\\n\",\n \" 1: \\\"left arm loc\\\",\\n\",\n \" 2: \\\"right arm loc\\\",\\n\",\n \" 3: \\\"cue loc\\\",\\n\",\n \" 4: \\\"middle loc\\\",\\n\",\n \" }\\n\",\n \" outcome_obs = {0: \\\"no_outcome\\\", 1: \\\"reward\\\", 2: \\\"punishment\\\"}\\n\",\n \" cue_obs = {0: \\\"no cue\\\", 1: \\\"cue-left\\\", 2: \\\"cue-right\\\"}\\n\",\n \" \\n\",\n \" actions = info[\\\"action\\\"]\\n\",\n \" observations = info[\\\"observation\\\"]\\n\",\n \" \\n\",\n \" num_timesteps = actions.shape[1]\\n\",\n \" \\n\",\n \" for t in range(num_timesteps):\\n\",\n \" action_idx = int(actions[0, t, 0]) # [batch, timestep, action_dim]\\n\",\n \" action_name = action_names.get(action_idx, f\\\"action_{action_idx}\\\")\\n\",\n \" \\n\",\n \" location_obs_idx = int(observations[0][0, t, 0]) # [modality][batch, timestep, obs_dim]\\n\",\n \" outcome_obs_idx = int(observations[1][0, t, 0])\\n\",\n \" cue_obs_idx = int(observations[2][0, t, 0])\\n\",\n \" \\n\",\n \" location_name = location_obs.get(location_obs_idx)\\n\",\n \" outcome_name = outcome_obs.get(outcome_obs_idx)\\n\",\n \" cue_name = cue_obs.get(cue_obs_idx)\\n\",\n \" \\n\",\n \" print(f\\\"t={t}: observed=({location_name}, {outcome_name}, {cue_name}) -> action={action_name}\\\")\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"With the classic T-maze's adjacency constraints (and the extra middle location), reaching the reward after sampling the cue takes multiple steps. With the current horizon (4) and `T=5`, you should see cue-seeking and movement toward the chosen arm; increase `policy_len` and/or `T` if you want longer sequences.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 31,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:07.923120Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:07.923047Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:07.952261Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:07.952001Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"t=0: observed=(center loc, no_outcome, no cue) -> action=move to cue\\n\",\n \"t=1: observed=(cue loc, no_outcome, cue-left) -> action=move to center\\n\",\n \"t=2: observed=(center loc, no_outcome, no cue) -> action=move to middle\\n\",\n \"t=3: observed=(middle loc, no_outcome, no cue) -> action=move to left arm\\n\",\n \"t=4: observed=(left arm loc, reward, no cue) -> action=move to center\\n\",\n \"t=5: observed=(left arm loc, reward, no cue) -> action=move to center\\n\"\n ]\n }\n ],\n \"source\": [\n \"print_agent_behavior(info_vanilla)\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 32,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:07.953763Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:07.953663Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:07.963337Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:07.963090Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"t=0: observed=(center loc, no_outcome, no cue) -> action=move to cue\\n\",\n \"t=1: observed=(cue loc, no_outcome, cue-left) -> action=move to center\\n\",\n \"t=2: observed=(center loc, no_outcome, no cue) -> action=move to middle\\n\",\n \"t=3: observed=(middle loc, no_outcome, no cue) -> action=move to left arm\\n\",\n \"t=4: observed=(left arm loc, reward, no cue) -> action=move to center\\n\",\n \"t=5: observed=(left arm loc, reward, no cue) -> action=move to center\\n\"\n ]\n }\n ],\n \"source\": [\n \"print_agent_behavior(info_si)\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now, to see how the two planning algorithms differ, let's examine how they evaluate policies... \\n\",\n \"\\n\",\n \"With `cue_validity = 1.0`, both planners should prefer information gathering, but the SI planner typically yields a sharper (more confident) posterior over policies. Compare how each planner's probabilities shift with the longer horizon.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 33,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:07.964611Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:07.964506Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:08.564500Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:08.564141Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Timestep 0:\\n\",\n \" move to center: 0.142\\n\",\n \" move to left arm: 0.142\\n\",\n \" move to right arm: 0.142\\n\",\n \" move to cue: 0.539\\n\",\n \" move to middle: 0.036\\n\",\n \"\\n\"\n ]\n }\n ],\n \"source\": [\n \"print_qpi(agent_vanilla, info_vanilla, print_t1=True)\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 34,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:08.565830Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:08.565750Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:08.781566Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:08.781263Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Timestep 0:\\n\",\n \" move to center: 0.001\\n\",\n \" move to left arm: 0.001\\n\",\n \" move to right arm: 0.001\\n\",\n \" move to cue: 0.810\\n\",\n \" move to middle: 0.186\\n\",\n \"\\n\"\n ]\n }\n ],\n \"source\": [\n \"print_qpi(agent_si, info_si, print_t1=True)\\n\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \".venv\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.11.12\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/inductive_inference/inductive_inference_example.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Imports\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"from pymdp import control\\n\",\n \"import jax.numpy as jnp\\n\",\n \"import jax.tree_util as jtu\\n\",\n \"from jax import random as jr\\n\",\n \"from jax import nn\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Set up generative model (random one with trivial observation model)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# Set up a generative model\\n\",\n \"num_states = [5, 3]\\n\",\n \"num_controls = [2, 2]\\n\",\n \"\\n\",\n \"# make some arbitrary policies (policy depth 3, 2 control factors)\\n\",\n \"policy_1 = jnp.array([[0, 1],\\n\",\n \" [1, 1],\\n\",\n \" [0, 0]])\\n\",\n \"policy_2 = jnp.array([[1, 0],\\n\",\n \" [0, 0],\\n\",\n \" [1, 1]])\\n\",\n \"policy_matrix = jnp.stack([policy_1, policy_2]) \\n\",\n \"\\n\",\n \"# observation modalities (isomorphic/identical to hidden states, just need to include for the need to include likleihood model)\\n\",\n \"num_obs = [5, 3]\\n\",\n \"num_factors = len(num_states)\\n\",\n \"num_modalities = len(num_obs)\\n\",\n \"\\n\",\n \"# sample parameters of the model (A, B, C)\\n\",\n \"key = jr.PRNGKey(1)\\n\",\n \"factor_keys = jr.split(key, num_factors)\\n\",\n \"\\n\",\n \"d = [0.1* jr.uniform(factor_key, (ns,)) for factor_key, ns in zip(factor_keys, num_states)]\\n\",\n \"qs_init = [jr.dirichlet(factor_key, d_f) for factor_key, d_f in zip(factor_keys, d)]\\n\",\n \"A = [jnp.eye(no) for no in num_obs]\\n\",\n \"\\n\",\n \"factor_keys = jr.split(factor_keys[-1], num_factors)\\n\",\n \"b = [jr.uniform(factor_keys[f], shape=(num_controls[f], num_states[f], num_states[f])) for f in range(num_factors)]\\n\",\n \"b_sparse = [jnp.where(b_f < 0.75, 1e-5, b_f) for b_f in b]\\n\",\n \"B = [jnp.swapaxes(jr.dirichlet(factor_keys[f], b_sparse[f]), 2, 0) for f in range(num_factors)]\\n\",\n \"\\n\",\n \"modality_keys = jr.split(factor_keys[-1], num_modalities)\\n\",\n \"C = [nn.one_hot(jr.randint(modality_keys[m], shape=(1,), minval=0, maxval=num_obs[m]), num_obs[m]) for m in range(num_modalities)]\\n\",\n \"\\n\",\n \"# trivial dependencies -- factor 1 drives modality 1, etc.\\n\",\n \"A_dependencies = [[0], [1]]\\n\",\n \"B_dependencies = [[0], [1]]\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Generate sparse constraints vectors `H` and inductive matrix `I`, using inductive parameters like depth and threshold \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# generate random constraints (H vector)\\n\",\n \"factor_keys = jr.split(key, num_factors)\\n\",\n \"H = [jr.uniform(factor_key, (ns,)) for factor_key, ns in zip(factor_keys, num_states)]\\n\",\n \"H = [jnp.where(h < 0.75, 0., 1.) for h in H]\\n\",\n \"\\n\",\n \"# depth and threshold for inductive planning algorithm. I made policy-depth equal to inductive planning depth, out of ignorance -- need to ask Tim or Tommaso about this\\n\",\n \"inductive_depth, inductive_threshold = 3, 0.5\\n\",\n \"I = control.generate_I_matrix(H, B, inductive_threshold, inductive_depth)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Evaluate posterior probability of policies and negative EFE using new version of `update_posterior_policies`\\n\",\n \"#### This function no longer computes info gain (for both states and parameters) since deterministic model is assumed, and includes new inductive matrix `I` and `inductive_epsilon` parameter\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# evaluate Q(pi) and negative EFE using the inductive planning algorithm\\n\",\n \"\\n\",\n \"E = jnp.ones(policy_matrix.shape[0])\\n\",\n \"pA = jtu.tree_map(lambda a: jnp.ones_like(a), A)\\n\",\n \"pB = jtu.tree_map(lambda b: jnp.ones_like(b), B)\\n\",\n \"\\n\",\n \"q_pi, neg_efe = control.update_posterior_policies_inductive(policy_matrix, qs_init, A, B, C, E, pA, pB, A_dependencies, B_dependencies, I, gamma=16.0, use_utility=True, use_inductive=True, inductive_epsilon=1e-3)\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"pymdp_dev_env\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.11.11\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/inductive_inference/inductive_inference_gridworld.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Imports\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:10.138587Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:10.138354Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:14.052446Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:14.052121Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"import jax.tree_util as jtu\\n\",\n \"from jax import numpy as jnp, random as jr\\n\",\n \"from jax import nn, vmap\\n\",\n \"from equinox import tree_at\\n\",\n \"\\n\",\n \"import numpy as np\\n\",\n \"\\n\",\n \"from pymdp.envs import GridWorld, rollout\\n\",\n \"from pymdp import control\\n\",\n \"from pymdp.agent import Agent\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Grid world generative model\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:14.054405Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:14.054246Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:14.378834Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:14.378553Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# size of the grid world\\n\",\n \"grid_shape = (7, 7)\\n\",\n \"\\n\",\n \"# start in the middle of the grid\\n\",\n \"env = GridWorld(shape=grid_shape, initial_position=(3,3), include_stay=False)\\n\",\n \"\\n\",\n \"desired_state = (6,6) # bottom right corner\\n\",\n \"# get linear index of desired state\\n\",\n \"desired_state_id = env.coords_to_index(shape=grid_shape, coord=desired_state)\\n\",\n \"\\n\",\n \"# create helpful num_obs and num_states lists (lists of observation dimensions per modality, and state dimensions per factor, respectively)\\n\",\n \"num_obs = [a.shape[0] for a in env.A]\\n\",\n \"num_states = [b.shape[0] for b in env.B]\\n\",\n \"num_controls = [b.shape[-1] for b in env.B]\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Planning and inductive inference parameters\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:14.380265Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:14.380186Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:14.445066Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:14.444718Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# number of agents\\n\",\n \"batch_size = 5\\n\",\n \"\\n\",\n \"planning_horizon, inductive_threshold = 1, 0.1\\n\",\n \"inductive_depth = 7\\n\",\n \"policy_matrix = control.construct_policies(num_states, num_controls, policy_len=planning_horizon)\\n\",\n \"\\n\",\n \"# inductive planning goal states\\n\",\n \"H = [jnp.broadcast_to(nn.one_hot(desired_state_id, num_states[0]), (batch_size, num_states[0]))] # list of factor-specific goal vectors (shape of each is (n_batches, num_states[f]))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Initialize an `Agent()`\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:14.446460Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:14.446379Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:15.109623Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:15.109349Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61059/4163094735.py:6: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agent = Agent(A, B, C, D, batch_size=batch_size, policies=policy_matrix, policy_len=planning_horizon,\\n\"\n ]\n }\n ],\n \"source\": [\n \"# create agent, using generative process parameters from the environment to initialize the generative model\\n\",\n \"A = env.A\\n\",\n \"B = env.B\\n\",\n \"C = [jnp.repeat(nn.one_hot(desired_state_id, num_states[0])[None, :], batch_size, axis=0)] # preferred outcomes (shape of each is (n_batches, num_obs[f]))\\n\",\n \"D = env.D\\n\",\n \"agent = Agent(A, B, C, D, batch_size=batch_size, policies=policy_matrix, policy_len=planning_horizon, \\n\",\n \" inductive_depth=inductive_depth, inductive_threshold=inductive_threshold,\\n\",\n \" H=H, use_utility=True, use_states_info_gain=False, use_param_info_gain=False, use_inductive=True)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Run active inference\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:15.110855Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:15.110771Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:16.107364Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:16.106994Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"T = 7 \\n\",\n \"last, info = rollout(agent, env, num_timesteps=T, rng_key = jr.PRNGKey(0))\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:16.108728Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:16.108649Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:16.111586Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:16.111341Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"(5, 8)\"\n ]\n },\n \"execution_count\": 6,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n }\n ],\n \"source\": [\n \"info['env_state'][0].shape\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:16.112658Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:16.112589Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:16.232366Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:16.232099Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Grid position for agent 2 at time 0: (3, 3)\\n\",\n \"Grid position for agent 2 at time 1: (3, 4)\\n\",\n \"Grid position for agent 2 at time 2: (3, 5)\\n\",\n \"Grid position for agent 2 at time 3: (3, 6)\\n\",\n \"Grid position for agent 2 at time 4: (4, 6)\\n\",\n \"Grid position for agent 2 at time 5: (5, 6)\\n\",\n \"Grid position for agent 2 at time 6: (6, 6)\\n\"\n ]\n }\n ],\n \"source\": [\n \"agent_id_to_track = 1\\n\",\n \"for t in range(T):\\n\",\n \" state_time_t = env.index_to_coords(shape=grid_shape, idx=info['env_state'][0][agent_id_to_track, t])\\n\",\n \" print(f\\\"Grid position for agent {agent_id_to_track+1} at time {t}: {state_time_t}\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Now the agent starts further from the goal and thus need more timesteps to reach it\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:16.233977Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:16.233839Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:16.249571Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:16.249295Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"# size of the grid world\\n\",\n \"grid_shape = (7, 7)\\n\",\n \"\\n\",\n \"# number of agents\\n\",\n \"batch_size = 5\\n\",\n \"\\n\",\n \"# start in the upper left corner this time\\n\",\n \"upper_left_initial_states = [jnp.repeat(jnp.array(env.coords_to_index(shape=grid_shape, coord=(0,0))), batch_size, axis=0)]\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Increase inductive planning depth in order to compute the needed inductive planning matrix \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:16.250817Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:16.250732Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:16.253357Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:16.253075Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"planning_horizon, inductive_threshold = 1, 0.1\\n\",\n \"inductive_depth = 14\\n\",\n \"policy_matrix = control.construct_policies(num_states, num_controls, policy_len=planning_horizon)\\n\",\n \"\\n\",\n \"# inductive planning goal states\\n\",\n \"H = [jnp.broadcast_to(nn.one_hot(desired_state_id, num_states[0]), (batch_size, num_states[0]))] # list of factor-specific goal vectors (shape of each is (n_batches, num_states[f]))\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:16.254701Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:16.254624Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:16.382125Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:16.381861Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61059/1146799413.py:5: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agent = Agent(A, B, C, D, batch_size=batch_size, policies=policy_matrix, policy_len=planning_horizon,\\n\"\n ]\n }\n ],\n \"source\": [\n \"# create agent, using generative process parameters from the environment to initialize the generative model\\n\",\n \"A, B = [jnp.broadcast_to(a, (batch_size,) + a.shape) for a in env.A], [jnp.broadcast_to(b, (batch_size,) + b.shape) for b in env.B]\\n\",\n \"C = [jnp.repeat(nn.one_hot(desired_state_id, num_states[0])[None, :], batch_size, axis=0)] # preferred outcomes (shape of each is (n_batches, num_obs[f]))\\n\",\n \"D = [nn.one_hot(upper_left_initial_states[0], num_states[0])] # need to do this since the D of the environment won't match the env state if you reset to a different state\\n\",\n \"agent = Agent(A, B, C, D, batch_size=batch_size, policies=policy_matrix, policy_len=planning_horizon, \\n\",\n \" inductive_depth=inductive_depth, inductive_threshold=inductive_threshold,\\n\",\n \" H=H, use_utility=True, use_states_info_gain=False, use_param_info_gain=False, use_inductive=True)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Run active inference\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:16.383442Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:16.383329Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:17.230297Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:17.229993Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"T = 14\\n\",\n \"# construct a partial initial_carry that only overwrites env_state/observation\\n\",\n \"init_obs, init_env_state = vmap(env.reset)(\\n\",\n \" jr.split(jr.PRNGKey(1), batch_size), state=upper_left_initial_states\\n\",\n \")\\n\",\n \"initial_carry_overwrite = {\\\"observation\\\": init_obs, \\\"env_state\\\": init_env_state}\\n\",\n \"last, info = rollout(agent, env, num_timesteps=T, rng_key = jr.PRNGKey(0), initial_carry=initial_carry_overwrite)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:17.231657Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:17.231576Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:17.252610Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:17.252328Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Grid position for agent 2 at time 0: (0, 0)\\n\",\n \"Grid position for agent 2 at time 1: (0, 1)\\n\",\n \"Grid position for agent 2 at time 2: (0, 2)\\n\",\n \"Grid position for agent 2 at time 3: (0, 3)\\n\",\n \"Grid position for agent 2 at time 4: (0, 4)\\n\",\n \"Grid position for agent 2 at time 5: (0, 5)\\n\",\n \"Grid position for agent 2 at time 6: (0, 6)\\n\",\n \"Grid position for agent 2 at time 7: (1, 6)\\n\",\n \"Grid position for agent 2 at time 8: (2, 6)\\n\",\n \"Grid position for agent 2 at time 9: (3, 6)\\n\",\n \"Grid position for agent 2 at time 10: (4, 6)\\n\",\n \"Grid position for agent 2 at time 11: (5, 6)\\n\",\n \"Grid position for agent 2 at time 12: (6, 6)\\n\",\n \"Grid position for agent 2 at time 13: (6, 6)\\n\"\n ]\n }\n ],\n \"source\": [\n \"agent_id_to_track = 1\\n\",\n \"for t in range(T):\\n\",\n \" state_time_t = env.index_to_coords(shape=grid_shape, idx=info['env_state'][0][agent_id_to_track, t])\\n\",\n \" print(f\\\"Grid position for agent {agent_id_to_track+1} at time {t}: {state_time_t}\\\")\"\n ]\n }\n ],\n \"metadata\": {\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.11.12\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/inference_and_learning/inference_methods_comparison.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:18.347670Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:18.347498Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:19.684289Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:19.683853Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"import jax.numpy as jnp\\n\",\n \"from jax import tree_util as jtu, vmap, jit\\n\",\n \"from jax.experimental import sparse\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import seaborn as sns\\n\",\n \"\\n\",\n \"from pymdp.inference import smoothing_ovf\\n\",\n \"from pymdp.algos import hmm_smoother_scan_colstoch\\n\",\n \"from pymdp.maths import log_stable\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Set up generative model and a sequence of observations. The A tensors, B tensors and observations are specified in such a way that only later observations ($o_{t > 1}$) help disambiguate hidden states at earlier time points. This will demonstrate the importance of \\\"smoothing\\\" or retrospective inference\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:19.685687Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:19.685565Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:19.993067Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:19.992755Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"num_states = [3, 2]\\n\",\n \"num_obs = [2]\\n\",\n \"n_batch = 2\\n\",\n \"\\n\",\n \"A_1 = jnp.array([[1.0, 1.0, 1.0], [0.0, 0.0, 1.]])\\n\",\n \"A_2 = jnp.array([[1.0, 1.0], [1., 0.]])\\n\",\n \"\\n\",\n \"A_tensor = A_1[..., None] * A_2[:, None]\\n\",\n \"\\n\",\n \"A_tensor /= A_tensor.sum(0)\\n\",\n \"\\n\",\n \"A = [jnp.broadcast_to(A_tensor, (n_batch, num_obs[0], 3, 2)) ]\\n\",\n \"\\n\",\n \"# create two transition matrices, one for each state factor\\n\",\n \"B_1 = jnp.broadcast_to(\\n\",\n \" jnp.array([[0.0, 1.0, 0.0], [0.0, 0.0, 1.0], [1.0, 0.0, 0.0]]), (n_batch, 3, 3)\\n\",\n \")\\n\",\n \"\\n\",\n \"B_2 = jnp.broadcast_to(\\n\",\n \" jnp.array([[0.0, 1.0], [1.0, 0.0]]), (n_batch, 2, 2)\\n\",\n \" )\\n\",\n \"\\n\",\n \"B = [B_1[..., None], B_2[..., None]]\\n\",\n \"\\n\",\n \"# for the single modality, a sequence over time of observations (one hot vectors)\\n\",\n \"obs = [jnp.broadcast_to(jnp.array([[1., 0.], # observation 0 is ambiguous with respect state factors\\n\",\n \" [1., 0], # observation 0 is ambiguous with respect state factors\\n\",\n \" [1., 0], # observation 0 is ambiguous with respect state factors\\n\",\n \" [0., 1.]])[:, None], (4, n_batch, num_obs[0]) )] # observation 1 provides information about exact state of both factors \\n\",\n \"C = [jnp.zeros((n_batch, num_obs[0]))] # flat preferences\\n\",\n \"D = [jnp.ones((n_batch, 3)) / 3., jnp.ones((n_batch, 2)) / 2.] # flat prior\\n\",\n \"E = jnp.ones((n_batch, 1))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Construct the `Agent`\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:19.995016Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:19.994907Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:20.425222Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:20.424904Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61062/464010401.py:4: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agents = Agent(\\n\"\n ]\n }\n ],\n \"source\": [\n \"pA = None\\n\",\n \"pB = None\\n\",\n \"\\n\",\n \"agents = Agent(\\n\",\n \" A=A,\\n\",\n \" B=B,\\n\",\n \" C=C,\\n\",\n \" D=D,\\n\",\n \" E=E,\\n\",\n \" pA=pA,\\n\",\n \" pB=pB,\\n\",\n \" policy_len=3,\\n\",\n \" categorical_obs=True,\\n\",\n \" action_selection=\\\"deterministic\\\",\\n\",\n \" sampling_mode=\\\"full\\\",\\n\",\n \" inference_algo=\\\"ovf\\\",\\n\",\n \" num_iter=16,\\n\",\n \" batch_size=n_batch\\n\",\n \")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### OVF Smoothing\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Using `obs` and `policies`, pass in the arguments `outcomes`, `past_actions`, `empirical_prior` and `qs_hist` to `agent.infer_states(...)`\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Run first timestep of inference using `obs[0]`, no past actions, empirical prior set to actual prior, no qs_hist\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:20.426515Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:20.426430Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:21.658480Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:21.658102Z\"\n }\n },\n \"outputs\": [],\n \"source\": [\n \"prior = agents.D\\n\",\n \"action_hist = []\\n\",\n \"qs_hist=None\\n\",\n \"for t in range(len(obs[0])):\\n\",\n \" first_obs = jtu.tree_map(lambda x: jnp.moveaxis(x[:t+1], 0, 1), obs)\\n\",\n \" beliefs = agents.infer_states(first_obs, prior, qs_hist=qs_hist)\\n\",\n \" actions = jnp.broadcast_to(agents.policies[0, 0], (2, 2))\\n\",\n \" prior = agents.update_empirical_prior(actions, beliefs)\\n\",\n \" qs_hist = beliefs\\n\",\n \" if t < len(obs[0]) - 1:\\n\",\n \" action_hist.append(actions)\\n\",\n \"\\n\",\n \"v_jso = jit(vmap(smoothing_ovf), backend='cpu')\\n\",\n \"actions_seq = jnp.stack(action_hist, 1)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:21.659932Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:21.659845Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:23.746863Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:23.746596Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"24.1 μs ± 2.27 μs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\\n\"\n ]\n }\n ],\n \"source\": [\n \"smoothed_beliefs = v_jso(beliefs, agents.B, actions_seq)\\n\",\n \"%timeit v_jso(beliefs, agents.B, actions_seq)[0][0].block_until_ready()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Try the version of `smoothing_ovf` with sparse tensors\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:23.748100Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:23.748018Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:27.438063Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:27.437786Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"28.4 μs ± 361 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\\n\"\n ]\n }\n ],\n \"source\": [\n \"sparse_B = jtu.tree_map(lambda b: sparse.BCOO.fromdense(b, n_batch=1), agents.B)\\n\",\n \"\\n\",\n \"smoothed_beliefs_sparse = v_jso(beliefs, sparse_B, actions_seq)\\n\",\n \"%timeit v_jso(beliefs, sparse_B, actions_seq)[0][0].block_until_ready()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can plot that pair of filtering / smoothing distributions for the single batch / single agent, that we ran\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:27.439187Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:27.439114Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:27.720017Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:27.719729Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# with dense matrices\\n\",\n \"fig, axes = plt.subplots(2, 2, figsize=(16, 8), sharex=True)\\n\",\n \"\\n\",\n \"sns.heatmap(beliefs[0][0].mT, ax=axes[0, 0], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"sns.heatmap(beliefs[1][0].mT, ax=axes[1, 0], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"\\n\",\n \"sns.heatmap(smoothed_beliefs[0][0][0].mT, ax=axes[0, 1], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"sns.heatmap(smoothed_beliefs[0][1][0].mT, ax=axes[1, 1], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"\\n\",\n \"axes[0, 0].set_title('Filtered beliefs')\\n\",\n \"axes[0, 1].set_title('Smoothed beliefs')\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:27.721291Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:27.721191Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:27.821278Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:27.821030Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# with sparse matrices\\n\",\n \"fig, axes = plt.subplots(2, 2, figsize=(16, 8), sharex=True)\\n\",\n \"\\n\",\n \"sns.heatmap(beliefs[0][0].mT, ax=axes[0, 0], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"sns.heatmap(beliefs[1][0].mT, ax=axes[1, 0], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"\\n\",\n \"sns.heatmap(smoothed_beliefs_sparse[0][0][0].mT, ax=axes[0, 1], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"sns.heatmap(smoothed_beliefs_sparse[0][1][0].mT, ax=axes[1, 1], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"\\n\",\n \"axes[0, 0].set_title('Filtered beliefs')\\n\",\n \"axes[0, 1].set_title(\\\"Smoothed beliefs\\\")\\n\",\n \"plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Compare to marginal message passing\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:27.822551Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:27.822425Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:28.734939Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:28.734565Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61062/1188368462.py:1: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" mmp_agents = agents = Agent(\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"mmp_agents = agents = Agent(\\n\",\n \" A=A,\\n\",\n \" B=B,\\n\",\n \" C=C,\\n\",\n \" D=D,\\n\",\n \" E=E,\\n\",\n \" pA=pA,\\n\",\n \" pB=pB,\\n\",\n \" policy_len=3,\\n\",\n \" control_fac_idx=None,\\n\",\n \" categorical_obs=True,\\n\",\n \" action_selection=\\\"deterministic\\\",\\n\",\n \" sampling_mode=\\\"full\\\",\\n\",\n \" inference_algo=\\\"mmp\\\",\\n\",\n \" num_iter=16,\\n\",\n \" batch_size=n_batch,\\n\",\n \")\\n\",\n \"\\n\",\n \"mmp_obs = [jnp.moveaxis(obs[0], 0, 1)]\\n\",\n \"post_marg_beliefs = mmp_agents.infer_states(mmp_obs, mmp_agents.D, past_actions=jnp.stack(action_hist, 1))\\n\",\n \"\\n\",\n \"#with sparse matrices\\n\",\n \"fig, axes = plt.subplots(1, 2, figsize=(16, 4), sharex=True)\\n\",\n \"\\n\",\n \"sns.heatmap(post_marg_beliefs[0][0].mT, ax=axes[0], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"sns.heatmap(post_marg_beliefs[1][0].mT, ax=axes[1], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"\\n\",\n \"fig.suptitle('Marginal smoothed beliefs');\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Compare to variational message passing\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:28.736227Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:28.736142Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:28.887900Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:28.887623Z\"\n }\n },\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_61062/4088240323.py:1: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" vmp_agents = agents = Agent(\\n\"\n ]\n },\n {\n \"data\": {\n \"text/plain\": [\n \"Text(0.5, 0.98, 'VMP smoothed beliefs')\"\n ]\n },\n \"execution_count\": 10,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"vmp_agents = agents = Agent(\\n\",\n \" A=A,\\n\",\n \" B=B,\\n\",\n \" C=C,\\n\",\n \" D=D,\\n\",\n \" E=E,\\n\",\n \" pA=pA,\\n\",\n \" pB=pB,\\n\",\n \" policy_len=3,\\n\",\n \" control_fac_idx=None,\\n\",\n \" categorical_obs=True,\\n\",\n \" action_selection=\\\"deterministic\\\",\\n\",\n \" sampling_mode=\\\"full\\\",\\n\",\n \" inference_algo=\\\"vmp\\\",\\n\",\n \" num_iter=16,\\n\",\n \" batch_size=n_batch,\\n\",\n \")\\n\",\n \"\\n\",\n \"vmp_obs = [jnp.moveaxis(obs[0], 0, 1)]\\n\",\n \"post_vmp_beliefs = vmp_agents.infer_states(vmp_obs, vmp_agents.D, past_actions=jnp.stack(action_hist, 1))\\n\",\n \"\\n\",\n \"#with sparse matrices\\n\",\n \"fig, axes = plt.subplots(1, 2, figsize=(16, 4), sharex=True)\\n\",\n \"\\n\",\n \"sns.heatmap(post_vmp_beliefs[0][0].mT, ax=axes[0], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"sns.heatmap(post_vmp_beliefs[1][0].mT, ax=axes[1], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"\\n\",\n \"fig.suptitle('VMP smoothed beliefs')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Associative-scan HMM (B-native, single-factor reduction)\\n\",\n \"\\n\",\n \"The associative-scan implementation expects a single hidden-state factor. For this multi-factor model, we collapse the two factors into a joint state space via a Cartesian product and run exact filtering/smoothing using the **B-native** (column-stochastic) formulation, then marginalize back to factor-wise beliefs for visualization.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {\n \"execution\": {\n \"iopub.execute_input\": \"2026-03-06T15:32:28.889131Z\",\n \"iopub.status.busy\": \"2026-03-06T15:32:28.889058Z\",\n \"iopub.status.idle\": \"2026-03-06T15:32:31.917104Z\",\n \"shell.execute_reply\": \"2026-03-06T15:32:31.916807Z\"\n }\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"\\n\",\n \"batch_idx = 0\\n\",\n \"T = obs[0].shape[0]\\n\",\n \"s1, s2 = num_states\\n\",\n \"\\n\",\n \"# single-modality observations for one batch\\n\",\n \"obs_single = obs[0][:, batch_idx, :] # (T, obs_dim)\\n\",\n \"\\n\",\n \"# collapse A over factors into a single-state emission matrix\\n\",\n \"A0 = A[0][batch_idx] # (obs_dim, s1, s2)\\n\",\n \"A_big = A0.reshape(num_obs[0], s1 * s2)\\n\",\n \"log_likelihoods = obs_single @ log_stable(A_big)\\n\",\n \"\\n\",\n \"# build joint transition (column-stochastic) via Kronecker product\\n\",\n \"B1 = B[0][batch_idx, :, :, 0] # (s1,s1) column-stochastic\\n\",\n \"B2 = B[1][batch_idx, :, :, 0] # (s2,s2) column-stochastic\\n\",\n \"B_big = jnp.kron(B1, B2)\\n\",\n \"\\n\",\n \"# joint prior\\n\",\n \"D1 = D[0][batch_idx]\\n\",\n \"D2 = D[1][batch_idx]\\n\",\n \"prior_big = jnp.kron(D1, D2)\\n\",\n \"\\n\",\n \"mll, filt_big, pred_big, smooth_big, cond_big = hmm_smoother_scan_colstoch(\\n\",\n \" prior_big, B_big, log_likelihoods\\n\",\n \")\\n\",\n \"\\n\",\n \"# reshape joint beliefs to factor-wise marginals\\n\",\n \"filt_joint = filt_big.reshape(T, s1, s2)\\n\",\n \"smooth_joint = smooth_big.reshape(T, s1, s2)\\n\",\n \"\\n\",\n \"filt_fac1 = filt_joint.sum(axis=2)\\n\",\n \"filt_fac2 = filt_joint.sum(axis=1)\\n\",\n \"smooth_fac1 = smooth_joint.sum(axis=2)\\n\",\n \"smooth_fac2 = smooth_joint.sum(axis=1)\\n\",\n \"\\n\",\n \"fig, axes = plt.subplots(2, 2, figsize=(16, 8), sharex=True)\\n\",\n \"sns.heatmap(filt_fac1.mT, ax=axes[0, 0], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"sns.heatmap(filt_fac2.mT, ax=axes[1, 0], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"\\n\",\n \"sns.heatmap(smooth_fac1.mT, ax=axes[0, 1], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"sns.heatmap(smooth_fac2.mT, ax=axes[1, 1], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"\\n\",\n \"axes[0, 0].set_title('Associative scan filtered beliefs (B-native)')\\n\",\n \"axes[0, 1].set_title('Associative scan smoothed beliefs (B-native)')\\n\",\n \"plt.show()\\n\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"pymdp_dev_env\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.11.12\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/learning/learning_gridworld.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Imports\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The autoreload extension is already loaded. To reload it, use:\\n\",\n \" %reload_ext autoreload\\n\"\n ]\n }\n ],\n \"source\": [\n \"%load_ext autoreload\\n\",\n \"%autoreload 2\\n\",\n \"\\n\",\n \"from jax import nn, vmap, lax, jit\\n\",\n \"from jax import numpy as jnp, random as jr\\n\",\n \"from jax import tree_util as jtu\\n\",\n \"from jax.scipy.special import gammaln, digamma\\n\",\n \"\\n\",\n \"import numpy as np\\n\",\n \"\\n\",\n \"from pymdp.envs import GridWorld, rollout\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp.maths import dirichlet_expected_value\\n\",\n \"\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import seaborn as sns\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Grid world generative model\\n\",\n \" \\n\",\n \"Here we will explore learning of the generative model inside a simple grid 7x7 world environment, where at each state agent can move into 4 possible directions. The agent can explore the environment for 100 time steps, after which it is reaturned to the original position. We will start first with an example where likelihood is fixed, and state transitions are unkown. Next we will explore the example where likelihood is unknown but the state transitions are known, and finally we will look at learning under joint uncertainty over likelihood and transitions (we would expect this case not to work in general with flat priors on both components). \\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# size of the grid world\\n\",\n \"grid_shape = (7, 7)\\n\",\n \"\\n\",\n \"# number of agents\\n\",\n \"batch_size = 20\\n\",\n \"\\n\",\n \"env = GridWorld(shape=grid_shape, initial_position=(3,3), include_stay=False)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Define KL divergence between Dirichlet distributions\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"@jit\\n\",\n \"def kl_div_dirichlet(alpha1, alpha2):\\n\",\n \" alpha0 = alpha1.sum(1, keepdims=True)\\n\",\n \" kl = gammaln(alpha0.squeeze(1)) - gammaln(alpha2.sum(1))\\n\",\n \" kl += jnp.sum(gammaln(alpha2) - gammaln(alpha1) + (alpha1 - alpha2) * (digamma(alpha1) - digamma(alpha0)), 1)\\n\",\n \"\\n\",\n \" return kl\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Initialize different sets of agents using `Agent()` class, use a different `alpha` (action selection temperature) for each set\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Here, the agents have to learn B matrix, with A matrix being fixed to the true observation mapping of generative process, and flat prior oevr initial hidden states\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# create agent with A matrix being fixed to the A of the generative process\\n\",\n \"num_obs = [a.shape[0] for a in env.A]\\n\",\n \"num_states = [b.shape[0] for b in env.B]\\n\",\n \"\\n\",\n \"_A = [jnp.array(a) for a in env.A]\\n\",\n \"C = [jnp.zeros(num_obs[0])]\\n\",\n \"pB = [jnp.ones_like(env.B[0]) / num_states[0]]\\n\",\n \"_B = jtu.tree_map(lambda b: dirichlet_expected_value(b), pB)\\n\",\n \"_D = [jnp.ones(num_states[0])/num_states[0]] # flat prior over initial states\\n\",\n \"\\n\",\n \"agents = []\\n\",\n \"for i in range(5):\\n\",\n \" agents.append( \\n\",\n \" Agent(\\n\",\n \" _A,\\n\",\n \" _B,\\n\",\n \" C,\\n\",\n \" _D,\\n\",\n \" E=None,\\n\",\n \" pA=None,\\n\",\n \" pB=pB,\\n\",\n \" policy_len=3,\\n\",\n \" use_utility=False,\\n\",\n \" use_states_info_gain=True,\\n\",\n \" use_param_info_gain=True,\\n\",\n \" gamma=jnp.ones(batch_size),\\n\",\n \" alpha=jnp.ones(batch_size) * i * .2,\\n\",\n \" categorical_obs=False,\\n\",\n \" action_selection=\\\"stochastic\\\",\\n\",\n \" inference_algo=\\\"exact\\\",\\n\",\n \" num_iter=1,\\n\",\n \" learn_A=False,\\n\",\n \" learn_B=True,\\n\",\n \" learn_D=False,\\n\",\n \" batch_size=batch_size,\\n\",\n \" learning_mode=\\\"offline\\\",\\n\",\n \" )\\n\",\n \" )\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Run multiple blocks of active inference on grid world for each batch of agents that was initialized different `alpha` values. \\n\",\n \"\\n\",\n \"#### Since the agents are using offline learning (`learning_mode = \\\"offline\\\"`), this means that parameter updates to the B tensors are performed at the end of each block.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"pB_ground_truth = 1e4 * env.B[0] + 1e-4\\n\",\n \"num_timesteps = 50\\n\",\n \"num_blocks = 40\\n\",\n \"key = jr.PRNGKey(0)\\n\",\n \"block_and_batch_keys = jr.split(key, num_blocks * (batch_size+1)).reshape((num_blocks, batch_size+1, -1))\\n\",\n \"divs = {i : [] for i in range(len(agents))}\\n\",\n \"for block in range(num_blocks):\\n\",\n \" block_keys = block_and_batch_keys[block]\\n\",\n \" for i, agent in enumerate(agents):\\n\",\n \" init_obs, init_states = vmap(env.reset)(block_keys[:-1])\\n\",\n \" last, info = jit(rollout, static_argnums=[1, 2])(agent, env, num_timesteps, block_keys[-1], initial_carry={\\\"observation\\\": init_obs, \\\"env_state\\\": init_states})\\n\",\n \" agents[i] = last['agent']\\n\",\n \" divs[i].append(kl_div_dirichlet(last['agent'].pB[0], pB_ground_truth).sum(-1).mean(-1))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Plot the KL divergence between the true parameters and believed parameters over time for the different groups of agents (agents with different levels of action stochasticity)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig, axes = plt.subplots(1, 1, figsize=(10, 5), sharex=True, sharey=True)\\n\",\n \"for i in range(len(agents)):\\n\",\n \" p = axes.plot(jnp.stack(divs[i]).mean(-1), lw=3, label=agents[i].alpha.mean())\\n\",\n \" axes.plot(jnp.stack(divs[i]), color=p[0].get_color(), alpha=.2)\\n\",\n \"\\n\",\n \"axes.legend(title='alpha')\\n\",\n \"axes.set_ylabel('KL divergence')\\n\",\n \"axes.set_xlabel('epoch')\\n\",\n \"fig.tight_layout()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Visualize the learned B tensor alongside the true environmental parameters after training\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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8BwEynDc1vM2ZZSFl7O2Qtp5TV7WCnVq1aenPrVatWSbNmzXSXxJAhQ/ReEg8++KDe1+H555/X+0yo8+o1PXv2lC1btsi+fftk/PjxEV++SVF7SfTp00fvH1GkSBFp0qSJ3H333bJ+/XrL16elpekjp2AoU+ICZmx4YhK7jgjuRgAKJs2QdsNoMTG/7ToirDoo6J4AvIv8zlt+23VEsH8ZAKeQ3+b9/J0fdr+DGLvL+vdJY2o1jfKMAPg9v33RKZFVHPjoo4/0skv9+/eXv//97/Lzzz/r86rr4Gx//etfZeDAgVK3bl35+OOP5YknnpAXXnhBZs6cqT9XdVCovSUWLVokjzzyiGzdulXKli2rl326+uqro/J9qA6MlStXyokTJ3TxY+3atZKeni4XX3yx5etTUlIkMTEx17FLNkdlbgAQSenBImGHn5DfAExFfpPfAMxEfpPfAMyUbmh+B0KRXGPIxV588UV55plnpG/fvrJ//3757LPPpHXr1rrAYNdZ8dhjj+n9Jf75z3/qinnx4sXliy++kP/5n//R3RINGjTI/hxV2FDdC1mbXmftMRFNau8K1dWhNr9WhZa8VPpvSezlmUq/ySbtWR12LqlGK0fmAkRaanB+ocd45OvuYecmNponfuH1/OaOLMCdyG/35vfN3/9kef6DBuUKNS4AbyC/C8/rP3/nF/vFAbGR6uP89sXyTUeOHNFLH6nlltShfPDBB3pfCLVvhFp6KSdVkFCFBVUZ/+677/SeEVWrVtVdCWrz6zvuuEMXA3JSBQn1OUq0ChLLli3TBRO158X27dtl+PDhUr9+fendu7fl61URRR05+fWCCsAsaZm+uDzZIr8BmIr8Jr8BmIn8Jr8BmCnN0Pw2c9b5VKxYMfn++++lTZs22ee6du0qDzzwgIwdO1a6deumCxA5uxzUcf311+vlmZo2bSrXXHONrFmzRm84PW3aNClZsmTY14l2d8SxY8ckOTlZF0nUUlG33Xab7v5Q3x/MYtUVwf4TwB/SQ75YXdC37DoiyEHAfOR3dNh1RAzctj3Pe50BwLmQ38hLRwTXHcB90g3NbzNn/SdUYSGra0E5cOCANG7cWFasWKEfq24DVUBQm1QfPHhQdyBkUefVL/+VK6+8UubOnat/8V+xYkW9+fWmTZukbdu2DnxXInfeeafs2LFDtxSq70kVR7KKKQDgJWnBomEHAMD9yG8AMBP5DQBmSjM0v82YZR6pfR3U0ktZHQs//fSTlCtXTqpVqyZVqlTRSzGpza1Vl4EqTNSoUUP+93//V1599VX9C39VyFi3bp1enkntHaGWbKpevbreh+Lsr5O1fwQQKXZ3AnPnMPzojCEXUUSWXa4l79xkeT7l4oZRnhGA/CK/Y8vq7lSru1jtXgsAWchv5IXVtYSf1QFnnTE0v82c9VmyigRZhYJvvvlGxowZo5dbUsWFmjVrSrt27eSdd97Rm1bfddddunihtGjRQhYuXCi//vqrJCQkSIkSJfR59bo+ffrk+jpZSztRkIAbfknHRrHwsowgOYs//x8aq6Lt5rRKlq99q161iM8LQDjy23l2xQeKFQDOhfxGQVF8AJyVYWh+x5lejFCyigSfffaZ3vtB7R2h9nxYvHixLkgod999t1SoUEFveH3mzJnsMb788kt9vlSpUvrxZZddpjsqzi5IxGLPCADA784Ei4QdAAD3I78BwEzkNwCY6Yyh+W1Mp4RabimruyFLVjHi/fffl/Hjx8vu3bt1F8Trr78uF198sX5u5cqVUr9+fb0nhFqG6fHHH5cbbrhBhg8fLkePHpUtW7bIyJEjs8dS/y1durTuilBf7+yvCbiFXUfEpD2r87SxNuBmZzLNuIjCWSxjB7gP+e1edh0Rj+z4Ll+bnALwJvIbkTZlzyrL8wczS1uep+MC8Fd+x5nQDZFVIDjb4cOHdWfE4MGD9d4QqsAwffp0XZCYN2+eNGzYULp16yYbNmzQr1cfz5kzRxceRowYIQ8//LD06NFD7r//fsuuCAoSAOCMjFBc2AEAcD/yGwDMRH4DgJkyDM1v13dKZHUw7NixQzZu3CjNmzfXm08rF154oe5yUPtFZO0FoYoSEydO1IWMgQMHyl/+8hf9uqxuC1WoSE1N1V0VWUs7ZT1HEQJeYNUVwcZTMI2plX6417O711ieH1HzqpjPBfAy8ts8dh0RVh0UdE8A3kV+I9KG1Gidr9dz3QH8ld+uL52o/R1uvPFGadq0qTz55JP6v6rwkJGRoZ/v1KmTFC1aVG9sXalSJf2c6oL49ttvdcEiqyCh5Cw6ZBUk1DhuKEio/TC6du0qVapU0XNZtGhRrudPnDihO0KqVq2q98to0KCBzJw507H5AkA0pQeLhB0AAPcjvwHATOQ3AJgp3dD8drRTIqtbQW08rZZLUsWFnA4dOiTPP/+8lC1bVhcZ1C/kZ8+eLcnJyVK7dm29N4SiuiHU0k1TpkyRW265ReLj4/M8h7O/plNOnjwpjRo10hts33rrrWHPJyUlySeffCJvv/22/jP75z//KX/96191EeOmm25yZM4wh11HhNX+Ewp7UMBpGYZW+uFedh0RrKUORBb57R1WOThw2/Z87VcBwBzkN9x43eF3FoB389uR38inp6fLs88+Ky+88IL88ssvuYoI6pfzpUqVyn6sigwdOnTQ5/7xj3/Ia6+9JgcPHpQFCxbopZjUL+XVWGoja6e7HQqjc+fO+rCzatUq6dmzp7Rv314/7t+/v7z88suydu1aihIAPCczaG6eA4Cfkd8AYCbyGwDMlGlofjtSlChWrJi0aNFCL0OkNqTu3r27TJgwQXcBqE2q77zzTrnvvvukQoUKekkjVYS499579Z4SgwYN0r+EV69XHQWqKKGWbfK61q1by4cffqg7KdT3vGLFCtm6dau8+OKLTk8NBrO7u2D2vi8sz/esdnWUZwT8zpR2Q5jPriOCPSiAgiG/vc2uI4IOCsB85DdM+p3F2F3rLc+PqdU0yjMC3Cfd0PyO+Z4Sav8GRe0N0bFjR3nuuefkyy+/lI8//ljvmaCWcVJ7QSxcuPD3CcbFyfz583VhYsmSJTJ8+HDdMaA6KtSG1T/99FOucb1q6tSpeh8JtYSV6ixRS1ep/TPatm3r9NQAIOIyM+PCDgCA+5HfAGAm8hsAzJRpaH7HpFMiMzNTL62kCgxZSyyVK1dObr/9dlm2bJkuMrz00kt60+pu3brJE088oQsTaukm9bnvvvuuXHnllbqLQlH7SiQkJOjz6jVt2rQxeummvBYlVPFGdUvUqFFDb4ytukZU14Ra3spKWlqaPnIKhjIlLmBmBQ2xY9cRYbWeI2s5IhpMbT+MFPLbeXYdEVP2rAo7N6RG6xjMCDAD+e3P/LbriEjeuSlf+50BcA757c/8NpVdRwT7xcGPMg3N76iWTlRBQSlSpIguSOzdu1f27dsnGRkZ+vwVV1wh1157rfz666+6IKGopZjuv/9+2blzp95DQn1ukyZNZPHixTJx4kRJSUmRjz76SBYtWiQzZ87UBQmvO3XqlIwaNUomTZqkl7NSe2morhK17JX6M7Gj/qwSExNzHbtkc0znDgAFkRmMCzv8hPwGYCrym/wGYCbym/wGYKZMQ/M7Yp0Shw4dkr59++rNq+vWravPqYKCcuDAAb0nhNqUuWbNmlK/fn2ZM2eOvuNfdTqojgfVBdCyZUv9+kaNGumOiTFjxuhfwo8bN04vWaSWcSpatKg89thjeo8Fv1Abg6tDFXZyUn++wWDQ9vOSk5MlKSkp17lbEntFbZ7wPquuiPG7v7J87aiazWMwI3hV0JB2w2ghv93LqiuCHAT+QH6T33npiLDqoKB7AnAW+U1+e4FdR4RVBwXdE/CKoKH5HbGihKoif/rppzJr1ixdYVb+85//yLPPPivXXHONLlRMmTJFNm3aJA8//LAuYDz//PO6U0Lti6A+54MPPtB7Q6ix+vXrp/dNWLlypbRr1053BKj9I8qXLy9edOLECdm+/Y8N4nbt2qU39i5btqxUr15d/xmo/TTU5uCqmKP+XN566y3dPWGnePHi+siJ1kMAJgga2n4YKeQ3AFOR3+Q3ADOR3+Q3ADMFDc3viBUlVHg/88wz8tRTT8lDDz0klStXll9++UX/4vz999/XG1mr5ZrUUbp0ad3toJZh6tOnj16uSX3O1q1b5ZJLLtHjqT0k2rdvL2vWrNG/kFd7RmQVJNSyUFldGF6xbt06XbzJklWhV/ttvPnmmzJ37lxduVcdJz///LMuTKg/7wEDBjg4a8D+TuCxu9bna+1HIKdQppkXVfhTfnOwUpFTlucfqO79JSnhfeQ38sKqK4L9JwBnkd/wMroi4GUhQ/O7wP0datmgrD0jsqhfoKtOB1WIyFqGqX///npTarUPQpabb75ZKlSoIF988YVelkh1SqjXPvnkk/p5NcaFF14oS5YskUcffTTsa3utIKGoAoz6vs8+VEEia6+NN954Q/bv36/3mNi8ebMuXHh9g28A/m0/PPsAALgf+Q0AZiK/AcBMQUPzu2hBCxJZ+xukpaXJsWPHdJFBLbv0wAMPyLRp03Qx4oILLpC7775bXnvtNVm/fr1eqkltcq32hVC/hFd7RBQrVkyqVKkiN954o/zf//2fnDx5UkqVKpXdfaG+lvrFO798B8xi1xHB2uvIkxCZD/PRGQZfIr9RQHYdEVbrgCvc9QpEGPkNn7Hr0CsRSLc8z8/2cK2QmfldoNKJKkioja1VAUJtWn3rrbfqPSKUIUOG6GWb5s2bpx83a9ZMrrvuOr1ZtbrDXxUklB07duglnlSnRIkSJXQRY8+ePdkFiZxfi4IEAPiMaj88+wAAuB/5DQBmIr8BwEyZZuZ3gTolvvzySxk8eLDujpg5c6YcP35cHnnkERk6dKhMnjxZFyjUf3v06KGLDA8++KBeskl1Q6g9ENQG2B9++KHMmDFDd0ooqqvCq/tFAPjzjoiB2/7Y6D3LjLp1YjAjeHlNxOnTp8vzzz8vBw8e1MsETp06VVq0aGH5WrVcXu/evXOdUx17p0+fjshcgD9jdTcwdwLDNOQ3Is0uB+m+BSKL/Ibf5HfPIvbNhJfze7oD2V2gTgm1xJLqbFCbV3fq1Elat24t5cqV0xtar169Wm9avXPnTvnHP/6hX9+qVSvp0qWLbNy4UX744Qf9eeobuOuuu8LGpiABAAgEw4/8Uh17au+dMWPGyIYNG/SFVV2zVKefHbUH0oEDB7IP1cEHAMg78hsAzER+A4A/83ueQ9ldoE6Jpk2bSps2bXThYfjw4fLJJ5/IHXfcobsfVLFB7Q1xzz33yEsvvaSXdlIFi+7du+uNq2+//XYZNmxY9lhqM2eWZwJg1RVh1T1h91p4TAQq/ZMmTZJ+/fplV/BVZ99HH30ks2bNkpEjR1p+jroeVapUqdBfG4jU3cCspQ7jkN+IEbuOCKs7WbmLFcgD8hs4J7tryax9n4ed61OtTQxmBEQmv53K7gJ1Spx//vm6LePpp5/Wyy19/vnn8sorr+g9JlQXxHfffacLD6prYvny5fpzrr/+er3/xAsvvJC9QXbWNwEAQE6BzEDYkR9nzpyR9evXS4cOHXLtUaQeq2uTnRMnTkiNGjWkWrVqetlBdT0DAOQd+Q0AZiK/AcB/+X3GwewuUKeE8tVXX8mCBQtk9uzZctlll+l1o9TyTPv375dXX31VpkyZIq+99lr2+lNq/wm15JPaCHvs2LGSmJhY0C8NwCfsOiIm7bEOxqQaraI8I8RMKPyUKmZnFbSzqAK5Os525MgRXTSvWLFirvPq8ebNmy2/ZL169fSdAA0bNpRjx47JxIkT9fKE6uJatWrVwn5HQIGwljqMQ37DhXeyPrt7jeVrR9S8KgYzAgxBfgMFYtUVwf4TMCW/jziY3QXqlFCuuOIKSU9Pl6+//lqvGzV//ny5/PLLZdy4cVKrVi1dVenTp4+ULVs2+3PUUk7jx4+X+Ph4vWwT/pCSkiLNmzeXMmXK6AJOt27dZMuWLdnP7969W3eVWB3qzx4AvF7pVzmpCto5D3UuUtT+Rz169JDGjRtLu3btdOH9wgsvlJdffjliXwMAvI78BgAzkd8AYKZAjPM7Utld4E6JEiVKyGOPPaa7IVRXhNqgWu3MrfaOyCnnnhEXXXSR7VpUfrdy5UoZNGiQLkxkZGTIqFGjpGPHjvL9999LqVKldDuM2jgkJ7VkltoZvXPnzo7NG3CCXUdE8s5NludTLm4Y5Rkh0gKZ4eeSk5P15ks5Wd2lpZQvX15fl3788cdc59XjvK57WKxYMbnyyitl+3brvU0AJ9l1RMze94Xl+Z7Vro7yjIDfkd9wI7uOCH52BP5AfgORY9cRwX5xcFt+l3cwuwvcKaGoX5ynpqbKe++9p3fkzipIBIPB7E4I9ozIm6VLl0qvXr30Ulhql3O1YfjevXv1ul6K+gui/jLkPBYuXCh33nmnlC5d2unpA0DUK/3qApqQkJDrsPufItWR17Rp0+x9jbKuTeqxqurnhWph/Oabb6Ry5coR+74AwOvIbwAwE/kNAP7L73gHs7vAnRJZateurQ9F3eFftGhRvXQTCketyaXkXP4qJ1WsUHt4TJ8+PcYzA9zL7q42q7vguAPO3QLBwo+h7gro2bOnNGvWTO9vNHnyZDl58qT07t1bP6/aDVUHX1YLo1p+sGXLllKnTh05evSo7kRTyxP27du38JMBYsSuI8JqPXXWUkc0kN/w6s+O53o94AXkNxB9dh0R7EEBJ/PbqewudFEi12BFIzqcb6mK1NChQ+Xqq6/W+3RYef311+XSSy/VG4kAgB/aD/NLde8dPnxYRo8eLQcPHtTrHaqutKwNnFQ3Ws4i+i+//CL9+vXTr73gggv03QKrVq2SBg0aFH4yAOAT5DcAmIn8BgB/5nd3h7I7EGLHadcZOHCgLFmyRD7//HPLXctPnTqlW2KeeOIJefjhh23Hsdpp/ZbEXhIXKBKVeQMmYS3H6EkNzi/0GPWeejHs3JYnholfkN+IhfG7v7I8f1GRM5bn2ZfC+8jvwiO//Zebdnv8ALFEfhce+Q3ACak+zm/WWXKZwYMHy+LFi+XTTz+1LEgoag+P3377TbfPnIvVTuu7ZHOUZg4AkW0/PPvwE/IbgKnIb/IbgJnIb/IbgJkChuY3nRIuod6GBx98UG9evWLFCqlbt67ta9u3b693R1fFiXOh0g/kn9W66wprr8e20n/p6PBK/3/Gub/SHynkNwAnkN+FR377D923cAPyu/DIb5jSoZcesr6/nP0nzJTq4/xmEwiXGDRokMyZM0c++OADKVOmjF6XS1HV+ZIlS2a/bvv27fLZZ5/Jxx9//Kdjql3Vz95ZnQsqAL+saWsy8huAqchv8huAmchv8huAmQKG5jdFCZeYMWNGdhdETm+88Yb06tUr+/GsWbP0sk4dO3aM+RwBP7DriBi4bbvl+Rl160R5Rv5kSrsh4CfkIPKC/Ibf2HVEJO/cZHk+5eKGUZ4RUDDkN+A++dm3iFUf/CtgaH5TlHCJvK6iNX78eH0AgJeZWukHAL8jvwHATOQ3AJgpYGh+U5QAgDywuxPYah1h1hD270UV8DJyEHlBfgPn7oiwWh88v3fDAtFAfgNms+uImLJnleX5ITVaR3lGiJWAoflNUQIA4DqBvDWPAQBchvwGADOR3wBgpoCh+U1RAgAKwepu4LG71lu+dkytpjGYkTeYWukH/MgqB7kT2L/Ib+Dc7HLw5b2fh517oHqbGMwI+B35DXiTXUfEpD2rw84l1WgVgxkh0gKG5jdFCQCIMLvig9USJwrLnHjnogrg3L90YwM+7yO/gYKxKkBY/cJI4ZdGiAbyG/AXq2sJN1iaKWBoflOUAAC4TiDo9AwAAAVBfgOAmchvADBTwND8pigBADFi1xHB3QjeqfQDODe7jghy0DvIbyBy7DoiyExEA/kNwO46krxzk+X5lIsbRnlG8HJ+xzk9AYjMmDFDGjZsKAkJCfpo1aqVLFmyJNdrVq9eLddee62UKlVKv6Zt27Zy6tQpx+YMANEUlxkKOwAA7kd+A4CZyG8AMFOcoflNp4QLVK1aVSZMmCB169aVUCgks2fPlptvvln+/e9/y2WXXaYLEjfccIMkJyfL1KlTpWjRovL1119LXBw1JcDLdyMM3LY97NyMunXED0xtPwQQ2Ry0uhu4QbF0y9feUbVlxOeF/CO/gejjTlZEA/kNwA7XEXcLGJrfFCVcoGvXrrkeP/PMM7p74ssvv9RFiWHDhslDDz0kI0eOzH5NvXr1HJgpAMSGqe2HAOB35DcAmIn8BgAzBQzNb4oSLpOZmSnz58+XkydP6mWcDh06JGvWrJF7771XWrduLTt27JD69evrwkWbNm2cni6AKLLqivDLGsJxhl5UAUSW17LND8hvwH13so7f/VXYuVE1m8dgRjAJ+Q0gv57dvabQe8vBv/nN+j8u8c0330jp0qWlePHiMmDAAFm4cKE0aNBAdu7cqZ9/8sknpV+/frJ06VJp0qSJXHfddbJt2zanpw0AURHIDIUdAAD3I78BwEzkNwCYKWBoftMp4RJqOaaNGzfKsWPH5L333pOePXvKypUrJRj8fWGwBx54QHr37q0/vvLKK2X58uUya9YsSUlJsR0zLS1NHzkFQ5kSFygS5e8GQKzvGn5kx3eW5yfWvkxMZGr7YaSQ30D+sZa6O5Df5Dfcx6orgszE2chv8hvIr/x0P1h17Sl07vk3v+mUcIn4+HipU6eONG3aVBcaGjVqJFOmTJHKlSvr51XXRE6XXnqp7N2795xjqnESExNzHbtkc1S/DwCIhLjMUNjhJ+Q3AFOR3+Q3ADOR3+Q3ADPFGZrfdEq4lOqQUFX6mjVrSpUqVWTLli25nt+6dat07tz5nGMkJydLUlJSrnO3JPaKynwBOMuuI2Lgtu153q/CTUxpN4wW8hvIP7u7e/2yF49bkN/kN8xAZuJs5Df5DUSTXUfEpD2rLc8n1WgV5Rl5R8DQ/KYo4ZKLnyowVK9eXY4fPy5z5syRFStWyLJlyyQQCMjw4cNlzJgxunuicePGMnv2bNm8ebNe5ulc1P4U6siJ1kMAJgj8vnKdb5HfAExFfpPfAMxEfpPfAMwUMDS/KUq4wKFDh6RHjx5y4MAB3SLYsGFDXZC4/vrr9fNDhw6V06dPy7Bhw+Tnn3/WxYnU1FSpXbu201MH4HJ2HRFW6zm6aS3HQIaZlX4A7mN3d++zu9cUal1cWCO/AW9mJneyeh/5DcAJdtcRU1d9cELA0PymKOECr7/++p++ZuTIkfoAAD8wZQ1EAEBu5DcAmIn8BgAzxRma3xQlAMCHrLoiknduyteaw9EUCJp5UQVgDquuiEd2fJevfXsQjvwG/HUnq1X3rds6cJE35DcAN7HriLDa+8jv+x4FDM1vihIAANcxtf0QAPyO/AYAM5HfAGCmgKH5TVECAHDOjggnOigCmYbu1ATAaHYdEdwJnHfkN+AvdjnInazmIb8BmMDqWmJ1zbF7rRcFDM1vihIAANcJGLomIgD4HfkNAGYivwHATAFD85uiBADgnOw6IgZu2x61r2lqpR+Av+4Etuug2Jd+QZ7XxfUa8huA3d2p7NvjbuQ3AFP5pSPCa/lNUQIA4DqBDDMvqgDgd+Q3AJiJ/AYAMwUMzW+KEgCAArG76/fWSFwPDW0/BOAv7ClhgfwGYMOuI+LZ3Wssz4+oeZW4gdvnFzHkNwCPmbJnleX5o8Hi3uq4yDQzv+OcngDCTZgwQQKBgAwdOjT7XPv27fW5nMeAAQMcnScAREsgMzPsAAC4H/kNAGYivwHATAFD85tOCZf56quv5OWXX5aGDcPXcO/Xr5+MGzcu+/F5550X49kBQGyY2n4IAHbs9p/wWrcF+Q0gv+w6DtyyB4Xd/F7e+7nl+QeqtxETkd8AvGZIjdb5er3VdceEfY8ChuY3nRIucuLECbn33nvl1VdflQsuCN8gUR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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"num_actions = env.B[0].shape[-1]\\n\",\n \"base_labels = [\\\"Up\\\", \\\"Right\\\", \\\"Down\\\", \\\"Left\\\", \\\"Stay\\\"]\\n\",\n \"action_labels = base_labels[:num_actions]\\n\",\n \"\\n\",\n \"row_labels = []\\n\",\n \"for agent in agents:\\n\",\n \" alpha_value = float(agent.alpha.mean(0).squeeze())\\n\",\n \" row_labels.append(f'alpha={alpha_value:.2f}')\\n\",\n \"\\n\",\n \"\\n\",\n \"fig, axes = plt.subplots(len(agents)+1, num_actions, figsize=(16, 8), sharex=True, sharey=True)\\n\",\n \"\\n\",\n \"\\n\",\n \"for i in range(num_actions):\\n\",\n \" for j, agent in enumerate(agents):\\n\",\n \" sns.heatmap(agent.B[0][0, ..., i], ax=axes[j, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" sns.heatmap(env.B[0][..., i], ax=axes[-1, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" axes[0, i].set_title(action_labels[i])\\n\",\n \"\\n\",\n \"for j, label in enumerate(row_labels):\\n\",\n \" axes[j, 0].set_ylabel(label, rotation=25, labelpad=60, ha='left', va='center')\\n\",\n \"axes[-1, 0].set_ylabel('true B', rotation=0, labelpad=40, ha='left', va='center')\\n\",\n \"\\n\",\n \"\\n\",\n \"fig.tight_layout()\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Here, the agents have to learn A matrix, with B matrix being fixed to the true observation mapping of generative process, and precise (and accurate) prior over initial hidden states\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"C = [jnp.zeros((batch_size, num_obs[0]))]\\n\",\n \"pA = [jnp.ones_like(a) / a.shape[0] for a in env.A]\\n\",\n \"_A = jtu.tree_map(lambda a: dirichlet_expected_value(a), pA)\\n\",\n \"B = [jnp.array(b) for b in env.B]\\n\",\n \"D = [jnp.array(d) for d in env.D] \\n\",\n \"\\n\",\n \"agents = []\\n\",\n \"for i in range(5):\\n\",\n \" agents.append( \\n\",\n \" Agent(\\n\",\n \" _A,\\n\",\n \" B,\\n\",\n \" C,\\n\",\n \" D,\\n\",\n \" E=None,\\n\",\n \" pA=pA,\\n\",\n \" pB=None,\\n\",\n \" policy_len=3,\\n\",\n \" use_utility=False,\\n\",\n \" use_states_info_gain=True,\\n\",\n \" use_param_info_gain=True,\\n\",\n \" gamma=jnp.ones(batch_size),\\n\",\n \" alpha=jnp.ones(batch_size) * i * .2,\\n\",\n \" categorical_obs=False,\\n\",\n \" action_selection=\\\"stochastic\\\",\\n\",\n \" inference_algo=\\\"exact\\\",\\n\",\n \" num_iter=1,\\n\",\n \" learn_A=True,\\n\",\n \" learn_B=False,\\n\",\n \" learn_D=False,\\n\",\n \" batch_size=batch_size,\\n\",\n \" learning_mode=\\\"offline\\\",\\n\",\n \" )\\n\",\n \" )\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Run multiple blocks of active inference on grid world for each batch of agents that was initialized different `alpha` values. \\n\",\n \"\\n\",\n \"#### Since the agents are using offline learning (`learning_mode = \\\"offline\\\"`), this means that parameter updates to the A matrix are performed at the end of each block.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"pA_ground_truth = 1e4 * env.A[0] + 1e-4\\n\",\n \"num_timesteps = 50\\n\",\n \"num_blocks = 20\\n\",\n \"key = jr.PRNGKey(0)\\n\",\n \"block_and_batch_keys = jr.split(key, num_blocks * (batch_size+1)).reshape((num_blocks, batch_size+1, -1))\\n\",\n \"\\n\",\n \"divs = {i: [] for i in range(len(agents))}\\n\",\n \"for block in range(num_blocks):\\n\",\n \" block_keys = block_and_batch_keys[block]\\n\",\n \" for i, agent in enumerate(agents):\\n\",\n \" init_obs, init_states = vmap(env.reset)(block_keys[:-1])\\n\",\n \" last, info = jit(rollout, static_argnums=[1, 2])(agent, env, num_timesteps, block_keys[-1], initial_carry={\\\"observation\\\": init_obs, \\\"env_state\\\": init_states})\\n\",\n \" agents[i] = last['agent']\\n\",\n \" divs[i].append(kl_div_dirichlet(agents[i].pA[0], pA_ground_truth).mean(-1))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Plot the KL divergence between the true parameters and believed parameters over time for the different groups of agents (agents with different levels of action stochasticity)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig, axes = plt.subplots(1, 1, figsize=(10, 5), sharex=True, sharey=True)\\n\",\n \"for i in range(len(agents)):\\n\",\n \" p = axes.plot(jnp.stack(divs[i]).mean(-1), lw=3, label=agents[i].alpha.mean())\\n\",\n \" axes.plot(jnp.stack(divs[i]), color=p[0].get_color(), alpha=.2)\\n\",\n \"\\n\",\n \"axes.legend(title='alpha')\\n\",\n \"axes.set_ylabel('KL divergence')\\n\",\n \"axes.set_xlabel('epoch')\\n\",\n \"fig.tight_layout()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Visualize the learned A matrices alongside the true environmental parameters after training\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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aLV3khm7i7GbYhm/yRTQrnTvB6Nrnlk5ezySv5xN3N8GM2eT2fvJBNrHsB26T76LrOjtJKEe3fv19PraSmc1KbMn/+fL0uhVq3Qk3tlJcqWKjCg6oSf/PNN3rNipSUFN3VoBbnvuaaa3SxIC9VsFDvUWJVsFi8eLEuqKg1NzZt2iSjRo2SRo0aSf/+/V1fr4osasvLpg8PwC+OZfui6S0X2QTYgWwimwBTkU/kE2AisolsAkx0zNJs8kXRokSJEvLtt99Khw7H7+bo1q2b3HjjjXL//fdL9+7ddYEib5eE2i666CI9/VPLli3lggsukFWrVukFsSdPnixlypQJ+zqx7q44cOCApKam6iKKmorqqquu0t0j6vvzKufdgdzdDC+ypTUPJ86dV3aE3qVzvcvaGIBNyCZvnDvReQEvIp/sP3fiug5eRDbZx62rYqbjus5tzUPAJhmWZpOdR30Szo6H3bt3S/PmzWXp0qV6SijVraCeU4toqzUqVAfDtddem/seVRxQRYxzzz1XZs2apaeH+uqrr/Ti3FdeeWXCvi91jDnHCcA7bP0AAeBtZBMAU5FPAExENgEwUYal2WTnUedDrSuhpnbKKVb89NNPUqlSJalVq5bUrFlTT/WkFt9WXQqqcFGnTh35+9//LtOnT9fFAFXsWLNmjZ7+Sa1doaaEql27tl4Hw/l1ctavQHy53X3jnIOQ+Qdhm6OWfoBATthZwfyosB3Z5A3OzorJ28KzaWgdsgl2IZ+8eV3nzCeyCbYhm7zB2VnBmjyw3VFLs8nOSa0cVBFBUYUEVbBQXRH/+Mc/pGnTprJ161YpW7asdOzYUb7//nvdNaGo4obSpk0bOXTokPz222/6vaVLl9b7c17n1sFBwQJANGVmFwvbACDRyCYApiKbAJiIcycAJsq0NJvsLLU4Oh5yigiffPKJjB07VtatWyeXXXaZvPfee1K3bl39XM+ePSU9PV0vyK0KGiVLltT7V65cKVWrVtWFDeXss8/WHRnlypWL+5oViIzzzuVZO0PnblauS2H+ZpjrqCUfGCgct66KR7euCnl8Z93z4nhEQOGQTd7kducydzfDNuSTNzmz5+Gtn4e95q66reN4REDhkE3e5OysSNu5POw1vVLax/GIAH9kkzX/Cq+mc3LKKVa89dZberFstd5E48aN5T//+Y+89tprek2KZcuWyY8//qgLE2qap23btskll1wiCxculNdff102btwoV199de5Y6v+qYKG6Kty+JgBE29GsYmEbACQa2QTAVGQTABNx7gTAREctzabitq1Tkde+ffv0WhQbNmzQBQm1sHblypX1c7Nnz5Zx48bJjh07JC0tTbp27Srdu3eXM844Q2677Ta58847Zf/+/fo9119/fdjYdFXYy62r4qbvN4U8frZB/TgeEXBimUHyxi+cnRXOu3S4QwcmIZv8e3fzKzs+O+m6PUAikU/+4NZVMW176NzyN9ZmbnmYg2zyB7drNtZahckyLc0m44sWOR0QmzdvlvXr10vr1q314thKlSpVZPTo0Xq9ipy1KKZMmSKPP/647pS46aab5F//+pd+naI6J9Q6F2qaKLXWRc7UUTnP5axzAe9xFinu37I27DVjT28ZxyMCjrOlyo3Yn/A6L8QVLsaRKGSTf7kVKGY6ChnORSqBeCKf/Mt5XsQCuTAJ2eRfziKFs4jh9hogXo5amk3Gl1rU+hJqfQo1/dN9992n/68KE5mZmfr5Ll26SPHixfVaFtWrV9fPqS6Kr7/+Whc0cgoWSt6iRE7BQo1jQsFCrcfRrVs3qVmzpj6WefPmhTyvFgsfOnSopKSkSJkyZfQ0WFOnTk3Y8QKInmPZxcI2AEg0sgmAqcgmACbi3AmAiY5Zmk0J7bTI6XY4evSono5JFR/y2rt3rzz22GNSsWJFXYRQ/2A/c+ZMSU1NlXr16um1KRTVTaHWppg0aZJe1yJnke2CcH7NRDl8+LA0a9ZMBgwYoBcKdxo5cqR89NFH8uqrr+qf2QcffCA333yzLnJcfvnlCTlmm7l1VbAIJRIlK9v4+jHixK2rYsK2FSGPR9YJnwIPiAWyCSfqrHDe3axwhzPihXxCfrnj7ApT6AxDvJBNOFFXBVNIIVGyLM2mhPyL/bFjx+TRRx+VJ554Qn755ZeQIoP6x/uyZcvmPlZFiM6dO+t97777rjz//POyZ88eefvtt/VUT+of7dVY1apVS3i3RFGoNTfUlp/ly5dL3759pVOnTvrxDTfcINOmTZPVq1dTtAAsl5ll5wcIAG8jmwCYinwCYCKyCYCJMi3NpoQULUqUKCFt2rTR0xypBbN79OghjzzyiO4iUAtlq8W1//nPf0rVqlX1lEmqSNG7d2+9psWQIUP0P9Kr16uOBFW0UNNCeV379u3lnXfe0Z0Y6nteunSpfPfdd/Lkk08m+tA8w9lZQRUc8WJLax4Sw9lZwR2EiBeyCSfi1lXBuheIF/IJ+XHLHbIJ8UI24USc/6bEeoaIl2OWZlPcSy1q/QhFrU1x8cUXy7///W9ZuXKlLFiwQK/ZoKaJUmtRzJ07988DTEqSOXPm6MLFwoULZdSoUbrjQHVkqAW1f/rpp5Bxverpp5/W61ioKbJUZ4qaGkut33H++ecn+tAAFFF2diBsA4BEI5sAmIpsAmAizp0AmCjb0myKS6dFVlaWnrpJFSBypnCqVKmSXH311bJ48WJdhHjqqaf0otrdu3eXe++9Vxcu1NRQ6r1vvPGGnHvuuboLQ1HrWlSoUEHvV6/p0KGD1VNDFbRooYo7qtuiTp06euFu1XWiui7U9FluMjIy9JZXdjBLkgJ2VtgSXQWftG152GuG1WkfxyOCV9naqhcpsqlo3O4OdN6lwx06iAayiWwqaj6RTYgV8ol8Kko20bWKWCGbyKbCcDsvojMMsZBpaTbF9KhVwUEpVqyYLlhs375dduzYIZmZmXr/OeecI3/729/kt99+0wULRU31dP3118sPP/yg17BQ723RooW899578vjjj8v48ePl/fffl3nz5snUqVN1wcLr/vjjD7nrrrtkwoQJerostZaH6kpR02qpn0l+1M8qOTk5ZNsiG+J67AAKtiiSc/MysgmwA9lENgGm8lM2KeQTYAfOncgmwERZlmZT1Dot9u7dKwMHDtSLazdo0EDvUwUHZffu3XpNCrVodN26daVRo0aSlpamOwZUp4TqmFBdBG3bttWvb9asme64GDt2rP5H+gceeEBPiaSmiSpevLjcfffdeo0Hv1ALl6tNFX7yUj/f7OzsfN+XmpoqI0eODNl3ZXK/mB2n17l1VTi7L+i8QCSClrTmRQvZFPu7dJgfFdFANpFNReXMHed6YQprhiES5BP5VBRudy5Pd5w7DeK8CREgm8imoqJrFbEQtDSbola0UBXVjz/+WGbMmKGrrcp///tfefTRR+WCCy7QhYxJkybJl19+KbfddpsucDz22GO600Kty6DeM3/+fL02hRpr0KBBet2GZcuWSceOHXVHgVq/onLlyuJFhw4dkk2bNuU+3rJli154vGLFilK7dm39M1DreajFy1WxR/1cXn75Zd19kZ9SpUrpLS/a9ADzZFnaqhcpsgmwA9lENgGmIp/IJ8BEZBPZBJgoy9JsilrRQgXVuHHj5MEHH5Rbb71VatSoIb/88ov+h/W33npLL7StpoNSW7ly5XS3hJrmacCAAXo6KPWe7777Ts4880w9nlrDolOnTrJq1Sr9D/ZqzYqcgoWadiqni8Mr1qxZo4s7OXKq1Wq9j5deeklmzZqlq9iqY+Xnn3/WhQv18x48eHACjxrOzgrmR0Ukgll2Vr1hLrc7cOgMQ2GRTYg2t64KZ/cFnRcoCPIJ0ebsrJixI7xrdUAt7nDGiZFNiPV1XdrO8LVWe6VwXQdvZlPEpRY1LVHOmhU51D+wq04JVajImebphhtu0Itmq3UYclxxxRVStWpV+eyzz/S0R6rTQr32vvvu08+rMapUqSILFy6UO+64I+xre61goagCjfq+nZsqWOSs9fHiiy/Krl279BoXGzZs0IUNry9ADvilVc+5AUCikU0ATEU2ATAR504ATBS0NJuKR1qwyFlfISMjQw4cOKCLEGpapxtvvFEmT56sixWnnnqq9OzZU55//nlZu3atngpKLcKt1qVQ/0iv1qgoUaKE1KxZUy677DJ55pln5PDhw1K2bNnc7g31tdQ/zPOP87CBW1dF6g9fhjwef8bxAh6gBC1ZBAl2c3ZWMHczToZsQjw4Oyu4gxAFQT4h1ty6KugMw8mQTYg1t3Mi57kT503wSjZFdNSqYKEW3lYFCrWo9j/+8Q+9RoUybNgwPS3U7Nmz9eNWrVrJhRdeqBfTVh0CqmChbN68WU8hpTotSpcurYsc27Ztyy1Y5P1aFCwAeJpq1XNuAJBoZBMAU5FNAEzEuRMAE2XZmU0RdVqsXLlShg4dqrsrpk6dKgcPHpTbb79dhg8fLhMnTtQFDPX/Pn366CLELbfcoqeEUt0Uag0GtUD3O++8I88++6zutFBUV4ZX16uAvzk7KyZsWxH2mpF12sXxiGCaYHbRx5gyZYo89thjsmfPHj3d3tNPPy1t2rRxfa2adq5///4h+1Rn25EjR4p+ILAGczcjHtmkkE8oDLe7A51rhrFeGDh3QiI4Oyuc506cN4FsggnnTq+4rLV6PedOvha09Louok4LNYWT6oxQi2t36dJF2rdvL5UqVdILbq9YsUIvqv3DDz/Iu+++q1/frl07ufTSS2X9+vWyc+dO/T518Nddd13Y2BQsAPhNICsQthWG6mxTa9yMHTtW1q1bpz88VDarjrj8qLWGdu/enbupTjcAiGY2KeQTgFggmwCYiOs6ACYKWHpdF1GnRcuWLaVDhw66MDFq1Cj56KOP5JprrtHdE6oYodam6NWrlzz11FN66ihV0OjRo4deWPvqq6+WESNG5I6lFptm+if4iVtXBXfp+FwRW/MmTJgggwYNyq1iqw64999/X2bMmCGjR492fY/K3erVqxfp68Jb3HKHdS98Lgptw+QTosHZWcEdhODcCSaeO9G1CrIJJnA7J3KeO3He5DNZdl7XRdRp8Ze//EW3dDz00EN6OqdPP/1UnnvuOb3Gheqi+Oabb3RhQnVdLFmyRL/noosu0utfPPHEE7kLeOd8AwDgZ0Wpeh89elTWrl0rnTt3DlkLSD1WGZyfQ4cOSZ06daRWrVp6+j6V2wAQzTtyyCcAsUI2ATAR13UATBSw9Louok4L5fPPP5e3335bZs6cKWeffbaek0pN/7Rr1y6ZPn26TJo0SZ5//vncua3U+hdqSim1UPf9998vycnJkX5pwHOcd+C8tXNVyOOrUs6L8xEhroLhu1RhN6e4m0MVi9WW1/79+3XxuFq1aiH71eMNGza4frmGDRvqanjTpk3lwIED8vjjj+tp/tQHSEpKSjS+I3iEs7Nizs6VYa+5JqVtHI8ItmSTQj4hVtzuDnTmE9nkr3wim2ACt64Krut8hus6WHLuxHWdzwTDd9lw7hRRp4VyzjnnyLFjx+SLL77Qc1LNmTNHmjRpIg888ICcfvrpuuIyYMAAqVixYu571FRRDz/8sJQsWVJPC4Xjxo8fL61bt5by5cvrAk/37t1l48aNuc9v3bpVd6W4bepnD8BeblVvlQmquJt3U/uiQa0z1KdPH2nevLl07NhRF6CrVKki06ZNi8r4ALwh3tmkkE8ACoJsAmAirusAmChg6XVdxJ0WpUuXlrvvvlt3U6iuCrWAtlo1XK1dkVfeNStOO+20fOe58rtly5bJkCFDdOEiMzNT7rrrLrn44ovl22+/lbJly+pWGrVoSV5qSi61anvXrl0TdtyIDecdOGk7l4e9pldK+zgeEWIpkBW+LzU1VS9ylJdbxbty5co6f3/88ceQ/epxQecOLFGihJx77rmyadOmwh46fMbt7hvW5PGuomSTQj4hkfnEmjz+yieyCabius5fuK6DLbiu85eApdd1EXdaKOof1tPT0+XNN9/Uq4XnFCyys7NzOylYs6JgFi1aJP369dNTbakV2NWC5tu3b9dzhinqD4f6g5B3mzt3rlx77bVSrly5RB8+gCIIZIdv6sOiQoUKIZvbB4jqXGvZsmXu+kE5Gaweq8p2Qag2v6+++kpq1KgR1e8LgH+zSSGfAMQK2QTARFzXATBRwNLruog7LXLUq1dPb4rqEChevLieGgpFo+b7UvJOr5WXKmaoNUSmTJkS5yNDIrjdfUMV3DsKuwiSk6qO9+3bV1q1aqXXEZo4caIcPnxY+vfvr59XLXmq0y2n1U9N49e2bVupX7++/Prrr7pjS03zN3DgwKh8P/AXZ/ZMc9zdrNzIHc6+zCaFfEKiODsrZu74LOw1fV3WxoAdOHeCl67rntkemk831yabbEU2wUvXdZO2hXaGDatDV5itApZe1xW5aBEyWPGoDudbqlo1fPhw+etf/6rXCXHzwgsvyFlnnaUXMQHgvVa9wlBdbvv27ZMxY8bInj179JyBqnsrZ5Ek1bWVt5j8yy+/yKBBg/RrTz31VF0xX758uTRu3Lio3woADylqNinkE4BY4NwJgInIJgAmClh6XRcIsiK2cW666SZZuHChfPrpp64rqv/xxx+6nebee++V2267Ld9x3FaCvzK5nyQFisXkuJFYzrmbFeZvjr/07DmFfk/DB58M27fx3hHiVWST/zy6dVXI4zvrhs7vjNgjm06ObPIf1r2wM5vc8snL2aSQT/7i7KhX6Kq3M5u8nk9kk7+84tK1ej1dq3GX7qPrOuZxMszQoUPlvffek48//ti1YKGoNUR+//133XpzIm4rwW+RDTE6cgDRnF/Qy8gmwA5kE9kEmMpP2aSQT4AdOHcimwATBSzNJjotDKF+G2655Ra9uPbSpUulQYMG+b62U6dOeuV2Vbw4EaremLBtRcjjkXUKtkAO4lv1PmtMeNX7vw+YX/WOFNkE1uSJP7Lp5MgmcAehPXczO/PJy9mkkE/gus7ObPJ6PpFNeHjr5yGP76rbOmHH4hfpPrquYxEKQwwZMkTS0tJk/vz5Ur58eT3nl6Iq1WXKlMl93aZNm+STTz6RBQsWnHRMteq7c+V3PjwA89hS5Y4WsgmwA9lENgGmIp/IJ8BEZBPZBJgoYGk2UbQwxLPPPpvbRZHXiy++KP369ct9PGPGDD1t1MUXXxz3Y4R9nHfgTN4Wegfh0DrcPeiVRZEAmzg7K1iTx0xkE/zGrauCdS/MRD7B79d1dF6YiWyC3zg7K5z/5qTw706JF7A0myhaGKKgs3Q9/PDDegPgHbZ+gADwNrIJgKnIJwAmIpsAmChgaTZRtAB8xFnh5u5mM9jaqgdEi1vuPLM99C6dm2tzh068kU1AeD5x7mQG8gl+5+ysmOaSTTeSTXFHNsHv3LoqnPlENsVfwNJsomgBAAlm6wcIAG8jmwCYinwCYCKyCYCJApZmE0ULwMfc7gxM27k85HGvlPZxPCJ/srVVD4glZ2fFzB3h86P2dZl/HtFDNgEFO3easePTE67bg+gjnwA56Z3LrzjOndzW7UF0kU3AyfPJed6kcO4UWwFLs4miBQAkmK1VbwDeRjYBMBX5BMBEZBMAEwUszSaKFgBO2Fnh7Lxwew38WfUG4smtq4L5UWOLbAIKxnl3oHPdC9a8iD7yCTg5Z2cF13WxRzYBJ+fWVcGMH7EVsDSbKFoAQILZ+gECwNvIJgCmIp8AmIhsAmCigKXZRNHCAM8++6zetm7dqh+fffbZMmbMGOnatWvua1asWCF33323rFq1SooVKybNmzeXxYsXS5kyZRJ45PADtwq3c2555pUvmqSsYKIPAbCSs7Pi9s3fhDx+vN7ZcT4ibyGbgMg4OyucXWEKnWFFQz4B0bmum7VzRcjj61LaxfGIvIdsAqKTT6wXFl22ZhNFCwOkpKTII488Ig0aNJBgMCgzZ86UK664Qv7zn//oAoYqWFxyySWSmpoqTz/9tBQvXly++OILSUpKSvShw6ecRYrJ28IXyB1ah0KG1+cXBEzjLFI8vPXzsNfcVbd1HI/IbmQTEB1uBYpntoeeO91cm/OmwiCfgOhwFimc2aSQTwVHNgHR4SxSvOK4cdZtCjx4L5soWhigW7duIY/HjRunOy9WrlypixYjRoyQW2+9VUaPHp37moYNGybgSAHEgq2tegC8jWwCYCryCYCJyCYAJgpYmk0ULQyTlZUlc+bMkcOHD0u7du1k7969ekqo3r17S/v27WXz5s3SqFEjXdjo0IH2KJjBrauCdr6CS7L0AwQwnVtXBdlUcGQTEDvOO5edU28qTL+ZP/IJiA23ropJ20IXyB1WhwVy80M2AbHh1lXhnPGD2T68l03ML2SIr776SsqVKyelSpWSwYMHy9y5c6Vx48byww8/6Ofvu+8+GTRokCxatEhatGghF154oXz//feJPmwAURDIDoZtAJBoZBMAU5FNAEzEuRMAEwUszSY6LQyhpntav369HDhwQN58803p27evLFu2TLKz/5x47MYbb5T+/fvrX5977rmyZMkSmTFjhowfPz7fMTMyMvSWV3YwS5ICxWL83QDhdy8/unVVyOM7654X5yMyVyBTfIVsgknZxAK5+SObyCbEj1tXhTOfyKbjyCfyCfHj7KxgTZ78kU1kE+LH2Vkx3eW6bhDnTlZnE50WhihZsqTUr19fWrZsqQsRzZo1k0mTJkmNGjX086rrIq+zzjpLtm/ffsIx1TjJyckh2xbZENPvA0DhJWUFwzYvI5sAO5BNZBNgKj9lk0I+AXbg3IlsAkyUZGk20WlhKNVhoSrWdevWlZo1a8rGjRtDnv/uu++ka9euJxwjNTVVRo4cGbLvyuR+MTle4GScnRXc3Xxc4M+GKt8gm2ASt9xxzi3v13nlySayCWblE50Xx5FP5BMSx9lZ4ZxX3s9zy5NNZBMSx62rgvUM7c4mihaGBL0qQNSuXVsOHjwoaWlpsnTpUlm8eLEEAgEZNWqUjB07VndfNG/eXGbOnCkbNmzQ00idiFofQ2150aYHmCdgSZU7WsgmwA5kE9kEmIp8Ip8AE5FNZBNgooCl2UTRwgB79+6VPn36yO7du3U7XdOmTXXB4qKLLtLPDx8+XI4cOSIjRoyQn3/+WRcv0tPTpV69eok+dCBibncHvuK4u/l6n9zdHMi08wME8CpnZ4XzDh2/3KVDNgFmnzs5u8L81BlGPgHmcOuq4LoOgAmc12xc19mFooUBXnjhhZO+ZvTo0XoD4D2BbDs/QAB4G9kEwFTkEwATkU0ATBSwNJsoWgAwhvMOHOcdOm6v8QJbFkEC/Mrt7pvpjrnl3eZQtR3ZBJjNravCL2vykE+A2ZzXbH7pDCObAPuu6/yw7kWSpdlE0QIAEszWVj0A3kY2ATAV+QTARGQTABMFLM0mihYAjOXWVTFr54qQx9eltBPb2dqqB/iZs7NiwrbQbBpZh2wCEH/OO5edXWFe6QwjnwC7+KUzjGwCvLfuhRc6LwKWZhNFCwBIsEBmdqIPAQDCkE0ATEU+ATAR2QTARAFLs4miBQCrODsr0nYuD3tNr5T2YpNAlp0fIADy76yYvC187uahdey6g5BsAuzn1lXhhbubySfAfn1Psp6hjWsZkk2A/ZydFfybU+JQtACABAtYuigSAG8jmwCYinwCYCKyCYCJApZmE0ULAFZzq3Cn/vBlyOPxZzQVo1naqgcgf25dFdMcc8vfaPq88mQT4Iu7m53ZpJBPAOLN2Vnh7AqzojOMbAJ88W9O1q17kWlnNiUl+gAQ7pFHHpFAICDDhw/P3depUye9L+82ePDghB4ngOgIZGWFbQCQaGQTAFORTQBMxLkTABMFLM0mOi0M8/nnn8u0adOkadPwO8MHDRokDzzwQO7jU045Jc5HB9jB2VkxYduKE849n2i2LooEoHCcdy6bfncz2QT4w40WrntBPgHe55Y7z2wPzaaba5NNAOLP2VnhzCbT8ilgaT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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"n_batches_to_show = min(5, agents[0].A[0].shape[0])\\n\",\n \"num_rows = len(agents) + 1\\n\",\n \"row_labels = []\\n\",\n \"for agent in agents:\\n\",\n \" alpha_value = float(agent.alpha.mean(0).squeeze())\\n\",\n \" row_labels.append(f'alpha={alpha_value:.2f}')\\n\",\n \"\\n\",\n \"fig, axes = plt.subplots(num_rows, n_batches_to_show, figsize=(16, 8), sharex=True, sharey=True)\\n\",\n \"\\n\",\n \"for i in range(n_batches_to_show):\\n\",\n \" for j, agent in enumerate(agents):\\n\",\n \" sns.heatmap(agent.A[0][i], ax=axes[j, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" sns.heatmap(env.A[0], ax=axes[-1, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" axes[0, i].set_title(f'batch={i + 1}')\\n\",\n \"\\n\",\n \"for j, label in enumerate(row_labels):\\n\",\n \" axes[j, 0].set_ylabel(label, rotation=25, labelpad=60, ha='left', va='center')\\n\",\n \"axes[-1, 0].set_ylabel('true A', rotation=0, labelpad=40, ha='left', va='center')\\n\",\n \"\\n\",\n \"fig.tight_layout()\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Here, once again the agents have to learn the A matrix, with B matrix being fixed to the true B matrix of generative process. This time, agents have a flat prior over initial hidden states\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# create agent with B matrix being fixed to the B of the generative process, and precise initial beliefs about hidden states\\n\",\n \"C = [jnp.zeros(num_obs[0])]\\n\",\n \"pA = [jnp.ones_like(a) / a.shape[0] for a in env.A]\\n\",\n \"_A = jtu.tree_map(lambda a: dirichlet_expected_value(a), pA)\\n\",\n \"B = [jnp.array(b) for b in env.B]\\n\",\n \"_D = [jnp.ones(num_states[0])/num_states[0]] # flat prior over initial states\\n\",\n \"\\n\",\n \"agents = []\\n\",\n \"for i in range(5):\\n\",\n \" agents.append( \\n\",\n \" Agent(\\n\",\n \" _A,\\n\",\n \" B,\\n\",\n \" C,\\n\",\n \" _D,\\n\",\n \" E=None,\\n\",\n \" pA=pA,\\n\",\n \" pB=None,\\n\",\n \" policy_len=3,\\n\",\n \" use_utility=False,\\n\",\n \" use_states_info_gain=True,\\n\",\n \" use_param_info_gain=True,\\n\",\n \" gamma=jnp.ones(batch_size),\\n\",\n \" alpha=jnp.ones(batch_size) * i * .2,\\n\",\n \" categorical_obs=False,\\n\",\n \" action_selection=\\\"stochastic\\\",\\n\",\n \" inference_algo=\\\"exact\\\",\\n\",\n \" num_iter=1,\\n\",\n \" learn_A=True,\\n\",\n \" learn_B=False,\\n\",\n \" learn_D=False,\\n\",\n \" batch_size=batch_size,\\n\",\n \" learning_mode=\\\"offline\\\",\\n\",\n \" )\\n\",\n \" )\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Run multiple blocks of active inference on grid world for each batch of agents that was initialized different `alpha` values. \\n\",\n \"\\n\",\n \"#### Since the agents are using offline learning (`learning_mode = \\\"offline\\\"`), this means that parameter updates to the A matrix are performed at the end of each block.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"pA_ground_truth = 1e4 * env.A[0] + 1e-4\\n\",\n \"num_timesteps = 50\\n\",\n \"num_blocks = 20\\n\",\n \"key = jr.PRNGKey(0)\\n\",\n \"block_and_batch_keys = jr.split(key, num_blocks * (batch_size+1)).reshape((num_blocks, batch_size+1, -1))\\n\",\n \"\\n\",\n \"divs = {i: [] for i in range(len(agents))}\\n\",\n \"for block in range(num_blocks):\\n\",\n \" block_keys = block_and_batch_keys[block]\\n\",\n \" for i, agent in enumerate(agents):\\n\",\n \" init_obs, init_states = vmap(env.reset)(block_keys[:-1])\\n\",\n \" last, info = jit(rollout, static_argnums=[1, 2])(agent, env, num_timesteps, block_keys[-1], initial_carry={\\\"observation\\\": init_obs, \\\"env_state\\\": init_states})\\n\",\n \" agents[i] = last['agent']\\n\",\n \" divs[i].append(kl_div_dirichlet(agents[i].pA[0], pA_ground_truth).mean(-1))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Plot the KL divergence between the true parameters and believed parameters over time for the different groups of agents (agents with different levels of action stochasticity)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig, axes = plt.subplots(1, 1, figsize=(10, 5), sharex=True, sharey=True)\\n\",\n \"for i in range(len(agents)):\\n\",\n \" p = axes.plot(jnp.stack(divs[i]).mean(-1), lw=3, label=agents[i].alpha.mean())\\n\",\n \" axes.plot(jnp.stack(divs[i]), color=p[0].get_color(), alpha=.2)\\n\",\n \"\\n\",\n \"axes.legend(title='alpha')\\n\",\n \"axes.set_ylabel('KL divergence')\\n\",\n \"axes.set_xlabel('epoch')\\n\",\n \"fig.tight_layout()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Visualize the learned A matrices alongside the true environmental parameters after training\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"n_batches_to_show = min(5, agents[0].A[0].shape[0])\\n\",\n \"num_rows = len(agents) + 1\\n\",\n \"row_labels = []\\n\",\n \"for agent in agents:\\n\",\n \" alpha_value = float(agent.alpha.mean(0).squeeze())\\n\",\n \" row_labels.append(f'alpha={alpha_value:.2f}')\\n\",\n \"\\n\",\n \"fig, axes = plt.subplots(num_rows, n_batches_to_show, figsize=(16, 8), sharex=True, sharey=True)\\n\",\n \"\\n\",\n \"for i in range(n_batches_to_show):\\n\",\n \" for j, agent in enumerate(agents):\\n\",\n \" sns.heatmap(agent.A[0][i], ax=axes[j, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" sns.heatmap(env.A[0], ax=axes[-1, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" axes[0, i].set_title(f'batch={i + 1}')\\n\",\n \"\\n\",\n \"for j, label in enumerate(row_labels):\\n\",\n \" axes[j, 0].set_ylabel(label, rotation=25, labelpad=60, ha='left', va='center')\\n\",\n \"axes[-1, 0].set_ylabel('true A', rotation=0, labelpad=40, ha='left', va='center')\\n\",\n \"\\n\",\n \"fig.tight_layout()\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Here, once again the agents have to learn the A matrix, but now have a flat/uninformative prior over the B matrix\\n\",\n \"#### We use a precise and accurate prior over hidden states\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"C = [jnp.zeros(num_obs[0])]\\n\",\n \"pA = [jnp.ones_like(env.A[0]) / num_obs[0]]\\n\",\n \"_A = jtu.tree_map(lambda a: dirichlet_expected_value(a), pA)\\n\",\n \"pB = [jnp.ones_like(env.B[0]) / num_states[0]]\\n\",\n \"_B = jtu.tree_map(lambda b: dirichlet_expected_value(b), pB)\\n\",\n \"D = [jnp.array(d) for d in env.D]\\n\",\n \"\\n\",\n \"agents = []\\n\",\n \"for i in range(5):\\n\",\n \" agents.append( \\n\",\n \" Agent(\\n\",\n \" _A,\\n\",\n \" _B,\\n\",\n \" C,\\n\",\n \" D,\\n\",\n \" E=None,\\n\",\n \" pA=pA,\\n\",\n \" pB=pB,\\n\",\n \" policy_len=3,\\n\",\n \" use_utility=False,\\n\",\n \" use_states_info_gain=True,\\n\",\n \" use_param_info_gain=True,\\n\",\n \" gamma=jnp.ones(batch_size),\\n\",\n \" alpha=jnp.ones(batch_size) * i * .2,\\n\",\n \" categorical_obs=False,\\n\",\n \" action_selection=\\\"stochastic\\\",\\n\",\n \" inference_algo=\\\"exact\\\",\\n\",\n \" num_iter=1,\\n\",\n \" learn_A=True,\\n\",\n \" learn_B=False,\\n\",\n \" learn_D=False,\\n\",\n \" batch_size=batch_size,\\n\",\n \" learning_mode=\\\"offline\\\",\\n\",\n \" )\\n\",\n \" )\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Run multiple blocks of active inference on grid world for each batch of agents that was initialized different `alpha` values. \\n\",\n \"\\n\",\n \"#### Since the agents are using offline learning (`learning_mode = \\\"offline\\\"`), this means that parameter updates to the A matrix are performed at the end of each block.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"pA_ground_truth = 1e4 * env.A[0] + 1e-4\\n\",\n \"pB_ground_truth = 1e4 * env.B[0] + 1e-4\\n\",\n \"num_timesteps = 50\\n\",\n \"num_blocks = 100\\n\",\n \"key = jr.PRNGKey(0)\\n\",\n \"block_and_batch_keys = jr.split(key, num_blocks * (batch_size+1)).reshape((num_blocks, batch_size+1, -1))\\n\",\n \"\\n\",\n \"divs1 = {i: [] for i in range(len(agents))}\\n\",\n \"divs2 = {i: [] for i in range(len(agents))}\\n\",\n \"for block in range(num_blocks):\\n\",\n \" block_keys = block_and_batch_keys[block]\\n\",\n \" for i, agent in enumerate(agents):\\n\",\n \" init_obs, init_states = vmap(env.reset)(block_keys[:-1])\\n\",\n \" last, info = jit(rollout, static_argnums=[1, 2])(agent, env, num_timesteps, block_keys[-1], initial_carry={\\\"observation\\\": init_obs, \\\"env_state\\\": init_states})\\n\",\n \" agents[i] = last['agent']\\n\",\n \" divs1[i].append(kl_div_dirichlet(agents[i].pA[0], pA_ground_truth).mean(-1))\\n\",\n \" divs2[i].append(kl_div_dirichlet(agents[i].pB[0], pB_ground_truth).sum(-1).mean(-1))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Plot the KL divergence between the true parameters and believed parameters over time for the different groups of agents (agents with different levels of action stochasticity)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig, axes = plt.subplots(1, 2, figsize=(12, 5), sharex=True, sharey=False)\\n\",\n \"for i in range(len(agents)):\\n\",\n \" p = axes[0].plot(jnp.stack(divs1[i]).mean(-1), lw=3, label=agents[i].alpha.mean())\\n\",\n \" axes[0].plot(jnp.stack(divs1[i]), color=p[0].get_color(), alpha=.2)\\n\",\n \"\\n\",\n \" p = axes[1].plot(jnp.stack(divs2[i]).mean(-1), lw=3, label=agents[i].alpha.mean())\\n\",\n \" axes[1].plot(jnp.stack(divs2[i]), color=p[0].get_color(), alpha=.2)\\n\",\n \"\\n\",\n \"axes[0].legend(title='alpha')\\n\",\n \"axes[0].set_ylabel('KL divergence')\\n\",\n \"axes[0].set_xlabel('epoch')\\n\",\n \"axes[1].set_xlabel('epoch')\\n\",\n \"axes[0].set_title('A matrix')\\n\",\n \"axes[1].set_title('B matrix')\\n\",\n \"fig.tight_layout()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Visualize the learned A matrices alongside the true environmental parameters after training\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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su0yMySpUqleP5Ir1mBYDolGZp1btQ8Y1Ye9F3rkU2ATAV+aS+Ued3ugUIB/3mamSTujRgNJENQiURfedeaZZmkzWfNKjpnLILFCvee+89adasmfz1r3+V+vXry2effSZz586VJk2ayPr16+W7777ThYn+/fvLN998I9dff72sWLFC3nrrLdm3b590794981jqX1WwUKMqQj0nABS2NG9sjg0AnEY2ATAV2QTARJw7ATBRmqXZFGfbOhVZff/993otir179+qChFpYu0KFCvpn8+fPl4kTJ8rRo0dl3rx50qlTJ+natatceOGFMmLECBk1apScOnVKP+aOO+6ImlEVfr7ZYSX6zd0y/O7MGwB2I5sAmIp8Ys07a9FvrkY28dmFzeg798qwNJuML1oERkAcOHBAdu7cKVdccYXUqFFD76tYsaKMHj1ar1cRWIti2rRp8swzz+iREvfcc4/cdddd+n6KGjmh1rlQ00SptS4CU0cFfhZY58LNGO5lh+xvFfSbu9lS5QYQXcgmAKYinwCYiGziswtbMD1UdEmzNJuML7Wo9SXU+hRq+qfx48frf1VhIiMjQ/+8Y8eOerFstZZFlSpV9M/UKIrdu3frgkagYKFkLUoEChbqOCYULNR6HF26dJGqVavqtixatCjo52qx8MGDB0u1atWkePHiehqsGTNmONZeAIUn3RebYwMAp5FNAExFNgEwEedOAEyUbmk2OTrSIjDaIS0tTU/HpIoPWZ08eVKefvppKVeunC5CqA/sZ8+eLWPGjJE6derotSkUNZpCrU0xdepUva5FYJHtvMj+nE5JTk6WRo0aSb9+/fRC4dkNHz5c1q5dK3PmzNF/s1WrVsm9996rixw33nhj3p+IBVPtRL+5mtdH/0osfwNr0XeuRTYBMBX5xPWBteg3VyOb9IdsTrcAeZGWlnMffedaXkuzyZFXZHp6ujz55JPy7LPPyunTp4OKDOrD+5IlS2beVkWI9u3b630ffPCBzJw5U06cOCHvv/++nupJfWivjlW5cmXHR0sUhFpzQ2252bRpk/Tp00fatm2rbw8cOFBefvll2bp1a/6KFgCMk+G18w0EgLuRTQBMRT4BMBHZBMBEGZZmkyNFi/j4eGnRooWe5kgtmN2jRw+ZPHmyHkWgFspWi2v/7W9/k0qVKukpk1SR4vbbb9drWtx33336Q3p1fzUiQRUt1LRQbteqVStZsmSJHomhfud169bJV199Jc8//3z+DsQcdXai31zNlqF5keT57/pFsA99515kE++/VqPvXI184jVuLfrN1cgmvWCs0y1AuOg710q3NJuKvNSi1o9Q1NoUHTp0kKeeekq2bNkiy5cv12s2qGmi1FoUCxcu/K2BMTGyYMECXbhYsWKFjBw5Uo84UCMy1ILaP/zwQ9Bx3erFF1/U61ioKbLUyBQ1NZZav+Pqq692umkACsjn8+TYAMBpZBMAU5FNAEzEuRMAE/kszaYiGWnh9Xr11E2qABGYwql8+fLSvXt3SUpK0kWIF154QS+q3bVrV3nkkUd04UJNDaUe+84770iTJk30KAxFrWtRpkwZvV/dp3Xr1lZPDZXXooUq7qjRFjVr1tQLd6tRJ2rUhZo+K5TU1FS9ZeXzeyXGY2eFDXArW4fqhStUNnnTU8kmS/kzMpxuwv9v707Ao6ru/49/JwkJeyo7yCogiwgIiEL5C1YEKUWptCJSwVhAFBfAokQruCG2KoJCxQ3FhYJaARcWEQV/CoqAKGgB2YRSEHFBCWSbuf/nHJqYSSaYTGZyz7n3/Xqeq8ydyclNTvKZe/O95xzECdkkEgrmkk22Cnn7hia/I5+4rgNMRDZx7mQ1zp08K9fSbIrrUauCg5KYmKgLFnv37pV9+/ZJ7v/+wHHmmWfKb37zG/nxxx91wUJRUz1deeWVsmvXLr2GhfrYTp06yRtvvCEPPvigTJ06Vd58801ZtGiRzJ49WxcsvO748eNy2223ybRp0/R0WWotDzUqRU2rpb4nxVHfq9TU1LBtV86Wcj12ACVbFKnw5mVkE2AHsilVduWSTYCJ/JRNCudOgB04d+LcCTBR0NJsitlIi0OHDsmIESP04totW7bU+1TBQTlw4IBek0ItGt20aVNp3bq1zJs3T48YUCMl1IgJNYrg3HPP1a/v0KGDHnExefJk/Uf6u+++W0+JpKaJSkpKkttvv12v8eAXauFytanCT0Hq+xsKhYr9uPT0dBk/fnzYvkG1R6lqUtyOFXFCn3maY8nQvFiJmE11RnNnh63oN88im/533uQUf64Fg9FvnkY+iQyqd61rxwMgMrKJcyer0W+e5ViaTTErWqiK6rvvvitz5szR1Vbl3//+t/ztb3+T888/XxcyZsyYIZ999pncfPPNusDxwAMP6JEWal0G9TGLFy/Wa1OotkaOHKnXbVi9erX07NlTjyhQ61fUqlVLvOjo0aOyY8eO/Me7d+/WC4/XqFFDGjdurL8Haj0PtXi5Kvao78tzzz2nR18UJyUlRW8FMUwPME/Q0qF60SKbADuQTWQTYCryiXwCTEQ2kU2AiYKWZlPMihYqqKZMmSL33HOP3HjjjVK/fn35/vvv9R/W//Wvf+mFttV0UGqrWrWqHi2hpnm6+uqr9XRQ6mO2b98up59+um5PrWHRq1cv+eijj/Qf7NWaFXkFCzXtVN4oDq9Yv369Lu7kyatWq/U+nn32WZk/f76uYqsRK999950uXKjv9+jRo0v3iQJ2/qD6Hv3maU7Qzqo3AG8jmwCYinwCYCKyib9dWI2+8yzH0myK+idSTUuUt2ZFHvUHdjVSQhUq8qZ5GjVqlF40W63DkOeSSy6ROnXqyAcffKCnPVIjLdRr77zzTv28aqN27dqydOlSueWWW4p8bq8VLBRVoFFfd+FNFSzy1vp45plnZP/+/XqNi61bt+rChtcXIAf8MlSv8AYAbiObAJiKbAJgIs6dAJjIsTSbkqItWOStr5CVlSVHjhzRRQg1rdM111wjM2fO1MWKU045RYYMGSJPPfWUbNiwQU8FpRbhVutSqD/SqzUqKlSoIA0aNJDf/e538o9//EMyMjKkSpUq+aM31OdSf5jnj/Mxwhx1dqLfPM2xZBEkAP5CNnHHmdXoO08jn1jzzlr0m6eRTQBM5FiaTVEdtSpYqIW3VYFCLap96aWX6jUqlJtuuklPC7VgwQL9uEuXLnLBBRfoxbTVCAFVsFB27typp5BSIy0qVqyoixxfffVVfsGi4OeiYAHA09RQvcIbALiNbAJgKrIJgIk4dwJgoqCd2RRV0eLDDz+U3/72t7Jv3z6ZPXu2jB07Vt5++239fzXiQhUwpk+fLseOHdNFiBtuuEH+7//+T4+mUKMrVAHjtdde0+tZqJEWihqVoRSecgpxuOuMzfyNfrN3i3IgTeGttGbNmiVNmzbVReBzzjlH1q1bV+xr1bRzeSPY8jb1cQAQ62xSyCcAsUY2cX1gzUa/2blFies6vRI3mw0bfWfv5qPruqjSWE3hpEZGqMW1+/btK927d5eaNWvqBbfXrl2rF9XetWuXvP766/r13bp1k/79+8umTZvkP//5j/44dfCXX365L9arAICTCQQDRbbSUCPb1Bo3kydPlo0bN+o1glQ2qxFxxVFrDR04cCB/UyPdACCW2aSQTwDigWwCYCKu6wCYKGDpdV1Ua1p07txZevTooQsTEyZMkHfeeUf++Mc/6tETqhih1qa44oor5JFHHtFTR6mCxuDBg/XC2n/4wx9k3Lhx+W2pxaaZ/qkcJdo5j5nv0W/eVsahedOmTZORI0dKWlqafqxGwL355psyZ84cmThxYsSPUblbr149MQY/4/ai77wrBsOGrc8nfr7tUfjOWPrO2zh34mfcFmSTv5BNEuBGZGvRdx4WtPO6Lqp3zF/96ld6kex7771XT+f0/vvvyxNPPKHXuFCjKD7//HNdmFCjLlauXKk/5sILL9TrXzz00EP5C3jnfQEA4GdlqXpnZ2fLhg0bpHfv3mFrAanHKoOLc/ToUWnSpIk0atRILrnkEp3bABDLO3LIJwDxQjYBMBHXdQBMFLD0ui6qkRbKxx9/LK+++qrMnTtXzjjjDMnMzNTTP+3fv1+efPJJmTFjhjz11FPStWtX/Xq11oWaUkot1H3XXXdJampqtJ8aZeBk57h9CCiBSbs+CXt8z+knfo/gUU7RXaqwm1fczaOKxWor6PDhw7p4XLdu3bD96vHWrVsjfrpWrVrpanj79u3lyJEj8uCDD+pp/tQbSMOGDcUNZJMd/rrr0yL7ppzexZVjgdnZ5JV8Ipvsce327WGPZ7dp49qxoPzzyW/ZpJBPdrhlx2dhjx9odZZrx4JywHWdhDLDv1aYadzOfxfZN71Ve1eOBeXAKbrLhnOnqMcmnnnmmZKTkyOffvqpnpNKLbDdrl07vch2s2bNdMVFLbRdo0aN/I9RU0Xdd999kpycrKeFws+mTp0qZ599tlSrVk0XeAYOHCjbtm3Lf37Pnj1FFjDJ29T3HoC3qt4qE1Rxt+Cm9sWCWmdo2LBh0rFjR+nZs6cuQNeuXVsef/zxmLQPwBvKO5sU8glASZBNAEzEdR0AEwUsva6LeqSFWvH79ttv16Mp1KgKtYD2o48+qteuKKjgmhWnnnpqsfNc+d3q1atlzJgxunCRm5srt912m/Tp00e++OILqVKlih5KoxYtKUhNyfXAAw9Iv379Svx5EioWrZjBPHefFn4HTmJV+s3LAsGi+9LT0/UiRwVFqnjXqlVL5+/XX38dtl89LuncgRUqVJCzzjpLduzYIW4hm+xw72kdiuwjn7yrLNnklXwKJFdw5fOi9B5r2SLscUJl+s5P+eS3bFISKlV07XOj5P7evF3Y48Rq9JuXcV0nEqgQ9Z8ZUY4ebl50RGpCJfrOqwKWXteVaRUo9Yf1FStWyCuvvKJXC88rWIRCofyRFKxZUTLLli2Tq666Sk+1pVZgVwua7927V88ZpqgfDvWDUHBbuHChXHbZZVK1alW3Dx9AGQRCRTf1ZlG9evWwLdIbiBq51rlz5/z1g/IyWD1Wle2SUMP8Nm/eLPXr14/p1wXAv9mkkE8A4oVsAmAirusAmChg6XVdmctozZs315uiRggkJSXpqaFQNmq+L6Xg9FoFqWKGWkNk1qxZpWrXCUYor8F49Ju3lXYRpMJUdXz48OHSpUsXvY7Q9OnTJSMjQ9LS0vTzakieGumWN9RPTeN37rnnSosWLeSHH37QI7bUNH8jRowQtzg5ua59bpQNfeddZc0mT+RTMOTO50XZ0XeexrkT1we2ot+8jWxSf8lkKnhr0XeeFbD0ui6mY39UwQJlp6pVY8eOlV//+td6nZBInn76aWnTpo1exASA94bqlYYa5fbNN9/IpEmT5ODBg3rOQDV6K2+RJDVqq2Ax+fvvv5eRI0fq155yyim6Yr5mzRpp27ZtWb8UAB5S1mxSyCcA8cC5EwATkU0ATBSw9Lou4LAitnGuvfZaWbp0qbz//vsRV1Q/fvy4Hk5zxx13yM0331xsO5FWgh9UZ7QkBBLjctyInVBWZtjjhBTmPrXF8uPPl/pjWt3zcJF92+4YJ15FNnknmxTyyQ5kU5TZVHsU2WSJUHZ22OOE5GTXjgUltzzzxag+rnA+eTmbis2n+teRTxYIHTsW9jihcmXXjgUlt/zo3Kg+jnMnrutswXWdvZb76LqOeZwMc/3118sbb7wh7777bsSChaLWEDl27JgeenMykVaC35W7JU5HDiCW8wt6GdkE2IFsSpVdwc/dPiwAEfgpm4rNp5zNbh8WgEI4d+K6DjBRwNJsYj4nQ6gBLzfccINeXHvVqlXSrFmzYl+rpoa6+OKLpXbt2idtM9JK8OqOQXEs+enEz+gzT4vFUD2bkE0eQ795Ftl04m5BCXCPj5XoN08jn0QurTlSnOwc144J0aHPvI1s+t+5EwCjBCzNJooWhhgzZozMmzdPFi9eLNWqVdNzfimqUl2pUqX81+3YsUPee+89WbJkyS+2qVZ9L7zyO8P0APPYUuWOFbIJsAPZRDYBpiKfyCfARGQT2QSYKGBpNlG0MMRjjz2m/9+rV6+w/c8884xcddVV+Y/nzJmjp43q06dPVJ/HCbGEiY3oN2+zteoNwNvIJgCmIp8AmIhs0lULt48A0aLvPCtgaTZRtDBESddDv++++/QGwDtsfQMB4G1kEwBTkU8ATEQ2ATBRwNJsomjhMwEqp1YoXMKi37zN1qF6McXc4/ai7zyLbOKOM6vRd55GPnF9YAuu6/yFbFLfBH7GrUXfeVbA0myiaAEALrP1DQSAt5FNAExFPgEwEdkEwEQBS7OJooXPBJKT3T4ElER2dthD+s3bbB2qF1OJ3K1vLfrOs8gmkUAii0naOuqLvvM28kldyXMpb+N1Hf3mbWSTejvm2sBW9J13BSzNJt4xAcBltla9AXgb2QTAVOQTABORTQBMFLA0myha+IwTsvQn1efoN2+zteodU07hGX9hDfrOs8gmEScn1+1DQEk54edK9J23kU8ATEQ28f5rM/rOuwKWZhNFCwBwma1vIAC8jWwCYCryCYCJyCYAJgpYmk0ULQzw2GOP6W3Pnj368RlnnCGTJk2Sfv365b9m7dq1cvvtt8tHH30kiYmJ0rFjR1m+fLlUqlSpdJ+MO2LtRL95WkKQ/pUQ3wNr0XeeRTYVvXsfFqHvPI184vrAWvSbp5FNvP9ajb7zrARLs4mihQEaNmwo999/v7Rs2VIcx5G5c+fKJZdcIp988okuYKiCxUUXXSTp6eny6KOPSlJSknz66aeSEM0iOUFLy2t+R795mq3zC8YUJ0j2ou88i2wCYCryiZsGrEW/eRrZBMBEAUuziaKFAQYMGBD2eMqUKXrkxYcffqiLFuPGjZMbb7xRJk6cmP+aVq1auXCkAOLB1qF6ALyNbAJgKvIJgInIJgAmCliaTRQtDBMMBuXll1+WjIwM6datmxw6dEhPCTV06FDp3r277Ny5U1q3bq0LGz169Ch1+w53dliJfvO2BEvfQAB4G9kEwFTkk4iTm+P2ISAK9Ju3kU0ATJRgaTZFMb8Q4mHz5s1StWpVSUlJkdGjR8vChQulbdu2smvXLv38nXfeKSNHjpRly5ZJp06d5IILLpAvv/zS7cMGEAOBkFNkAwC3kU0ATEU2ATAR504ATBSwNJsYaWEINd3Tpk2b5MiRI/LKK6/I8OHDZfXq1RIKnZh47JprrpG0tDT977POOktWrlwpc+bMkalTpxbbZlZWlt4KCjlBSQgkxvmrAVAagVzxFbIJsAPZRDYBpiKfRELikE9WKHR7a4D7Rr2MbBIJJQjZZKtE+s2rApZmE++YhkhOTpYWLVpI586ddSGiQ4cOMmPGDKlfv75+Xo26KKhNmzayd+/ek7ap2klNTQ3bdoe+iOvXAaD0EoJOkc3LImXTruDnbh8WgELIJrIJMJWfsknhug6wA+dOqbIrZ4vbhwXAI9nESAtDqREWqmLdtGlTadCggWzbti3s+e3bt0u/fv1O2kZ6erqMHz8+bN+g2qMkEAjE5ZgRO4XjI5BAn3lZ4MSAKt8oLpsAmIVsEhlUZzR3xdqKfvM08knk0pojXTseAJGRTf87d7Jk6hkUQr95VsDSbKJoYUjQqwJE48aN5aeffpJ58+bJqlWrZPny5brAMGHCBJk8ebIefdGxY0eZO3eubN26VU8jdTJqfQy1FcQwPcA8AUuq3LFCNgF2IJvIJsBU5BP5BJiIbCKbABMFLM0mihYGOHTokAwbNkwOHDigh9O1b99eFywuvPBC/fzYsWMlMzNTxo0bJ999950uXqxYsUKaN29e+k/GXWd2ot88LZBr5xtITPEzbi/6zrPIJn3l7fYRIFr0naeRTyIB5h63gpObE/aYfvM2son3X6vRd54VsDSbKFoY4Omnn/7F10ycOFFvALwnwDBMAAYimwCYinwCYCKyCYCJApZmE0ULv0nkjlgr0W+eZssiSHHlWDrJIug7DyObmNvXavSdp5FPAExENvH+azX6zrMSLM0mihYA4DJbh+oB8DayCYCpyCcAJiKbAJgoYGk2UbTwG8fOH1Tfo988zdahegC8jWxiJJHV6DtPI58AmIhsEnGCQbcPAVGi77wrYGk2UbQAAJcFcvnDCgDzkE0ATEU+ATAR2QTARAFLs4mihd9YWl3zPfrN0wJBO99AYsnhZ9xa9J13kU3qm8CaUtai7zyNfGI0kbXoN08jmwCYKGBpNlG0AACXBSxdFAmAt5FNAExFPgEwEdkEwEQBS7OJooXPOLk5bh8CokC/eZylQ/ViKZAQcPsQUAKRTnXoOw8jm2ATRlb4C/nE3OOWot88jmySQHIFtw8BUf6Nib7zsFw7s4mzewPdf//9EggEZOzYsfn7evXqpfcV3EaPHu3qcQKIjUAwWGQDALeRTQBMRTYBMBHnTgBMFLA0mxhpYZiPP/5YHn/8cWnfvn2R50aOHCl33313/uPKlSuX89EBiAtLh+oB8DiyibnHbe4r+s7byCdGF1mj0B+G6DdvI5tEHL4H1qLvvCtoZ99StDDI0aNHZejQofLkk0/KvffeW+R5VaSoV6+eK8cGIH4CuXZUuQH4C9kEwFTkEwATkU0ATBSwNJsoWhhkzJgx0r9/f+ndu3fEosWLL74oL7zwgi5cDBgwQO64445Sj7YIJDFHnY1zndJvHmfJ0Ly44q4ze9F33kU28fNtM/rO28gnACYimwCYKGhnNlG0MMT8+fNl48aNenqoSK644gpp0qSJNGjQQD777DO59dZbZdu2bfLqq6+W+7ECiLHcXLePAACKIpsAmIp8AmAisgmAiXLtzCaKFgbYt2+f3HTTTbJixQqpWLFixNeMGjUq/99nnnmm1K9fXy644ALZuXOnNG/ePOLHZGVl6a2gkBOUhEBijL8CAGUS9Ne822QTYAmyiWwCTEU+iZMg5JMFnNycsMeBRPrM08gmCeVmk022svRufHg3mxg3bYANGzbIoUOHpFOnTpKUlKS31atXyyOPPKL/HYwQHOecc47+/44dO4ptd+rUqZKamhq27crdEtevBUCUVe/Cm4eRTYAlyCayCTCVj7JJIZ8AS3DuJLuCn7t9WAA8kk2MtDCAGjGxefPmsH1paWnSunVrPQ1UYoS7MTZt2qT/r0ZcFCc9PV3Gjx8ftm9Q/euY49dGifSZp1m6KFK0ImZT7VEijp3Vf9+j37yLbCKbbEa/eRv5JIPqjHbteAAUg2w6ce4EwCy5dmYTfwk1QLVq1aRdu3ZhW5UqVaRmzZr632oKqHvuuUePyNizZ4+89tprMmzYMDnvvPOkffv2xbabkpIi1atXD9sYpgeYufB64a20Zs2aJU2bNtVTzKmRWOvWrTvp619++WVdGFWvV1POLVmyRMoL2QT4J5tsyieyCbCHn7JJIZ8AO3BdRzYBJnIsva6jaGGB5ORkefvtt6VPnz66s2+++WYZNGiQvP76624fGgADhuotWLBA3+EyefJk2bhxo3To0EH69u2rp52LZM2aNTJkyBD585//LJ988okMHDhQb1u2MM0AgNgOI7Y+n9ToVDY7NvrOzi1afs8mAGbiuk6ckMNmwUbf2bv56bou4DhOlF8xbNS36nC3DwElEDp2LOxxQuXKrh0LSmf50bml/pi+la4s2s7x50v88arCffbZZ8vMmTP141AoJI0aNZIbbrhBJk6cWOT1gwcPloyMDHnjjTfy95177rnSsWNHmT17trihb8WhrnxelE4oO7vIvoTkZFeOBaWzPPPFcs8mL+RTpO8BzBTKygx7nJBS0bVjQcmVNlOK+930WzYp5JMdyCZ/Z1Np2/JCNvVJvsKVz4vScXJziuwLJFVw5VhQOm9lz/PNdR1rWviNJYutoBD6zdOiHZqnZGdn66nj1HyieRISEqR3796ydu3aiB+j9heee1RVyBctWiRuifqOAbiOvvOusmSTZ/IpIeDO50XZ0XeexrkT67ZYi3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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"n_batches_to_show = min(5, agents[0].A[0].shape[0])\\n\",\n \"num_rows = len(agents) + 1\\n\",\n \"row_labels = []\\n\",\n \"for agent in agents:\\n\",\n \" alpha_value = float(agent.alpha.mean(0).squeeze())\\n\",\n \" row_labels.append(f'alpha={alpha_value:.2f}')\\n\",\n \"\\n\",\n \"fig, axes = plt.subplots(num_rows, n_batches_to_show, figsize=(16, 8), sharex=True, sharey=True)\\n\",\n \"\\n\",\n \"for i in range(n_batches_to_show):\\n\",\n \" for j, agent in enumerate(agents):\\n\",\n \" sns.heatmap(agent.A[0][i], ax=axes[j, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" sns.heatmap(env.A[0], ax=axes[-1, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" axes[0, i].set_title(f'batch={i + 1}')\\n\",\n \"\\n\",\n \"for j, label in enumerate(row_labels):\\n\",\n \" axes[j, 0].set_ylabel(label, rotation=25, labelpad=60, ha='left', va='center')\\n\",\n \"axes[-1, 0].set_ylabel('true A', rotation=0, labelpad=40, ha='left', va='center')\\n\",\n \"\\n\",\n \"fig.tight_layout()\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Visualize the B tensor (just the expected value of the posterior which in absence of learning is same as the prior) alongside the true environmental parameters after training\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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WWWzzHunbtKg8//LBMmjRJunXrZlrz0s+RcPvwww/NvoLbtm0zBQ2dGaEV9Mcee8zn+/irGOGmlXr93j///LOUKlVKevToIZMnTzY/HwDkJ7a0GwIAvJHfAGAn8hsA7JRkaX7bWUr5C1pYSL+F0unTp822TTqIWmm3gRYQRowYIWfOnDEdCG56/Pfff/c87tChQ6YIsH//fnnuuefMudwFCff2Tnnlvvvuk2PHjpkiiV7HrFmzPMUUAMhPbN0TEQBCHfkNAHYivwHATkmW5ne+KkrorAh3p4OuX375xTP3QWdCfPXVV2a4tXtbpurVq8udd94p8+bNM4/T5+rw6Pr165tB0vq4Jk2ayIEDB+Tzzz832z0p7ZZIP/AaAJC7Up3hPgsAEPzIbwCwE/kNAHZKtTS/w/JLMcI9sFqLEdrd0L17d2nQoIH8+OOPZjB027Zt5fvvv5cPPvjAq6DQokULuXTpkly8eNE8t1ChQua4u3uiXbt20rhxY69iRESEHRUnALBVsjPCZwEAgh/5DQB2Ir8BwE7JluZ3WH4pRqidO3dK+/btzeyIwoULy7p166RGjRrmvj59+ki5cuXMwOvk5GTPOfbu3WuOa+FC1atXz3RUDBo0yOf7UYwAgLyR7Az3WQCA4Ed+A4CdyG8AsFOypfltTVEis/kN7mLEihUrpGnTpvL3v/9d6tata7Zaevvtt02Hw44dO+Ts2bOm8KCFhp9++knuuOMO2bhxo7zzzjty5MgR6dmzp+dc+rVo0aJmK6e8nhkBAPiP5LRwnwUACH7kNwDYifwGADslW5rfYbbMichsfsP58+dNZ8Tw4cPNbAgtMMyePVtq1aoly5YtM9s3devWTQ4ePGger39esmSJKTyMHTtWRo8eLf369ZMHHnjA59y6lRMzIwAgMFJdYT4LABD8yG8AsBP5DQB2SrU0v4N+PyJ3B8OxY8ckNjZWmjdvLtWqVTPHypYtK+PGjTPzItyzILQo8eKLL5pCxiOPPCIPPfSQeZzSzgctVGzZssXMmnBv7eS+jyIEAAQHWyr7AABv5DcA2In8BgA7JVua30FfOtH5DnfddZfZnmnixInmqxYe3EOnO3XqZGY9xMTESIUKFcx92gVx+PBhU7BwFyRU+qKDuyCh5wmGgoTOw+jatatUqlTJXMuqVau87tdh3NoRUqVKFTMvQ7epmjNnTsCuFwD8KcUZ7rMAAMGP/AYAO5HfAGCnFEvzO6CdEu5uBR08rdslZRwkfe7cOXnhhRekVKlSpsigb8gvWrRIoqOjpXbt2mY2hNJuCN26aebMmWauRGRk5BVfQ7AMr05ISJCGDRvKwIEDpXv37j73R0VFybZt22Tx4sXmd/bBBx/IP//5T1PEuPvuuwNyzQDgL2nOoK+ZAwAyQX4DgJ3IbwCwU5ql+R2Qd+RTUlLkueeek2nTpsmFCxe8igj65nyRIkU8t7XI0KFDB3Ns7dq1Mn/+fDlz5oy8//77ZismfVNez1W+fPmAdzvkROfOnc3Kyu7du6V///7Srl07c3vIkCEyd+5c2bdvH0UJAPlOapqdL6oAEOrIbwCwE/kNAHZKtTS/A3LVBQoUkBYtWphtiHQgtZo6darUr19f+vTpY7oBVLly5cyWRvHx8WZI9aOPPmregNcixIoVK+TLL780j9Ntm2wuSFyJ1q1by5o1a+TUqVNmu6mPPvpIvvvuO+nYsWOgLw0Acp2t7YcAEOrIbwCwE/kNAHZKsTS/87wooW+oK50NoW+oP//887J3717ZsGGDmZmg2zjpLIiVK1f+5wLDwmT58uWmO2Ljxo0yZswY0zGgHRU6sPqXX37xOm9+9corr5g5ErqFlXaW6NZVOj+jTZs2gb40AMh1TqfDZwEAgh/5DQB2Ir8BwE5OS/M7T7ZvSktLM50MWmBwdzSULl1aevbsKZs3bzZFhpdfftkMrdaOiCeffNIUJnTrJn3uu+++K40bN5ZatWqZ5+pcieLFi5vj+phbbrkl33dKaFFCizfaLVG9enUzGHvYsGFm+yrd3iozSUlJZqXndKVJmMOOihmA0GVr+2FuIb8B2Ir8Jr8B2In8Jr8B2CnV0vz261VrQUGFh4ebgsSJEyfk5MmTkpqaao7fdNNNcuutt8rFixdNQcK9FdMDDzwgx48fNzMk9LlNmjSRdevWyYsvvihTpkyR9evXy6pVq2TOnDmmIJHfXb58WcaPHy/Tp08321npLA3tKunVq5f5nWRFf1clSpTwWsdTD+fptQNAdgc1ZVyhhPwGYCvym/wGYCfym/wGYKc0S/M7167y3LlzZt7D999/7zmmBQV1+vRpU3zQ7Yd0mHPv3r0lOTnZfOJfOx3i4uJMF4Bbw4YNTcdETEyMuf3UU0/JfffdZ7Zx0lkSI0aMMDMWunTpIqFAB4Pr0sJOevr7dTqdWT4vOjrazONIv2pF1M+DKwaAnHE5HT4rlJDfAGxFfpPfAOxEfpPfAOzksjS/c237Jq0i6/DlBQsWmAqz+uabb8xQ6vbt28t1110nM2fONMOpR48eLYMGDZIXXnjBFCt0LoI+Z/Xq1WY2hJ5r8ODBZm7Cjh07pG3btqYjQOdHlClTRvKjS5cuydGjRz23f/jhB4mNjZVSpUpJtWrVzO9A52nocHAt5ujv5c033zTdE1kpWLCgWenRegjABmmWth/mFvIbgK3Ib/IbgJ3Ib/IbgJ3SLM3vXLtqDe/JkyfL/PnzTWeEunDhgnnjXLca+sc//mG2a7r//vtl7ty5cvDgQbMNk77prts1aUHju+++88yG0BkS7dq1k08//dTc1uPugoR7W6j8ZP/+/eZn1qWioqLMnydMmGBuL126VJo3b25+f9pxMnXqVPP7Hjp0aICvHABynyvN4bMAAMGP/AYAO5HfAGAnl6X5ne2ihG4blLE4oAOrtdNBCxHubZiGDBlihlLrHAS3e+65R8qVKyeffPKJ2ZZIOyX0sRMnTjT36znKli0rGzdulMcff9zne7u3hcpPtACjP3fGtXDhQs+sjTfeeENOnTplZkx8++23pnCR3wd8AwhNtrYfAkCoI78BwE7kNwDYyWVpfodltyCh8w20OJCUlGTmSSjddunhhx+WWbNmmS6JIkWKSJ8+feTs2bNy4MAB8xj3kGt9E37fvn1SoEABqVSpktx1112mSJGQkOB5o127L/R76ZvzAIDQ4XKG+SwAQPAjvwHATuQ3ANjJZWl+Z+sqtSChhQgtQNxwww3SvXt3MyNC6RBqLUgsW7bM3G7WrJncdtttZli1fsI/IuI/YyyOHTsmFStWNJ0ShQoVMh0VP/30kylkZPxedAMAQIjRdsOMCwAQ/MhvALAT+Q0AdkqzM7+zVZTYu3ev3HnnnXLy5EmZM2eOjBw5Uj788EPzVbdl0gLFjBkz5I8//jBFhkcffVQ+/vhj0w2xfPlyU6BYs2aNDBw40HRKqJIlS+bbeREAgKvjcvqu7Jg9e7bUqFHDFL9btmxpOvSyotvlaRE8/dLnAQCuHPkNAHYivwEgdPN7dgCyO1tFCd1iSTsbNmzYIJ06dZLWrVtL6dKlZcWKFbJnzx557LHH5Pjx47J27Vrz+FatWkmXLl0kNjZWfv75Z/M8/QF69+4dEvMiAABXx5Hm8FlXSzv2dPZOTEyMHDx40Mwu0tcs95aDmdEZSKdPn/Ys7eADAFw58hsA7ER+A0Bo5veyAGV3tooSTZs2NUOttfDQo0cPqVevnjmmWzFpsaF69erSt29fefnll80xLVj06tVLLl68KD179jSdFjrsWjEvAgDgj/bD6dOny+DBg2XAgAFSt25d09l3zTXXyIIFC7J8jlb4K1So4Fnly5fP4Q8CACGG/AYAO5HfABCS+T09QNmdraLEtddea4ZQP/PMM2a7pV27dslrr71mZkxoF8RXX30lo0aNMl0TW7duNc+5/fbbzfyJadOmmds6INv9QwAAkJuV/uTkZDlw4IB06NDBa0aR3tbXpqxcunTJFNarVq1qiuf6egYAuHLkNwDYifwGgNDL7+QAZne2x3F/9tln8v7775sqinZKJCYmmu2ZTp06JfPmzZObbrpJ5s+fLy1atDCP11kTuuWTdk/Ex8ebogYAAJly+S4tZmvHXfrlLnBnFBcXZ4rmGav1evvMmTOZPuf66683nwRYvXq1LF68WJxOp9meULcdBABcIfIbAOxEfgNAyOV3XACzO9tFCS066NZMX3zxhdk3SgdY169f3wyxrlmzpqmq6CDrUqVKeZ7TvXt3efbZZyUyMpJtmzKYMmWKNG/eXIoVK2YKON26dZMjR4547v/xxx99hoi4l/7uASC/V/o1J0uUKOG19Fhu0flH/fr1k0aNGknbtm1N4b1s2bIyd+7cXPseAJDfkd8AYCfyGwDs5Mjj/M6t7I7I7gXoVO0nnnjCdEPMnDnTDKh+5ZVXzOyI9LT44N6iqXLlyjJu3Ljsfst8bceOHTJs2DBTmEhNTZXx48dLx44d5euvv5YiRYqYdhgdHJKebpn1wgsvSOfOnQN23QDgD44032PR0dFm+FJ6WXXdlSlTxrwunT171uu43tb9Dq9EgQIFpHHjxnL06NGruXQACGnkNwDYifwGgNDL7zIBzO5sd0oofeN8y5Yt8t5775mJ3O6ChLZtuDshmBlxZTZt2iQPPvig2QpLp5zrwPATJ06Yfb2U/gNJP0BE18qVK+W+++6TokWLBvryASBXOZy+S19Aixcv7rWy+p8i7chr2rSpZ66R+7VJb2tV/0poC+OhQ4ekYsWKufZzAUB+R34DgJ3IbwAIvfyODGB2Z7tTwq127dpmKf2Ef0REhNm6CTmjczdU+u2v0tNihc7wmD17dh5fGQD439UO1suMfiqgf//+0qxZMzPfaMaMGZKQkGBmISltN9QOPncLo24/ePPNN0udOnXkt99+M51ouj3hoEGDcnwtABAqyG8AsBP5DQChmd9RAcruHBclvE4WkaunC1lakRo5cqT87W9/M3M6Mv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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"num_actions = env.B[0].shape[-1]\\n\",\n \"base_labels = [\\\"Up\\\", \\\"Right\\\", \\\"Down\\\", \\\"Left\\\", \\\"Stay\\\"]\\n\",\n \"action_labels = base_labels[:num_actions]\\n\",\n \"\\n\",\n \"row_labels = []\\n\",\n \"for agent in agents:\\n\",\n \" alpha_value = float(agent.alpha.mean(0).squeeze())\\n\",\n \" row_labels.append(f'alpha={alpha_value:.2f}')\\n\",\n \"\\n\",\n \"fig, axes = plt.subplots(len(agents)+1, num_actions, figsize=(16, 8), sharex=True, sharey=True)\\n\",\n \"\\n\",\n \"for i in range(num_actions):\\n\",\n \" for j, agent in enumerate(agents):\\n\",\n \" sns.heatmap(agent.B[0][0, ..., i], ax=axes[j, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" sns.heatmap(env.B[0][..., i], ax=axes[-1, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" axes[0, i].set_title(action_labels[i])\\n\",\n \"\\n\",\n \"for j, label in enumerate(row_labels):\\n\",\n \" axes[j, 0].set_ylabel(label, rotation=25, labelpad=60, ha='left', va='center')\\n\",\n \"axes[-1, 0].set_ylabel('true B', rotation=0, labelpad=40, ha='left', va='center')\\n\",\n \"\\n\",\n \"\\n\",\n \"fig.tight_layout()\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Here, once again the agents have to learn the A matrix, but now have an informative prior over the B matrix: we fix it to the expected transition distribution under a flat prior over actions, i.e. the agent knows generally that motion on the grid is restricted to the locality, but have no sense of how particular actions relate to particular transitions.\\n\",\n \"#### We use a flat prior over initial hidden states\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"C = [jnp.zeros(num_obs[0])]\\n\",\n \"pA = [jnp.ones_like(env.A[0]) / num_obs[0]]\\n\",\n \"_A = jtu.tree_map(lambda a: dirichlet_expected_value(a), pA)\\n\",\n \"B_collapsed_actions = jnp.clip(env.B[0].sum(-1), max=1)\\n\",\n \"pB = [jnp.expand_dims(B_collapsed_actions, -1) + jnp.ones_like(env.B[0]) / num_states[0]]\\n\",\n \"_B = jtu.tree_map(lambda b: dirichlet_expected_value(b), pB)\\n\",\n \"\\n\",\n \"agents = []\\n\",\n \"for i in range(5):\\n\",\n \" agents.append( \\n\",\n \" Agent(\\n\",\n \" _A,\\n\",\n \" _B,\\n\",\n \" C,\\n\",\n \" _D,\\n\",\n \" E=None,\\n\",\n \" pA=pA,\\n\",\n \" pB=pB,\\n\",\n \" policy_len=3,\\n\",\n \" use_utility=False,\\n\",\n \" use_states_info_gain=True,\\n\",\n \" use_param_info_gain=True,\\n\",\n \" gamma=jnp.ones(batch_size),\\n\",\n \" alpha=jnp.ones(batch_size) * i * .2,\\n\",\n \" categorical_obs=False,\\n\",\n \" action_selection=\\\"stochastic\\\",\\n\",\n \" inference_algo=\\\"exact\\\",\\n\",\n \" num_iter=1,\\n\",\n \" learn_A=True,\\n\",\n \" learn_B=False,\\n\",\n \" learn_D=False,\\n\",\n \" batch_size=batch_size,\\n\",\n \" learning_mode=\\\"offline\\\",\\n\",\n \" )\\n\",\n \" )\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Run multiple blocks of active inference on grid world for each batch of agents that was initialized different `alpha` values. \\n\",\n \"\\n\",\n \"#### Since the agents are using offline learning (`learning_mode = \\\"offline\\\"`), this means that parameter updates to the A matrix are performed at the end of each block.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"pA_ground_truth = 1e4 * env.A[0] + 1e-4\\n\",\n \"pB_ground_truth = 1e4 * env.B[0] + 1e-4\\n\",\n \"num_timesteps = 50\\n\",\n \"num_blocks = 100\\n\",\n \"key = jr.PRNGKey(0)\\n\",\n \"block_and_batch_keys = jr.split(key, num_blocks * (batch_size+1)).reshape((num_blocks, batch_size+1, -1))\\n\",\n \"\\n\",\n \"divs1 = {i: [] for i in range(len(agents))}\\n\",\n \"divs2 = {i: [] for i in range(len(agents))}\\n\",\n \"for block in range(num_blocks):\\n\",\n \" block_keys = block_and_batch_keys[block]\\n\",\n \" for i, agent in enumerate(agents):\\n\",\n \" init_obs, init_states = vmap(env.reset)(block_keys[:-1])\\n\",\n \" last, info = jit(rollout, static_argnums=[1,2])(agent, env, num_timesteps, block_keys[-1], initial_carry={\\\"observation\\\": init_obs, \\\"env_state\\\": init_states})\\n\",\n \" agents[i] = last['agent']\\n\",\n \" divs1[i].append(kl_div_dirichlet(agents[i].pA[0], pA_ground_truth).mean(-1))\\n\",\n \" divs2[i].append(kl_div_dirichlet(agents[i].pB[0], pB_ground_truth).sum(-1).mean(-1))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Plot the KL divergence between the true parameters and believed parameters over time for the different groups of agents (agents with different levels of action stochasticity)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig, axes = plt.subplots(1, 2, figsize=(12, 5), sharex=True, sharey=False)\\n\",\n \"for i in range(len(agents)):\\n\",\n \" p = axes[0].plot(jnp.stack(divs1[i]).mean(-1), lw=3, label=agents[i].alpha.mean())\\n\",\n \" axes[0].plot(jnp.stack(divs1[i]), color=p[0].get_color(), alpha=.2)\\n\",\n \"\\n\",\n \" p = axes[1].plot(jnp.stack(divs2[i]).mean(-1), lw=3, label=agents[i].alpha.mean())\\n\",\n \" axes[1].plot(jnp.stack(divs2[i]), color=p[0].get_color(), alpha=.2)\\n\",\n \"\\n\",\n \"axes[0].legend(title='alpha')\\n\",\n \"axes[0].set_ylabel('KL divergence')\\n\",\n \"axes[0].set_xlabel('epoch')\\n\",\n \"axes[1].set_xlabel('epoch')\\n\",\n \"axes[0].set_title('A matrix')\\n\",\n \"axes[1].set_title('B matrix')\\n\",\n \"fig.tight_layout()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Visualize the learned A matrices alongside the true environmental parameters after training\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"n_batches_to_show = min(5, agents[0].A[0].shape[0])\\n\",\n \"num_rows = len(agents) + 1\\n\",\n \"row_labels = []\\n\",\n \"for agent in agents:\\n\",\n \" alpha_value = float(agent.alpha.mean(0).squeeze())\\n\",\n \" row_labels.append(f'alpha={alpha_value:.2f}')\\n\",\n \"\\n\",\n \"fig, axes = plt.subplots(num_rows, n_batches_to_show, figsize=(16, 8), sharex=True, sharey=True)\\n\",\n \"\\n\",\n \"for i in range(n_batches_to_show):\\n\",\n \" for j, agent in enumerate(agents):\\n\",\n \" sns.heatmap(agent.A[0][i], ax=axes[j, i], cmap='viridis')\\n\",\n \" sns.heatmap(env.A[0], ax=axes[-1, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" axes[0, i].set_title(f'batch={i + 1}')\\n\",\n \"\\n\",\n \"for j, label in enumerate(row_labels):\\n\",\n \" axes[j, 0].set_ylabel(label, rotation=25, labelpad=60, ha='left', va='center')\\n\",\n \"axes[-1, 0].set_ylabel('true A', rotation=0, labelpad=40, ha='left', va='center')\\n\",\n \"\\n\",\n \"fig.tight_layout()\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Visualize the B tensor (just the expected value of the posterior which in absence of learning is same as the prior) alongside the true environmental parameters after training\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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cuqVy5stStW1ffCXX48GF59dVX9fMjR46UWbNmyX333SdDhw6V9957T9544w1ZtWqVOIXTcxoAFPIbAMxEfoeGVR8A2CXd0PymKGEYtVRTQcs1AYBbpFu+kD5/+/btcuWVV+Y+zmnFVt1mr7zyihw5ckQOHTqU+3yDBg30BXTcuHEyc+ZMqV27trz44ovSu3fvkOYBAF5DfgOAmchvADBTuqH57bMsywpp5jBKz5gbQx7D6ZV+p88PcLvU7CUhj/Hpd7UDzl1W59/iZUXJb3IQQHGQ3879+zcAnA/5bV5+s+oDAK/nN50SAADHybTYPwEATER+A4CZyG8AMFOmoflNUQKuWyvR6fMD8PvSLS5PoSAHAdiF/AYAM5Hf0cV+cQC8nt9mzhoA4GrpVkm7pwAAKAbyGwDMRH4DgJnSDc1vihKw5c5cOyr93DkMmCPTirV7Cq7k9JwGYD7yGwDMRH7bj3+zAOCl/KYoAQBwnHQrzu4pAACKgfwGADOR3wBgpnRD85uiBMTrayVy5zDgPOnZZrYfeiGnizIGAO8hvwHATOS3c/H3bABuzG8zt+f2qFOnTsnYsWOlXr16UqZMGencubNs27bN7mkBQNidtWIDDgCA85HfAGAm8hsAzHTW0PymU8Igw4YNk88++0z+9re/Sa1ateS1116THj16yBdffCEXXXSRmMSESr/TOzwAN8swdKMmNyHXABQH+R2I7lsAJiC/zVOUzmauO4B7ZRia33RKGOLMmTPy5ptvyhNPPCFdu3aVRo0aycMPP6z/O2fOHLunBwBhbz889wAAOB/5DQBmIr8BwEzphuY3nRKGyMrKEr/fL6VLl853Xi3j9MEHH9g2L68pyv4T53s9gPPLtLg8mYYcBKCQ34HovgVgAvLbPEW5ZnDdAdwr09D8NnPWHlShQgXp1KmTPProo9KsWTOpXr26/P3vf5ctW7bobgkAcJN0Qy+qAOB15DcAmIn8BgAzpRua32bO2qPUXhJDhw7V+0fExsZKmzZt5JZbbpEdO3YEfX1GRoY+8sq2/BLjM2PDE5PQQQGEV4Yh7YaRYmJ+FyUHyUDAvcjvwuU3f3cE4DTkt3l//y4KrjuAe2UYmt/sKWGQhg0bysaNG+X06dPy3XffydatWyUzM1MuvvjioK9PSUmRihUr5jsOyp6ozxsAiiozOzbg8BLyG4CpyG/yG4CZyG/yG4CZMg3Nb59lWZbdk0Dx/Pjjj9KgQQO9+fWIESMKVekfUHGIayr9JuPOYbhZavaSkMe4d/fAgHNPtVwsXuH2/OaOLMCZyG/n5je5CeB8yO/Quf3v30XFdQeIjlQP5zfLNxlk3bp1ompITZo0kf3798v48eOladOmkpiYGPT1pUqV0kdeXr2gAjBLht/blyfyG4CpyG/yG4CZyG/yG4CZMgzNbzNn7VEnT56U5ORk+fe//y2VK1eWG264QR5//HEpWdLMtcO8LNjdBdyJAPwm02J1QTdjTVvAvcjvyGDfHgCRRn4jL647gDkyDc1vihIGuemmm/QBAG6Xkc3lCQBMRH4DgJnIbwAwU4ah+W3mrAEX4s5h4DdnDb2oIjTkIGA+8ju66L4FEC7kNwqD6w7gPGcNzW8zZw14CP9IBy86a+iaiHBGDhZlDADhRX7bj787AigO8hvFxXUEsNdZQ/PbzFkDAFwty9A1EQHA68hvADAT+Q0AZsoyNL8pSgCGYuMpuNlZf6zdU4AByDbAechv56KDAsD5kN8It6J0NStcdwBv5TdFCQCA45zNNvOiCgBeR34DgJnIbwAw01lD85uiBOAybDwFN8jKNrP9EM5FDgLRQX6bh+5bAAr5jXAr6jWD6w7grfw2c9YutGnTJunXr5/UqlVLfD6frFixIt/zp0+fltGjR0vt2rWlTJky0rx5c5k7d65t8wWASMrMjg04AADOR34DgJnIbwAwU6ah+U2nhEOkpaVJy5YtZejQofKHP/wh4PmkpCR577335LXXXpP69evLO++8I3/5y190EeO6666zZc4wB2sIwzRZhq6JCOciB4HoIL/dg+5bwFvIb9iN6w7grfymKOEQffr00UdBNm/eLIMHD5bu3bvrxyNGjJDnn39etm7dSlECgOv4s312TwEAUAzkNwCYifwGADP5Dc1vihKG6Ny5s7z99tu6k0J1R2zYsEH27dsnzzzzjN1Tg8G4cxhOZUq7IcxHDgLhRX67G5kJuBf5DSfiugO4N78pShjiueee090Rak+JEiVKSExMjMybN0+6du1q99QAIOz8frY8AgATkd8AYCbyGwDM5Dc0vylKGFSU+Oijj3S3RL169fTG2KNGjdJdEz169Aj6ORkZGfrIK9vyS4zPzAoanHk3AnciIBJMbT8MF/LbfuQgUDzktzfzmztZAfOR397Mb1Nx3QHMz28zSykec+bMGXnggQdk+vTp0q9fP0lISJDRo0fLwIED5amnnirw81JSUqRixYr5joOyJ6pzB4Di8GfHBBxeQn4DMBX5TX4DMBP5TX4DMJPf0PymU8IAmZmZ+lBLNuUVGxsr2dnZBX5ecnKyJCUl5Ts3oOKQiM0T7hfs7gLuREAkZBvafhgu5LdzkYPA+ZHf5HdedJ0B5iC/yW834LoDL8o2NL8pSjjE6dOnZf/+/bmPDx48KLt27ZLKlStL3bp1pVu3bjJ+/HgpU6aMXr5p48aN8uqrr+ruiYKUKlVKH3nRegjABNmGth+GC/kNwFTkN/kNwEzkN/kNwEzZhuY3RQmH2L59u1x55ZW5j3Mq9IMHD5ZXXnlFFi1apCv3t912m/zwww+6MPH444/LyJEjbZw1wFqOiAzLb+ZFFd5U1Bws6jiASchvFAZdZ4DzkN9wM64lcDPL0PymKOEQ3bt3F8uyCny+Ro0a8vLLL0d1TgBgF1PbDwHA68hvADAT+Q0AZso2NL8pSgCICDooEBLLzEo/kBe5Bk8iv1FM/N0RsBn5DY+hqxmuYZmZ3zEmdRKMHTvW9jn4fL7co3r16nLjjTfKt99+a+u8AMB1VPvhuQcAwPnIbwAwE/kNAGbym5nfruqUUMsf+f1+KVEict/W8OHDZcqUKfprqWKEKpTcfvvt8s9//jNiXxPw6l1w3IngXeFaE3H27Nny5JNPytGjR6Vly5by3HPPSYcOHYK+Vu3fk5iYmO+c2uwuPT09LHMBfg85CDcgvxFudFAA0UF+w2uKer3gugM35/dsG7LbiE6JIUOGyMaNG2XmzJm5XQrffPONbNiwQX+8Zs0aadu2rf4BfPDBB/r1/fv3zzeGKh6oTocc2dnZkpKSIg0aNJAyZcroH/jSpUt/dy5ly5bV+zvUrFlTOnbsKKNHj5adO3dG5PsGAK/y+X0BR1EtXrxYkpKSZPLkyTqnVc737t1bjh07VuDnxMfHy5EjR3IPOuEAoGjIbwAwE/kNAN7M78U2ZbcRnRKqGLFv3z5p0aKF7lJQLrzwQl2YUCZMmCBPPfWUXHzxxVKpUqVCjakKEq+99prMnTtXGjduLJs2bdIdD2rcbt26FWqMH374Qd544w25/PLLQ/juABR0dwF3InhYduhDTJ8+XXe35VTwVd6vWrVK5s+fr68bwahCtyo8A3YgB+EK5DeihO5bIMzIb+C8uO7Arfk93absNqJTomLFihIXF5fbpaCO2NjY3OdVoaJnz57SsGFDqVy58u+Ol5GRIVOnTtU/XFX5UcUM1V2hihLPP//8eT/3//7v/6R8+fJSrlw5qVKliuzdu1ePAwBwTqX/7NmzsmPHDunRo0fuuZiYGP14y5YtBX7e6dOnpV69elKnTh25/vrr5fPPPw/p+wAAryG/AcBM5DcAeC+/z9qY3UZ0Svyedu3aFen1+/fvl19++UUXMs59I1q3bn3ez73tttvkwQcf1B9///33urjRq1cv/QZWqFChGLMHUBDWEPYuX3bwgrI68lLL9qnjXCdOnNB7DFWvXj3fefV4z549Qb9mkyZNdJE5ISFBTp48qTvwOnfurC+utWvXDvVbAoqFHIRpyG/Yja4zoHjIb6B4uO7A5Pw+YWN2G9Ep8XtU10JeqqKjNqLOKzMzM181R1GtKLt27co9vvjii9/dV0J1bTRq1EgfV1xxhbz00kvy1Vdf6fW3QqGWk2rfvr0ubFSrVk3viaG6MHKopapy9tM491iyZElIXxsAHCfbF3ConFQZnPdQ58KlU6dOMmjQIGnVqpVexm/ZsmV6Sb/f66ADAORBfgOAmchvADBTdnTzO1zZbUynhFq+SVVuCkP9ID777LN851TRoWTJkvrj5s2b68rQoUOHCr1/REFylpE6c+ZMSOOojbxHjRqlCxNZWVnywAMP6A4MVShRRRfVDqM2DsnrhRde0Duj9+nTJ6SvDZiGO4fdzxck7pOTk/XmS3kFu0tLqVq1qs5n1dGWl3pc2HUP1TVDdc+p7jrAachBOBX5DSciM4HfR34D4cN1B6bkd1Ubs9uYTon69evLxx9/rDsGVGtJdnbBu3hcddVVsn37dnn11Vd1F4PaPTxvkUJ1I9x7770ybtw4WbBggRw4cEDvLv7cc8/px+ejln06evSoPnbv3i133nmnlC5dWhcQQrF27Vq9r8Wll16qdzl/5ZVXdNFELQulqF+QnP00co7ly5fLTTfdpPe4AAC3r4moLqDx8fH5joL+p0gVstu2bSvr16/PPaeuG+qxquoXhiqEf/rpp1KzZs2wfV8A4HbkNwCYifwGAO/ld5yN2W1Mp4QqIgwePFh3OaiuhIMHDxb4WrV59cSJE+W+++6T9PR0GTp0qG4rUT+gHI8++qjuqFCtK19//bVccMEF0qZNG92hcD7z5s3Th1KpUiW9ftbq1av1elrhpNbkUgrauFsVK1T3x+zZs8P6dQGv3I3AnQjmrYlYVOquAHXdUPsOdejQQWbMmCFpaWmSmJion1fXhYsuuii3hXHKlCnSsWNHvTzfTz/9pDvRvv32Wxk2bFjokwGihByE3chvmIQ7WYHfkN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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"num_actions = env.B[0].shape[-1]\\n\",\n \"base_labels = [\\\"Up\\\", \\\"Right\\\", \\\"Down\\\", \\\"Left\\\", \\\"Stay\\\"]\\n\",\n \"action_labels = base_labels[:num_actions]\\n\",\n \"\\n\",\n \"row_labels = []\\n\",\n \"for agent in agents:\\n\",\n \" alpha_value = float(agent.alpha.mean(0).squeeze())\\n\",\n \" row_labels.append(f'alpha={alpha_value:.2f}')\\n\",\n \"\\n\",\n \"\\n\",\n \"fig, axes = plt.subplots(len(agents)+1, num_actions, figsize=(16, 8), sharex=True, sharey=True)\\n\",\n \"\\n\",\n \"\\n\",\n \"for i in range(num_actions):\\n\",\n \" for j, agent in enumerate(agents):\\n\",\n \" sns.heatmap(agent.B[0][0, ..., i], ax=axes[j, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" sns.heatmap(env.B[0][..., i], ax=axes[-1, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" axes[0, i].set_title(action_labels[i])\\n\",\n \"\\n\",\n \"for j, label in enumerate(row_labels):\\n\",\n \" axes[j, 0].set_ylabel(label, rotation=25, labelpad=60, ha='left', va='center')\\n\",\n \"axes[-1, 0].set_ylabel('true B', rotation=0, labelpad=40, ha='left', va='center')\\n\",\n \"\\n\",\n \"\\n\",\n \"fig.tight_layout()\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Here, once again the agents have to learn the A matrix, but now have an informative prior over the B matrix: we fix it to the expected transition distribution under a flat prior over actions, i.e. the agent knows generally that motion on the grid is restricted to the locality, but have no sense of how particular actions relate to particular transitions.\\n\",\n \"#### We use a precise and accruate prior over initial hidden states\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"C = [jnp.zeros(num_obs[0])]\\n\",\n \"pA = [jnp.ones_like(env.A[0]) / num_obs[0]]\\n\",\n \"_A = jtu.tree_map(lambda a: dirichlet_expected_value(a), pA)\\n\",\n \"B_collapsed_actions = jnp.clip(env.B[0].sum(-1), max=1)\\n\",\n \"pB = [jnp.expand_dims(B_collapsed_actions, -1) + jnp.ones_like(env.B[0]) / num_states[0]]\\n\",\n \"_B = jtu.tree_map(lambda b: dirichlet_expected_value(b), pB)\\n\",\n \"\\n\",\n \"agents = []\\n\",\n \"for i in range(5):\\n\",\n \" agents.append( \\n\",\n \" Agent(\\n\",\n \" _A,\\n\",\n \" _B,\\n\",\n \" C,\\n\",\n \" D,\\n\",\n \" E=None,\\n\",\n \" pA=pA,\\n\",\n \" pB=pB,\\n\",\n \" policy_len=3,\\n\",\n \" use_utility=False,\\n\",\n \" use_states_info_gain=True,\\n\",\n \" use_param_info_gain=True,\\n\",\n \" gamma=jnp.ones(batch_size),\\n\",\n \" alpha=jnp.ones(batch_size) * i * .2,\\n\",\n \" categorical_obs=False,\\n\",\n \" action_selection=\\\"stochastic\\\",\\n\",\n \" inference_algo=\\\"exact\\\",\\n\",\n \" num_iter=1,\\n\",\n \" learn_A=True,\\n\",\n \" learn_B=False,\\n\",\n \" learn_D=False,\\n\",\n \" batch_size=batch_size,\\n\",\n \" learning_mode=\\\"offline\\\",\\n\",\n \" )\\n\",\n \" )\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Run multiple blocks of active inference on grid world for each batch of agents that was initialized different `alpha` values. \\n\",\n \"\\n\",\n \"#### Since the agents are using offline learning (`learning_mode = \\\"offline\\\"`), this means that parameter updates to the A matrix are performed at the end of each block.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"pA_ground_truth = 1e4 * env.A[0] + 1e-4\\n\",\n \"pB_ground_truth = 1e4 * env.B[0] + 1e-4\\n\",\n \"num_timesteps = 50\\n\",\n \"num_blocks = 100\\n\",\n \"key = jr.PRNGKey(0)\\n\",\n \"block_and_batch_keys = jr.split(key, num_blocks * (batch_size+1)).reshape((num_blocks, batch_size+1, -1))\\n\",\n \"\\n\",\n \"divs1 = {i: [] for i in range(len(agents))}\\n\",\n \"divs2 = {i: [] for i in range(len(agents))}\\n\",\n \"for block in range(num_blocks):\\n\",\n \" block_keys = block_and_batch_keys[block]\\n\",\n \" for i, agent in enumerate(agents):\\n\",\n \" init_obs, init_states = vmap(env.reset)(block_keys[:-1])\\n\",\n \" last, info = jit(rollout, static_argnums=[1,2])(agent, env, num_timesteps, block_keys[-1], initial_carry={\\\"observation\\\": init_obs, \\\"env_state\\\": init_states})\\n\",\n \" agents[i] = last['agent']\\n\",\n \" divs1[i].append(kl_div_dirichlet(agents[i].pA[0], pA_ground_truth).mean(-1))\\n\",\n \" divs2[i].append(kl_div_dirichlet(agents[i].pB[0], pB_ground_truth).sum(-1).mean(-1))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Plot the KL divergence between the true parameters and believed parameters over time for the different groups of agents (agents with different levels of action stochasticity)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig, axes = plt.subplots(1, 2, figsize=(12, 5), sharex=True, sharey=False)\\n\",\n \"for i in range(len(agents)):\\n\",\n \" p = axes[0].plot(jnp.stack(divs1[i]).mean(-1), lw=3, label=agents[i].alpha.mean())\\n\",\n \" axes[0].plot(jnp.stack(divs1[i]), color=p[0].get_color(), alpha=.2)\\n\",\n \"\\n\",\n \" p = axes[1].plot(jnp.stack(divs2[i]).mean(-1), lw=3, label=agents[i].alpha.mean())\\n\",\n \" axes[1].plot(jnp.stack(divs2[i]), color=p[0].get_color(), alpha=.2)\\n\",\n \"\\n\",\n \"axes[0].legend(title='alpha')\\n\",\n \"axes[0].set_ylabel('KL divergence')\\n\",\n \"axes[0].set_xlabel('epoch')\\n\",\n \"axes[1].set_xlabel('epoch')\\n\",\n \"axes[0].set_title('A matrix')\\n\",\n \"axes[1].set_title('B matrix')\\n\",\n \"fig.tight_layout()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Visualize the learned A matrices alongside the true environmental parameters after training\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"n_batches_to_show = min(5, agents[0].A[0].shape[0])\\n\",\n \"num_rows = len(agents) + 1\\n\",\n \"row_labels = []\\n\",\n \"for agent in agents:\\n\",\n \" alpha_value = float(agent.alpha.mean(0).squeeze())\\n\",\n \" row_labels.append(f'alpha={alpha_value:.2f}')\\n\",\n \"\\n\",\n \"fig, axes = plt.subplots(num_rows, n_batches_to_show, figsize=(16, 8), sharex=True, sharey=True)\\n\",\n \"\\n\",\n \"for i in range(n_batches_to_show):\\n\",\n \" for j, agent in enumerate(agents):\\n\",\n \" sns.heatmap(agent.A[0][i], ax=axes[j, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" sns.heatmap(env.A[0], ax=axes[-1, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" axes[0, i].set_title(f'batch={i + 1}')\\n\",\n \"\\n\",\n \"for j, label in enumerate(row_labels):\\n\",\n \" axes[j, 0].set_ylabel(label, rotation=25, labelpad=60, ha='left', va='center')\\n\",\n \"axes[-1, 0].set_ylabel('true A', rotation=0, labelpad=40, ha='left', va='center')\\n\",\n \"\\n\",\n \"fig.tight_layout()\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Visualize the B tensor (just the expected value of the posterior which in absence of learning is same as the prior) alongside the true environmental parameters after training\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"num_actions = env.B[0].shape[-1]\\n\",\n \"base_labels = [\\\"Up\\\", \\\"Right\\\", \\\"Down\\\", \\\"Left\\\", \\\"Stay\\\"]\\n\",\n \"action_labels = base_labels[:num_actions]\\n\",\n \"\\n\",\n \"row_labels = []\\n\",\n \"for agent in agents:\\n\",\n \" alpha_value = float(agent.alpha.mean(0).squeeze())\\n\",\n \" row_labels.append(f'alpha={alpha_value:.2f}')\\n\",\n \"\\n\",\n \"\\n\",\n \"fig, axes = plt.subplots(len(agents)+1, num_actions, figsize=(16, 8), sharex=True, sharey=True)\\n\",\n \"\\n\",\n \"\\n\",\n \"for i in range(num_actions):\\n\",\n \" for j, agent in enumerate(agents):\\n\",\n \" sns.heatmap(agent.B[0][0, ..., i], ax=axes[j, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" sns.heatmap(env.B[0][..., i], ax=axes[-1, i], cmap='viridis', vmax=1., vmin=0.)\\n\",\n \" axes[0, i].set_title(action_labels[i])\\n\",\n \"\\n\",\n \"for j, label in enumerate(row_labels):\\n\",\n \" axes[j, 0].set_ylabel(label, rotation=25, labelpad=60, ha='left', va='center')\\n\",\n \"axes[-1, 0].set_ylabel('true B', rotation=0, labelpad=40, ha='left', va='center')\\n\",\n \"\\n\",\n \"\\n\",\n \"fig.tight_layout()\\n\"\n ]\n }\n ],\n \"metadata\": {},\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/legacy/agent_demo.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Active Inference Demo: Constructing a basic generative model from the \\\"ground up\\\"\\n\",\n \"This demo notebook provides a full walk-through of how to build a POMDP agent's generative model and perform active inference routine (inversion of the generative model) using the `Agent()` class of `pymdp`. We build a generative model from 'ground up', directly encoding our own A, B, and C matrices.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Imports\\n\",\n \"\\n\",\n \"First, import `pymdp` and the modules we'll need.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import os\\n\",\n \"import sys\\n\",\n \"import pathlib\\n\",\n \"import numpy as np\\n\",\n \"import copy\\n\",\n \"\\n\",\n \"path = pathlib.Path(os.getcwd())\\n\",\n \"module_path = str(path.parent) + '/'\\n\",\n \"sys.path.append(module_path)\\n\",\n \"\\n\",\n \"from pymdp.agent import Agent # noqa: E402\\n\",\n \"from pymdp import utils # noqa: E402\\n\",\n \"from pymdp.maths import softmax # noqa: E402\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## The world (as represented by the agent's generative model)\\n\",\n \"\\n\",\n \"### Hidden states\\n\",\n \"\\n\",\n \"We assume the agent's \\\"represents\\\" (this should make you think: generative _model_ , not _process_ ) its environment using two latent variables that are statistically independent of one another - we can thus represent them using two _hidden state factors._\\n\",\n \"\\n\",\n \"We refer to these two hidden state factors are `GAME_STATE` and `PLAYING_VS_SAMPLING`. \\n\",\n \"\\n\",\n \"#### 1. `GAME_STATE`\\n\",\n \"The first factor is a binary variable representing whether some 'reward structure' that characterises the world. It has two possible values or levels: one level that will lead to rewards with high probability (`GAME_STATE = 0`, a state/level we will call `HIGH_REW`), and another level that will lead to \\\"punishments\\\" (e.g. losing money) with high probability (`GAME_STATE = 1`, a state/level we will call `LOW_REW`). You can think of this hidden state factor as describing the 'pay-off' structure of e.g. a two-armed bandit or slot-machine with two different settings - one where you're more likely to win (`HIGH_REW`), and one where you're more likely to lose (`LOW_REW`). Crucially, the agent doesn't _know_ what the `GAME_STATE` actually is. They will have to infer it by actively furnishing themselves with observations\\n\",\n \"\\n\",\n \"#### 1. `PLAYING_VS_SAMPLING`\\n\",\n \"\\n\",\n \"The second factor is a ternary (3-valued) variable representing the decision-state or 'sampling state' of the agent itself. The first state/level of this hidden state factor is just the starting or initial state of the agent (`PLAYING_VS_SAMPLING = 0`, a state that we can call `START`); the second state/level is the state the agent occupies when \\\"playing\\\" the multi-armed bandit or slot machine (`PLAYING_VS_SAMPLING = 1`, a state that we can call `PLAYING`); and the third state/level of this factor is a \\\"sampling state\\\" (`PLAYING_VS_SAMPLING = 2`, a state that we can call `SAMPLING`). This is a decision-state that the agent occupies when it is \\\"sampling\\\" data in order to _find out_ the level of the first hidden state factor - the `GAME_STATE`. \\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"factor_names = [\\\"GAME_STATE\\\", \\\"PLAYING_VS_SAMPLING\\\"]\\n\",\n \"num_factors = len(factor_names) # this is the total number of hidden state factors\\n\",\n \"\\n\",\n \"HIGH_REW, LOW_REW = 0, 1 # let's assign the indices names so that when we build the A matrices, things will be more 'semantically' obvious\\n\",\n \"START, PLAYING, SAMPLING = 0, 1, 2 # let's assign the indices names so that when we build the A matrices, things will be more 'semantically' obvious\\n\",\n \"\\n\",\n \"num_states = [len([HIGH_REW,LOW_REW]), len([START, PLAYING, SAMPLING])] # this is a list of the dimensionalities of each hidden state factor \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Observations \\n\",\n \"\\n\",\n \"The observation modalities themselves are divided into 3 modalities. You can think of these as 3 independent sources of information that the agent has access to. You could think of thus in direct perceptual terms - e.g. 3 different sensory organs like eyes, ears, & nose, that give you qualitatively-different kinds of information. Or you can think of it more abstractly - like getting your news from 3 different media sources (online news articles, Twitter feed, and Instagram).\\n\",\n \"\\n\",\n \"#### 1. Observations of the game state - `GAME_STATE_OBS`\\n\",\n \"The first observation modality is the `GAME_STATE_OBS` modality, and corresponds to observations that give the agent information about the `GAME_STATE`. There are three possible outcomes within this modality: `HIGH_REW_EVIDENCE` (`GAME_STATE_OBS = 0`), `LOW_REW_EVIDENCE` (`GAME_STATE_OBS = 1`), and `NO_EVIDENCE` (`GAME_STATE_OBS = 2`). So the first outcome can be described as lending evidence to the idea that the `GAME_STATE` is `HIGH_REW`; the second outcome can be described as lending evidence to the idea that the `GAME_STATE` is `LOW_REW`; and the third outcome within this modality doesn't tell the agent one way or another whether the `GAME_STATE` is `HIGH_REW` or `LOW_REW`. \\n\",\n \"\\n\",\n \"#### 2. Reward observations - `GAME_OUTCOME`\\n\",\n \"The second observation modality is the `GAME_OUTCOME` modality, and corresponds to arbitrary observations that are functions of the `GAME_STATE`. We call the first outcome level of this modality `REWARD` (`GAME_OUTCOME = 0`), which gives you a hint about how we'll set up the C matrix (the agent's \\\"utility function\\\" over outcomes). We call the second outcome level of this modality `PUN` (`GAME_OUTCOME = 1`), and the third outcome level `NEUTRAL` (`GAME_OUTCOME = 2`). By design, we will set up the `A` matrix such that the `REWARD` outcome is (expected to be) more likely when the `GAME_STATE` is `HIGH_REW` (`0`) and when the agent is in the `PLAYING` state, and that the `PUN` outcome is (expected to be) more likely when the `GAME_STATE` is `LOW_REW` (`1`) and the agent is in the `PLAYING` state. The `NEUTRAL` outcome is not expected to occur when the agent is playing the game, but will be expected to occur when the agent is in the `SAMPLING` state. This `NEUTRAL` outcome within the `GAME_OUTCOME` modality is thus a meaningless or 'null' observation that the agent gets when it's not actually playing the game (because an observation has to be sampled nonetheless from _all_ modalities).\\n\",\n \"\\n\",\n \"#### 3. \\\"Proprioceptive\\\" or self-state observations - `ACTION_SELF_OBS`\\n\",\n \"The third observation modality is the `ACTION_SELF_OBS` modality, and corresponds to the agent observing what level of the `PLAYING_VS_SAMPLING` state it is currently in. These observations are direct, 'unambiguous' mappings to the true `PLAYING_VS_SAMPLING` state, and simply allow the agent to \\\"know\\\" whether it's playing the game, sampling information to learn about the game state, or where it's sitting at the `START` state. The levels of this outcome are simply thus `START_O`, `PLAY_O`, and `SAMPLE_O`, where the `_O` suffix simply distinguishes them from their corresponding hidden states, for which they provide direct evidence. \\n\",\n \"\\n\",\n \"#### Note about the arbitrariness of 'labelling' observations, before defining the `A` and `C` matrices.\\n\",\n \"\\n\",\n \"There is a bit of a circularity here, in that that we're \\\"pre-empting\\\" what the A matrix (likelihood mapping) should look like, by giving these observations labels that imply particular roles or meanings. An observation per se doesn't mean _anything_, it's just some discrete index that distinguishes is from another observation. It's only through its probabilistic relationship to hidden states (encoded in the `A` matrix, as we'll see below) that we endow an observation with meaning. For example: by already labelling `GAME_STATE_OBS=0` as `HIGH_REW_EVIDENCE`, that's a hint about how we're going to structure the `A` matrix for the `GAME_STATE_OBS` modality.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"modality_names = [\\\"GAME_STATE_OBS\\\", \\\"GAME_OUTCOME\\\", \\\"ACTION_SELF_OBS\\\"]\\n\",\n \"num_modalities = len(modality_names)\\n\",\n \"\\n\",\n \"HIGH_REW_EVIDENCE, LOW_REW_EVIDENCE, NO_EVIDENCE = 0, 1, 2\\n\",\n \"REWARD, PUN, NEUTRAL = 0, 1, 2\\n\",\n \"START_O, PLAY_O, SAMPLE_O = 0, 1, 2\\n\",\n \"\\n\",\n \"num_obs = [len([HIGH_REW_EVIDENCE, LOW_REW_EVIDENCE, NO_EVIDENCE]), len([REWARD, PUN, NEUTRAL]), len([START_O, PLAY_O, SAMPLE_O])]\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Setting up observation likelihood matrix - first main component of generative model\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"A = utils.obj_array_zeros([[o] + num_states for _, o in enumerate(num_obs)])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Set up the **first** modality's likelihood mapping, correspond to how `\\\"GAME_STATE_OBS\\\"` i.e. `modality_names[0]` are related to hidden states.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"A[0][NO_EVIDENCE,:, START] = 1.0 # they always get the 'no evidence' observation in the START STATE\\n\",\n \"A[0][NO_EVIDENCE, :, PLAYING] = 1.0 # they always get the 'no evidence' observation in the PLAYING STATE\\n\",\n \"\\n\",\n \"# the agent expects to see the HIGH_REW_EVIDENCE observation with 80% probability, if the GAME_STATE is HIGH_REW, and the agent is in the SAMPLING state\\n\",\n \"A[0][HIGH_REW_EVIDENCE, HIGH_REW, SAMPLING] = 0.8\\n\",\n \"# the agent expects to see the LOW_REW_EVIDENCE observation with 20% probability, if the GAME_STATE is HIGH_REW, and the agent is in the SAMPLING state\\n\",\n \"A[0][LOW_REW_EVIDENCE, HIGH_REW, SAMPLING] = 0.2\\n\",\n \"\\n\",\n \"# the agent expects to see the LOW_REW_EVIDENCE observation with 80% probability, if the GAME_STATE is LOW_REW, and the agent is in the SAMPLING state\\n\",\n \"A[0][LOW_REW_EVIDENCE, LOW_REW, SAMPLING] = 0.8\\n\",\n \"# the agent expects to see the HIGH_REW_EVIDENCE observation with 20% probability, if the GAME_STATE is LOW_REW, and the agent is in the SAMPLING state\\n\",\n \"A[0][HIGH_REW_EVIDENCE, LOW_REW, SAMPLING] = 0.2\\n\",\n \"\\n\",\n \"# quick way to do this\\n\",\n \"# A[0][:, :, 0] = 1.0\\n\",\n \"# A[0][:, :, 1] = 1.0\\n\",\n \"# A[0][:, :, 2] = np.array([[0.8, 0.2], [0.2, 0.8], [0.0, 0.0]])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Set up the **second** modality's likelihood mapping, correspond to how `\\\"GAME_OUTCOME\\\"` i.e. `modality_names[1]` are related to hidden states.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"A[1][NEUTRAL, :, START] = 1.0 # regardless of the game state, if you're at the START, you see the 'neutral' outcome\\n\",\n \"\\n\",\n \"A[1][NEUTRAL, :, SAMPLING] = 1.0 # regardless of the game state, if you're in the SAMPLING state, you see the 'neutral' outcome\\n\",\n \"\\n\",\n \"# this is the distribution that maps from the \\\"GAME_STATE\\\" to the \\\"GAME_OUTCOME\\\" observation , in the case that \\\"GAME_STATE\\\" is `HIGH_REW`\\n\",\n \"HIGH_REW_MAPPING = softmax(np.array([1.0, 0])) \\n\",\n \"\\n\",\n \"# this is the distribution that maps from the \\\"GAME_STATE\\\" to the \\\"GAME_OUTCOME\\\" observation , in the case that \\\"GAME_STATE\\\" is `LOW_REW`\\n\",\n \"LOW_REW_MAPPING = softmax(np.array([0.0, 1.0]))\\n\",\n \"\\n\",\n \"# fill out the A matrix using the reward probabilities\\n\",\n \"A[1][REWARD, HIGH_REW, PLAYING] = HIGH_REW_MAPPING[0]\\n\",\n \"A[1][PUN, HIGH_REW, PLAYING] = HIGH_REW_MAPPING[1]\\n\",\n \"\\n\",\n \"A[1][REWARD, LOW_REW, PLAYING] = LOW_REW_MAPPING[0]\\n\",\n \"A[1][PUN, LOW_REW, PLAYING] = LOW_REW_MAPPING[1]\\n\",\n \"\\n\",\n \"\\n\",\n \"# quick way to do this\\n\",\n \"# A[1][2, :, 0] = np.ones(num_states[0])\\n\",\n \"# A[1][0:2, :, 1] = softmax(np.eye(num_obs[1] - 1)) # relationship of game state to reward observations (mapping between reward-state (first hidden state factor) and rewards (Good vs Bad))\\n\",\n \"# A[1][2, :, 2] = np.ones(num_states[0])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Set up the **third** modality's likelihood mapping, correspond to how `\\\"ACTION_SELF_OBS\\\"` i.e. `modality_names[2]` are related to hidden states.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"A[2][START_O,:,START] = 1.0\\n\",\n \"A[2][PLAY_O,:,PLAYING] = 1.0\\n\",\n \"A[2][SAMPLE_O,:,SAMPLING] = 1.0\\n\",\n \"\\n\",\n \"# quick way to do this\\n\",\n \"# modality_idx, factor_idx = 2, 2\\n\",\n \"# for sampling_state_i in num_states[factor_idx]:\\n\",\n \"# A[modality_idx][sampling_state_i,:,sampling_state_i] = 1.0\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Control state factors\\n\",\n \"\\n\",\n \"The 'control state' factors are the agent's representation of the control states (or actions) that _it believes_ can influence the dynamics of the hidden states - i.e. hidden state factors that are under the influence of control states are are 'controllable'. In practice, we often encode _every_ hidden state factor as being under the influence of control states, but the 'uncontrollable' hidden state factors are driven by a trivially-1-dimensional control state or action-affordance. This trivial action simply 'maintains the default environmental dynamics as they are' i.e. does nothing. This will become more clear when we set up the transition model (the `B` matrices) below.\\n\",\n \"\\n\",\n \"#### 1. `NULL`\\n\",\n \"This reflects the agent's lack of ability to influence the `GAME_STATE` using policies or actions. The dimensionality of this control factor is 1, and there is only one action along this control factor: `NULL_ACTION` or \\\"don't do anything to do the environment\\\". This just means that the transition dynamics along the `GAME_STATE` hidden state factor have their own, uncontrollable dynamics that are not conditioned on this `NULL` control state - or rather, _always_ conditioned on an unchanging, 1-dimensional `NULL_ACTION`.\\n\",\n \"\\n\",\n \"#### 1. `PLAYING_VS_SAMPLING_CONTROL`\\n\",\n \"This is a control factor that reflects the agent's ability to move itself between the `START`, `PLAYING` and `SAMPLING` states of the `PLAYING_VS_SAMPLING` hidden state factor. The levels/values of this control factor are `START_ACTION`, `PLAY_ACTION`, and `SAMPLE_ACTION`. When we describe the `B` matrices below, we will set up the transition dynamics of the `PLAYING_VS_SAMPLING` hidden state factor, such that they are totally determined by the value of the `PLAYING_VS_SAMPLING_CONTROL` factor. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"control_names = [\\\"NULL\\\", \\\"PLAYING_VS_SAMPLING_CONTROL\\\"]\\n\",\n \"num_control_factors = len(control_names) # this is the total number of controllable hidden state factors\\n\",\n \"\\n\",\n \"NULL_ACTION = 0\\n\",\n \"START_ACTION, PLAY_ACTION, SAMPLE_ACTION = 0, 1, 2\\n\",\n \"\\n\",\n \"num_control = [len([NULL_ACTION]), len([START_ACTION, PLAY_ACTION, SAMPLE_ACTION])] # this is a list of the dimensionalities of each hidden state factor \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### (Controllable-) Transition Dynamics\\n\",\n \"\\n\",\n \"Importantly, some hidden state factors are _controllable_ by the agent, meaning that the probability of being in state $i$ at $t+1$ isn't merely a function of the state at $t$, but also of actions (or from the generative model's perspective, _control states_ ). So each transition likelihood or `B` matrix encodes conditional probability distributions over states at $t+1$, where the conditioning variables are both the states at $t-1$ _and_ the actions at $t-1$. This extra conditioning on control states is encoded by a third, lagging dimension on each factor-specific `B` matrix. So they are technically `B` \\\"tensors\\\" or an array of action-conditioned `B` matrices.\\n\",\n \"\\n\",\n \"For example, in our case the 2nd hidden state factor (`PLAYING_VS_SAMPLING`) is under the control of the agent, which means the corresponding transition likelihoods `B[1]` are index-able by both previous state and action.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"control_fac_idx = [1] # this is the (non-trivial) controllable factor, where there will be a >1-dimensional control state along this factor\\n\",\n \"B = utils.obj_array(num_factors)\\n\",\n \"\\n\",\n \"p_stoch = 0.0\\n\",\n \"\\n\",\n \"# we cannot influence factor zero, set up the 'default' stationary dynamics - \\n\",\n \"# one state just maps to itself at the next timestep with very high probability, by default. So this means the reward state can\\n\",\n \"# change from one to another with some low probability (p_stoch)\\n\",\n \"\\n\",\n \"B[0] = np.zeros((num_states[0], num_states[0], num_control[0])) \\n\",\n \"B[0][HIGH_REW, HIGH_REW, NULL_ACTION] = 1.0 - p_stoch\\n\",\n \"B[0][LOW_REW, HIGH_REW, NULL_ACTION] = p_stoch\\n\",\n \"\\n\",\n \"B[0][LOW_REW, LOW_REW, NULL_ACTION] = 1.0 - p_stoch\\n\",\n \"B[0][HIGH_REW, LOW_REW, NULL_ACTION] = p_stoch\\n\",\n \"\\n\",\n \"# setup our controllable factor.\\n\",\n \"B[1] = np.zeros((num_states[1], num_states[1], num_control[1]))\\n\",\n \"B[1][START, :, START_ACTION] = 1.0 \\n\",\n \"B[1][PLAYING, :, PLAY_ACTION] = 1.0\\n\",\n \"B[1][SAMPLING, :, SAMPLE_ACTION] = 1.0\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Prior preferences\\n\",\n \"\\n\",\n \"Now we parameterise the C vector, or the prior beliefs about observations. This will be used in the expression of the prior over actions, which is technically a softmax function of the negative expected free energy of each action. It is the equivalent of the exponentiated reward function in reinforcement learning treatments.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"C = utils.obj_array_zeros([num_ob for num_ob in num_obs])\\n\",\n \"C[1][REWARD] = 1.0 # make the observation we've a priori named `REWARD` actually desirable, by building a high prior expectation of encountering it \\n\",\n \"C[1][PUN] = -1.0 # make the observation we've a prior named `PUN` actually aversive,by building a low prior expectation of encountering it\\n\",\n \"\\n\",\n \"# the above code implies the following for the `neutral' observation:\\n\",\n \"C[1][NEUTRAL] = 0.0 # we don't need to write this - but it's basically just saying that observing `NEUTRAL` is in between reward and punishment\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Initialise an instance of the `Agent()` class:\\n\",\n \"\\n\",\n \"All you have to do is call `Agent(generative_model_params...)` where `generative_model_params` are your A, B, C's... and whatever parameters of the generative model you want to specify\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"agent = Agent(A=A, B=B, C=C, control_fac_idx=control_fac_idx)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Generative process:\\n\",\n \"Important note how the generative process doesn't have to be described by A and B matrices - can just be the arbitrary 'rules of the game' that you 'write in' as a modeller. But here we just use the same transition/likelihood matrices to make the sampling process straightforward.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# transition/observation matrices characterising the generative process\\n\",\n \"A_gp = copy.deepcopy(A)\\n\",\n \"B_gp = copy.deepcopy(B)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Initialise the simulation\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# initial state\\n\",\n \"T = 20 # number of timesteps in the simulation\\n\",\n \"observation = [NO_EVIDENCE, NEUTRAL, START_O] # initial observation\\n\",\n \"state = [HIGH_REW, START] # initial (true) state\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Create some string names for the state, observation, and action indices to help with print statements\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"states_idx_names = [ [\\\"HIGH_REW\\\", \\\"LOW_REW\\\"], \\\\\\n\",\n \" [\\\"START\\\", \\\"PLAYING\\\", \\\"SAMPLING\\\"]]\\n\",\n \"\\n\",\n \"obs_idx_names = [ [\\\"HIGH_REW_EV\\\", \\\"LOW_REW_EV\\\", \\\"NO_EV\\\"], \\\\\\n\",\n \" [\\\"REWARD\\\", \\\"PUN\\\", \\\"NEUTRAL\\\"], \\\\\\n\",\n \" [\\\"START\\\", \\\"PLAYING\\\", \\\"SAMPLING\\\"] ]\\n\",\n \"\\n\",\n \"action_idx_names = [ [\\\"NULL\\\"], [\\\"MOVE TO START\\\", \\\"PLAY\\\", \\\"SAMPLE\\\"] ]\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Run simulation\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"for t in range(T):\\n\",\n \" \\n\",\n \" print(f\\\"\\\\nTime {t}:\\\")\\n\",\n \" \\n\",\n \" print(f\\\"State: {[(factor_names[f], states_idx_names[f][state[f]]) for f in range(num_factors)]}\\\")\\n\",\n \" print(f\\\"Observations: {[(modality_names[g], obs_idx_names[g][observation[g]]) for g in range(num_modalities)]}\\\")\\n\",\n \" \\n\",\n \" # update agent\\n\",\n \" belief_state = agent.infer_states(observation)\\n\",\n \" agent.infer_policies()\\n\",\n \" action = agent.sample_action()\\n\",\n \" \\n\",\n \" # update environment\\n\",\n \" for f, s in enumerate(state):\\n\",\n \" state[f] = utils.sample(B_gp[f][:, s, int(action[f])])\\n\",\n \"\\n\",\n \" for g, _ in enumerate(observation):\\n\",\n \" observation[g] = utils.sample(A_gp[g][:, state[0], state[1]])\\n\",\n \"\\n\",\n \" print(f\\\"Beliefs: {[(factor_names[f], belief_state[f].round(3).T) for f in range(num_factors)]}\\\")\\n\",\n \" print(f\\\"Action: {[(control_names[a], action_idx_names[a][int(action[a])]) for a in range(num_factors)]}\\\")\"\n ]\n }\n ],\n \"metadata\": {\n \"interpreter\": {\n \"hash\": \"43ee964e2ad3601b7244370fb08e7f23a81bd2f0e3c87ee41227da88c57ff102\"\n },\n \"kernelspec\": {\n \"display_name\": \"Python 3.7.10 64-bit ('pymdp_env': conda)\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.7.10\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/legacy/free_energy_calculation.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Computing the variational free energy in categorical models\\n\",\n \"\\n\",\n \"[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/infer-actively/pymdp/blob/main/docs/notebooks/free_energy_calculation.ipynb)\\n\",\n \"\\n\",\n \"*Author: Conor Heins*\\n\",\n \"\\n\",\n \"This notebook walks the user through the computation of the variational free energy (or *VFE*) for discrete generative models, composed of categorical distributions. We can represent these sorts of generative models easily in array-focused programming languages like `NumPy` and `MATLAB` using matrices and vectors.\\n\",\n \"\\n\",\n \"In the discrete state-space formulation, the variational free energy is very straightforward to compute when we take advantage of the NDarray representation of probability distributions. The highly-optimized matrix algebra built into today's numerical computing paradigms can be exploited to write simple, one-line expressions for information-theoretic terms (like Kullback-Leibler divergences, cross-entropies, log-likelihoods, etc.). All these terms end up being variants of things like inner products, matrix-vector products or matrix-matrix multiplications.\\n\",\n \"\\n\",\n \"This notebook is inspired by the supplementary MATLAB script for the paper [\\\"A Step-by-Step Tutorial on Active Inference Modelling and its Application to Empirical Data\\\"](https://www.sciencedirect.com/science/article/pii/S0022249621000973) by Ryan Smith, Karl Friston, and Christopher Whyte. The original MATLAB script is called `VFE_calculation_example.m`, and can be found on [Ryan Smith's GitHub repository](https://github.com/rssmith33/Active-Inference-Tutorial-Scripts), which also contains a set of tutorial scripts that are supplementary to their paper.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"*Note*: When running this notebook in Google Colab, you may have to run `!pip install inferactively-pymdp` at the top of the notebook, before you can `import pymdp`. That cell is left commented out below, in case you are running this notebook from Google Colab.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# ! pip install inferactively-pymdp\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Imports\\n\",\n \"\\n\",\n \"First, import `pymdp` and the modules we'll need.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import os\\n\",\n \"import sys\\n\",\n \"import pathlib\\n\",\n \"import numpy as np\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"from IPython.display import display, Latex\\n\",\n \"\\n\",\n \"path = pathlib.Path(os.getcwd())\\n\",\n \"module_path = str(path.parent) + '/'\\n\",\n \"sys.path.append(module_path)\\n\",\n \"\\n\",\n \"from pymdp import utils, maths\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### A simple generative model composed of a likelihood and a prior\\n\",\n \"\\n\",\n \"We begin by constructing a simple generative model composed of two sets of categorical distributions: a likelihood distribution $P(o|s)$ and a prior distribution $P(s)$. \\n\",\n \"\\n\",\n \"Because both of these distributions are categorical distributions, we can represent them easily in code using matrices and vectors. The likelihood distribution is a conditional distribution that tells the probability that the generative model assigns to different observations, given different hidden states. Since observations and hidden states are both discrete, this can be efficiently represented as a matrix, each of whose **columns** store the conditional probabilities of all the observations (the **rows**), given a particular hidden state. Each hidden state setting is thus indexed by a column. For this reason, each column of this matrix is a categorical probability distributions and its entries must sum to one. \\n\",\n \"\\n\",\n \"The prior is represented as a 1-D vector and stores the prior probabilities that the generative model assigns to each hidden state. \\n\",\n \"\\n\",\n \"Finally, to set ourselves up later for showing model inversion and free energy calculations, we initialize an observation that we assume the agent or generative model has \\\"gathered\\\" or \\\"seen.\\\" In `pymdp` we can represent these observations either as one-hot vectors (a `1` in one entry, and `0`'s everywhere else) or more sparsely as simple indices (integers) that represent *which* of the observations was observed. Because observations are not distributions (or technically, they are Dirac distributions), you don't need to store a whole vector of elements, you can just store a particular index.\\n\",\n \"\\n\",\n \"Below we create 3 main variables: \\n\",\n \"\\n\",\n \"- An `observation` that represents a real observation that the agent or generative model \\\"sees\\\". \\n\",\n \"- The `prior` distribution that represents the agent's prior beliefs about the hidden states\\n\",\n \"- the `likliheood_dist` that represents the agent's beliefs about how hidden states probabilistically relate to observations.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"## Define a quick helper function for printing arrays nicely (see https://gist.github.com/braingineer/d801735dac07ff3ac4d746e1f218ab75)\\n\",\n \"def matprint(mat, fmt=\\\"g\\\"):\\n\",\n \" col_maxes = [max([len((\\\"{:\\\"+fmt+\\\"}\\\").format(x)) for x in col]) for col in mat.T]\\n\",\n \" for x in mat:\\n\",\n \" for i, y in enumerate(x):\\n\",\n \" print((\\\"{:\\\"+str(col_maxes[i])+fmt+\\\"}\\\").format(y), end=\\\" \\\")\\n\",\n \" print(\\\"\\\")\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Observation: 0\\n\",\n \"\\n\",\n \"Prior:[0.5 0.5]\\n\",\n \"\\n\",\n \"Likelihood:\\n\",\n \"0.8 0.2 \\n\",\n \"0.2 0.8 \\n\"\n ]\n }\n ],\n \"source\": [\n \"num_obs = 2 # dimensionality of observations (2 possible observation levels)\\n\",\n \"num_states = 2 # dimensionality of observations (2 possible hidden state levels)\\n\",\n \"\\n\",\n \"observation = 0 # index representation\\n\",\n \"# observation = np.array([1, 0]) # one hot representation\\n\",\n \"# observation = utils.onehot(0, num_obs) # one hot representation, but use one of pymdp's utility functions to create a one-hot\\n\",\n \"\\n\",\n \"prior = np.array([0.5, 0.5]) # simply set it by hand\\n\",\n \"# prior = np.ones(num_states) / num_states # create a uniform prior distribution by creating a vector of ones and dividing each by the number of states\\n\",\n \"# prior = utils.norm_dist(np.ones(num_states)) # use one of pymdp's utility functions to normalize any vector into a probability distribution\\n\",\n \"\\n\",\n \"likelihood_dist = np.array([ [0.8, 0.2],\\n\",\n \" [0.2, 0.8] ])\\n\",\n \"\\n\",\n \"if isinstance(observation, np.ndarray):\\n\",\n \" print(f'Observation:{observation}\\\\n')\\n\",\n \"else:\\n\",\n \" print(f'Observation: {observation}\\\\n')\\n\",\n \"print(f'Prior:{prior}\\\\n')\\n\",\n \"print('Likelihood:')\\n\",\n \"matprint(likelihood_dist)\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Bayesian inference\\n\",\n \"\\n\",\n \"Before we define variational free energy for this generative model, let's step through the computations involved in inverting this model using Bayes' rule, i.e. computing the optimal Bayesian posterior over hidden states, given our sensory observation (which we will formally refer to as $o_t$). By performing exact Bayesian inference first, we can directly compares its results to that of variational free energy minimization. This will help us better understand the meaning of the free energy calculations that come later.\\n\",\n \"\\n\",\n \"#### 1. Compute the likelihood over hidden states, given the observation \\n\",\n \"\\n\",\n \"Now that we have a generative model and have fixed a particular observatio $o_t$ (`observation`), we have to perform Bayes' rule to compute the posterior. Mathematically, this can be expressed as follows:\\n\",\n \"\\n\",\n \"### $ \\\\hspace{60mm} P(s | o _t) = \\\\frac{P(o = o_t | s)P(s)}{P(o = o_t)} $\\n\",\n \"\\n\",\n \"Computing the posterior via Bayes' rule (also known as \\\"model inversion\\\") is the essence of optimal statistical inference, when one has a generative model of how one's data is caused, and some data. \\n\",\n \"\\n\",\n \"To start with, let's computing the likelihood term $P(o = o_t | s)$. We can represent the computation of the likelihood with this line of `NumPy`: ``likelihood_dist[observation,:]``. By doing so, we are providing a numerical answer to the question: \\\"What is the likelihood that State 1 vs State 2 caused the actual sensory data $o_t$ that I've observed?\\\".\\n\",\n \"\\n\",\n \" Mathematically, our likelihood function $P(o = o_t | s)$ (in the statistics literature also referred to as $L(\\\\theta)$) is a *function of the hidden states*. The particular function over hidden states we use is *defined* by the observation $o_t$. So you can think of the likelihood as a multi-dimensional function or simply a space of functions, where the particular function you use for inference is determined by your data.\\n\",\n \"\\n\",\n \"This act of computing the likelihood via an indexing operation ``likelihood_dist[observation,:]``, is similar in spirit to the operation of *conditioning*. We are, in some sense, \\\"conditioning\\\" on a particular observation (slicing out a \\\"row\\\" of our ``likelihood_dist`` matrix), and then looking at the *induced* likelihood over possible causes (hidden states) that could've have been the latent source of that observation. This operation captures the essence of what we mean when we speak of \\\"inverting\\\" generative models. Generative models are referred to as *generative* because they can be used to generate fictive observations, given some fixed setting of latent parameters. *Inversion* is thus moving in the opposite direction -- given some sensory data, what is the consequent likelihood over the *causes* or hidden states that might have generated that data?\\n\",\n \"\\n\",\n \"**Note**: We can also compute the likelihood using a matrix-vector product, if the observation is represented as a one-hot vector.\\n\",\n \"\\n\",\n \"```\\n\",\n \"likelihood_s = likelihood_dist.T @ observation\\n\",\n \"```\\n\",\n \"\\n\",\n \"You can see think of this as a weighted average of the rows of the likelihood matrix, where the weights are provided by the observations. Since we have insisted that the observations are a one-hot vector, this is equivalent to just selecting a single row of the likelihood matrix (the one indexed by the entry of the observation that is `1.0`).\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$P(o=o_t|s):$\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[0.8 0.2]\\n\",\n \"==================\\n\",\n \"\\n\"\n ]\n }\n ],\n \"source\": [\n \"\\n\",\n \"if isinstance(observation, np.ndarray): # use the matrix-vector version if your observation is a one-hot vector\\n\",\n \" likelihood_s = likelihood_dist.T @ observation\\n\",\n \"elif isinstance(observation, int): # use the index version if your observation is an integer index\\n\",\n \" likelihood_s = likelihood_dist[observation,:] \\n\",\n \"display(Latex('$P(o=o_t|s):$'))\\n\",\n \"print(f'{likelihood_s}')\\n\",\n \"print('==================\\\\n')\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### 2. The joint distribution $P(o = o_t, s) = P(o = o_t|s)P(s)$ \\n\",\n \"\\n\",\n \"To compute the full numerator on the right-hand side of the Bayes' rule equation, we need to compute the joint distribution $P(o = o_t|s)P(s)$.\\n\",\n \"\\n\",\n \"The joint distribution, which also fully defines the generative model, is the product of the likelihood and prior distributions. The joint distribution expresses the joint probability of observations and hidden states, given the likelihood distribution and the prior over hidden states. If we condition on an actual observation $o_t$, as we have done here, then this joint distribution is, like the likelihood, a function of hidden states. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$P(o = o_t,s) = P(o = o_t|s)P(s):$\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"[0.4 0.1]\\n\",\n \"==================\\n\",\n \"\\n\"\n ]\n }\n ],\n \"source\": [\n \"joint_prob = likelihood_s * prior # element-wise product of the likelihood of each hidden state, given the observation, with the prior probability assigned to each hidden state\\n\",\n \"display(Latex('$P(o = o_t,s) = P(o = o_t|s)P(s):$'))\\n\",\n \"print(f'{joint_prob}')\\n\",\n \"print('==================\\\\n')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### 3. Marginal probability or marginal likelihood: $\\\\sum_s P(o = o_t, s) = P(o = o_t)$\\n\",\n \"\\n\",\n \"Let's remind ourselves of Bayes' rule below:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} P(s | o _t) = \\\\frac{P(o = o_t | s)P(s)}{P(o = o_t)} $\\n\",\n \"\\n\",\n \"So far, using the likelihood, the observation, and the prior, we have computed the numerator of this term: the unnormalized joint distribution $P(o = o_t,s)$. All that's left is to do is then divide this term by the denominator $P(o=o_t)$. This term is also referred to as the model evidence or the marginal likelihood. \\n\",\n \"\\n\",\n \"This can be thought of as the probability of having seen the particular observation you saw, under all possible settings of the hidden states. This can be computed by marginalizing the joint distribution, using the prior probabilities of the hidden states:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm}P(o) = \\\\sum_s P(o|s)P(s)$\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"p_o = joint_prob.sum()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"#### 4. Compute the posterior $P(s|o=o_t)$\\n\",\n \"\\n\",\n \"Now to compute the Bayes-optimal posterior, simply divide the numerator by the denominator!\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$P(s|o = o_t) = \\\\frac{P(o = o_t,s)}{P(o=o_t)}$:\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Posterior over hidden states: [0.8 0.2]\\n\",\n \"==================\\n\"\n ]\n }\n ],\n \"source\": [\n \"posterior = joint_prob / p_o # divide the joint by the marginal\\n\",\n \"display(Latex('$P(s|o = o_t) = \\\\\\\\frac{P(o = o_t,s)}{P(o=o_t)}$:'))\\n\",\n \"print(f'Posterior over hidden states: {posterior}')\\n\",\n \"print('==================')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### The variational free energy\\n\",\n \"\\n\",\n \"The variational free energy is an upper bound on **surprise**: surprise is define as $ - \\\\ln p(o)$, and is also known as the negative (log) evidence. By minimizing free energy, we are **minimizing** surprise and thus **maximizing** log evidence. This evidence is simply the (log of the) term we computed in the previous step, the normalizing denominator used in Bayes' rule. We can thus first compute the surprise associated with the observation we saw earlier:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$- \\\\ln P(o=o_t)$:\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Surprise: 0.693\\n\",\n \"==================\\n\"\n ]\n }\n ],\n \"source\": [\n \"surprise = - np.log(p_o)\\n\",\n \"\\n\",\n \"display(Latex('$- \\\\ln P(o=o_t)$:'))\\n\",\n \"print(f'Surprise: {surprise.round(3)}')\\n\",\n \"print('==================')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"By minimizing variational free energy with respect to the parameters of an arbitrary, parametrized distribution, also known as the approximate or variational posterior $Q(s)$, we are forcing the surprise to go down, and the model evidence to go up. In doing so, the approximate posterior distribution will get \\\"closer\\\" to the true posterior distribution (the $P(s|o)$ we computed above), $Q(s) \\\\approx P(s|o)$.\\n\",\n \"\\n\",\n \"This idea of minimizing a bound on surprise, is the core principle underlying the variational free energy principle, active inference, and the statistical methodology of variational principles more generally. This comes in handy because in many realistic scenarios where agents or systems need to make inferences about the hidden causes of sensory perturbations, performing Bayesian inference exactly becomes intractable (due mostly to the computation of the $P(o)$ denominator term, also known as the normalizing constant). Variational inference turns this intractable marginalization problem into a tractable optimization problem, where one only needs to change the approximate posterior $Q(s)$ in order to minimize a bound on surprise.\\n\",\n \"\\n\",\n \"But what is the variational free energy exactly, mathematically? It is commonly written as the expectation, under the approximate posterior, of the log ratio between the approximate posterior and the generative model:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} \\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln \\\\frac{Q(s)}{P(o, s)}] $\\n\",\n \"\\n\",\n \"Because of the rules of logarithms, we can also express this as an expected difference between the log posterior and the log generative model:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} \\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(o, s)] $\\n\",\n \"\\n\",\n \"By doing taking advantage of some more mathematical relationships (the factorization of the joint, rules for logarithms of products, and the definition of the conditional expectation), we can re-write this as an upper bound on surprise:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} \\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(s|o)] - \\\\ln P(o) $\\n\",\n \"\\n\",\n \"By re-arranging this equality and taking advantage of the fact that the quantity $\\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(s|o)]$ (also known as the Kullback-Leibler divergence) is greater than or equal to 0, we can easily show that the VFE is an upper bound on surprise:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} \\\\mathcal{F} \\\\geq - \\\\ln P(o) $\\n\",\n \"\\n\",\n \"Let's now compute the VFE numerically for our generative model and fixed observation. Given we already defined those two things ($o_t$ and $P(o,s)$), the last thing we need to do, is to define an initial setting of our approximate posterior $Q(s)$, and compute the variational free energy using one of the formulas above.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$\\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln \\\\frac{Q(s)}{P(o, s)}] = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(o, s)]:$\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Variational free energy (F) = 0.916\\n\",\n \"==================\\n\"\n ]\n }\n ],\n \"source\": [\n \"# to begin with, set our initial Q(s) equal to our prior distribution -- i.e. a flat/uninformative belief about hidden states\\n\",\n \"initial_qs = np.array([0.5, 0.5])\\n\",\n \"\\n\",\n \"# redefine generative model and observation, for ease\\n\",\n \"observation = 0\\n\",\n \"likelihood_dist = np.array([[0.8, 0.2], [0.2, 0.8]])\\n\",\n \"prior = utils.norm_dist(np.ones(2))\\n\",\n \"\\n\",\n \"# compute the joint or generative model using the factorization: P(o=o|s)P(s)\\n\",\n \"joint_prob = likelihood_dist[observation,:] * prior\\n\",\n \"\\n\",\n \"# compute the variational free energy using the expected log difference formulation\\n\",\n \"initial_F = initial_qs.dot(np.log(initial_qs) - np.log(joint_prob))\\n\",\n \"## @NOTE: because of log-rules, `initial_F` can also be computed using the division inside the logarithm:\\n\",\n \"# initial_F = initial_qs.dot(np.log(initial_qs/joint_prob))\\n\",\n \"\\n\",\n \"display(Latex('$\\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln \\\\\\\\frac{Q(s)}{P(o, s)}] = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(o, s)]:$'))\\n\",\n \"print(f'Variational free energy (F) = {initial_F.round(3)}')\\n\",\n \"print('==================')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now let's then change the approximate posterior $Q(s)$ and see what happens to the variational free energy.\\n\",\n \"\\n\",\n \"By definition, optimal inference (and 'perfect' VFE minimization) obtains when we set the approximate posterior $Q(s)$ to be equal to the true posterior, $Q(s) = P(s|o)$. \\n\",\n \"\\n\",\n \"As an extreme case, let's do this and then measure the variational free energy. We can see that it has decreased, relative to it's initial setting when the approximate posterior was equal to the prior $P(s)$.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$\\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln \\\\frac{Q(s)}{P(o, s)}] = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(o, s)]:$\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"F = 0.693\\n\",\n \"==================\\n\"\n ]\n }\n ],\n \"source\": [\n \"final_qs = posterior.copy() # now we just assert that the approximate posterior is equal to the true posterior\\n\",\n \"final_F = final_qs.dot(np.log(final_qs) - np.log(joint_prob))\\n\",\n \"\\n\",\n \"display(Latex('$\\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln \\\\\\\\frac{Q(s)}{P(o, s)}] = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(o, s)]:$'))\\n\",\n \"print(f'F = {final_F.round(3)}')\\n\",\n \"print('==================')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Notice that the free energy is 0.693 -- if you recall, this is exactly the **surprise** or negative log marginal likelihood $-\\\\ln P(o = o_t)$, related to the marginal likelihood quantity $P(o=o_t)$ that we had to compute when performing exact Bayesian inference earlier. \\n\",\n \"\\n\",\n \"It is easy to see why this equality should hold, when we consider the VFE in terms of the surprise bound:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} \\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(s|o)] - \\\\ln P(o) $\\n\",\n \"\\n\",\n \"When $Q(s) = P(s|o)$, as we have enforced with the line ``final_qs = posterior.copy()`` above, the first term $\\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(s|o)]$ will become 0. This is a property of the Kullback-Leibler divergence between two distributions $\\\\operatorname{D}_{KL}(Q \\\\parallel P) = \\\\mathbb{E}_{Q}[\\\\ln Q - \\\\ln P]$. \\n\",\n \"\\n\",\n \"So since that KL divergence is 0, this is a case when the bound on surprise is exact:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} \\\\mathcal{F} = 0 - \\\\ln P(o) = - \\\\ln P(o)$\\n\",\n \"\\n\",\n \"In other words, minimizing free energy \\\"as much as possible\\\" in the case of this generative model, means that the approximate posterior equals the true posterior, and the free energy bound becomes \\\"tight\\\", i.e. the free energy simply IS the negative log evidence!\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$-\\\\ln P(o):$\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"0.693\\n\",\n \"==================\\n\",\n \"\\n\"\n ]\n }\n ],\n \"source\": [\n \"# compute the surprise (which we can do analytically for this simple generative model)\\n\",\n \"p_o = joint_prob.sum()\\n\",\n \"surprise = - np.log(p_o)\\n\",\n \"display(Latex('$-\\\\ln P(o):$'))\\n\",\n \"print(f'{surprise.round(3)}')\\n\",\n \"print('==================\\\\n')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Bonus material: auto-differentiation to perform gradient descent on the variational free energy\\n\",\n \"\\n\",\n \"In this section, we are going to numerically differentiate the variational free energy with respect to the parameters of the approximate posterior. We can take advantage of modern autodifferentiation software, that can calculate the derivatives of arbitrary computer programs, to compute these derivatives without doing any analytic differentiation.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import autograd.numpy as np_auto # Thinly-wrapped version of Numpy that is auto-differentiable\\n\",\n \"from autograd import grad # this is the function that we use to evaluate derivatives\\n\",\n \"from functools import partial\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"First, let's create a variational free energy function, that takes as input the variational posterior `qs`, an observation `obs`, the likelihood matrix `likelihood` and a prior distribution `prior`.\\n\",\n \"\\n\",\n \"By defining this computation as a function, we can calculate its derivatives automatically using the autodifferentiation package `autograd`, which allows users to pass gradients through arbitrary Python code. It includes a special version of `numpy` (`autograd.numpy`) that has a differentiable back-end. We will thus use this \\\"special\\\" verison of `numpy` when we instantiate our arrays and perform numerical operations on them.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# define the variational free energy as a function of the approximate posterior, an observation, and the generative model\\n\",\n \"def vfe(qs, obs, likelihood, prior):\\n\",\n \" \\\"\\\"\\\"\\n\",\n \" Quick docstring below on inputs\\n\",\n \" Arguments:\\n\",\n \" =========\\n\",\n \" `qs` [1D np_auto.ndarray]: variational posterior over hidden states\\n\",\n \" `obs` [int]: index of the observation\\n\",\n \" `likelihood` [2D np_auto.ndarray]: likelihood distribution P(o|s), relating hidden states probabilistically to observations\\n\",\n \" `prior` [1D np_auto.ndarray]: prior over hidden states\\n\",\n \" \\\"\\\"\\\"\\n\",\n \"\\n\",\n \" likelihood_s = likelihood[obs,:]\\n\",\n \"\\n\",\n \" joint = likelihood_s * prior\\n\",\n \"\\n\",\n \" vfe = qs @ (np_auto.log(qs) - np_auto.log(joint))\\n\",\n \"\\n\",\n \" return vfe\\n\",\n \"\\n\",\n \"# initialize an observation, an initial variational posterior, a prior, and a likelihood matrix\\n\",\n \"obs = 0\\n\",\n \"init_qs = np_auto.array([0.5, 0.5])\\n\",\n \"prior = np_auto.array([0.5, 0.5])\\n\",\n \"likelihood_dist = np_auto.array([ [0.8, 0.2],\\n\",\n \" [0.2, 0.8] ])\\n\",\n \"\\n\",\n \"# this use of `partial` creates a version of the vfe function that is a function of Qs only, \\n\",\n \"# with the other parameters (the observation, the generative model) fixed as constant parameters\\n\",\n \"vfe_qs = partial(vfe, obs = obs, likelihood = likelihood_dist, prior = prior)\\n\",\n \"\\n\",\n \"# By calling `grad` on a function, we get out a function that can be used to compute the gradients of the VFE with respect to its input (in our case, `qs`)\\n\",\n \"grad_vfe_qs = grad(vfe_qs)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now that we have a variational free energy function, and a derivative function that will give us the gradients of the VFE, with respect $Q(s)$, we can use it to perform a gradient descent on VFE, with respect to the parameters of $Q(s)$. In other words, we will implement this discretized differential equation to update the approximate posterior:\\n\",\n \"\\n\",\n \"#### $ \\\\hspace{60mm} Q(s)_{t+1} =Q(s)_{t} - \\\\frac{\\\\partial \\\\mathcal{F}}{\\\\partial Q(s)_{t}} $\\n\",\n \"\\n\",\n \"Where the gradient term $\\\\frac{\\\\partial \\\\mathcal{F}}{\\\\partial Q(s)_{t}}$ will simply be the output of the gradient function `grad_vfe_qs` we've defined above.\\n\",\n \"\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# number of iterations of gradient descent to perform\\n\",\n \"n_iter = 40\\n\",\n \"\\n\",\n \"qs_hist = np_auto.zeros((n_iter, 2))\\n\",\n \"qs_hist[0,:] = init_qs\\n\",\n \"\\n\",\n \"vfe_hist = np_auto.zeros(n_iter)\\n\",\n \"vfe_hist[0] = vfe_qs(qs = init_qs)\\n\",\n \"\\n\",\n \"learning_rate = 0.1 # learning rate to prevent gradient steps that are too big (overshooting)\\n\",\n \"for i in range(n_iter-1): \\n\",\n \"\\n\",\n \" dFdqs = grad_vfe_qs(qs_hist[i,:])\\n\",\n \"\\n\",\n \" ln_qs = np_auto.log(qs_hist[i,:]) - learning_rate * dFdqs # transform qs to log-space to perform gradient descent\\n\",\n \" qs_hist[i+1,:] = maths.softmax(ln_qs) # re-normalize to make it a proper, categorical Q(s) again\\n\",\n \"\\n\",\n \" vfe_hist[i+1] = vfe_qs(qs = qs_hist[i+1,:]) # measure final variational free energy\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Since we were storing the history of the variational free energy over the course of the gradient descent, we can plot its trajectory below.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"Text(0.5, 1.0, 'Gradient descent on VFE')\"\n ]\n },\n \"execution_count\": 16,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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vgPe7+joGn3H0HQQ3IpQRjQdQR9C3ZFMZ7LfBginLfIBjv41aCkTKNoJZkE0EtxicJhgbvMe7+S4L7OrxI8F6MITg3bdWIJe9jL8Hf6seAvxEkY6UE/1u/AI529wfS76FPzONgx8xWDl6m2ZvaGwCqmneO6yI9zMJsTkRERKRdqnEQERGRDlPiICIiIh2mxEFEREQ6TImDiIiIdJgSBxEREemwbBtfv1cVlVX69CN76n5NIiIime2ll17a5u6p7rCalhKHBLEBw3jm7y9QUtTpwd5ERESyjpl1enwZNVUkeX3r7qhDEBERyVhKHJKs2qzEQUREJB0lDgkMeG3zrqjDEBERyVhKHBIUF8Z4TTUOIiIiaSlxSFBSVMCqLapxEBERSUeJQ4J+hTHerNvLvsaWqEMRERHJSEocEpQUFeCuKytERETSUeKQoKQwGL9BzRUiIiKpKXFIUFwUo6jA1EFSREQkDSUOCQwYP7SMVbokU0REJCUlDkkmVVeoxkFERCQNJQ5JJg+rYP12XVkhIiKSihKHJJOry3GH1VtU6yAiIpJMiUOSSdUVgIaeFhERSUWJQ5JxQ0qDKyt0SaaIiMg7KHFIUlgQ4/Ch5axWB0kREZF3UOKQwqTqctU4iIiIpKDEIYXJ1RWsr9vH3sbmqEMRERHJKBmROJjZHDNbaWarzey6FOsHmdn9ZrbYzF40s2ntlTWzwWb2mJmtCqeDOhrP5OpyQFdWiIiIJIs8cTCzAuBm4GxgKnCRmU1N2uwrwEJ3Pwa4BPhRB8peBzzu7pOAx8P5Djl4ZYUSBxERkUSRJw7ATGC1u69x90bgbmBu0jZTCb78cfdXgXFmVt1O2bnA7eHz24HzOhrQ2MGlFBfENPS0iIhIkkxIHEYB6xPma8NliRYBFwCY2UxgLDC6nbLV7r4JIJwOS/XiZnaFmS0wswVbt24Fwisrqso0loOIiEiSTEgcLMUyT5q/ARhkZguBTwOvAM0dLNsmd7/V3WvcvaaqqurA8sm6Z4WIiMg7FEYdAEEtwZiE+dHAxsQN3L0euBzAzAxYGz5K2yi72cxGuPsmMxsBbOlMUJOGlfPgoo3saWimrF8mvE0iIiLRy4Qah/nAJDMbb2bFwIXAg4kbmNnAcB3Ax4C/hslEW2UfBC4Nn18KPNCZoOIdJHVlhYiIyEGRJw7u3gxcDTwCrADucfdlZnalmV0ZbnYksMzMXiW4guKatsqGZW4AzjCzVcAZ4XyHxS/JVD8HERGRgzKiDt7d5wHzkpbdkvD878CkjpYNl78NnN7VmMYOKaO4MMYq1TiIiIgcEHmNQ6YqiBkTqspV4yAiIpJAiUMbJleXs0pXVoiIiBygxKENk6sr2LBjH7sbdM8KERERUOLQpknDgg6SGkFSREQkoMShDfFLMtVcISIiElDi0IbDBpfSrzCmDpIiIiIhJQ5tiF9ZoUsyRUREAkoc2hFcWaEaBxEREVDi0K5J1RVs3LmfXfubog5FREQkckoc2jE53kFSzRUiIiJKHNoTv2eFmitERESUOLRr9KBSSopivKZLMkVERJQ4tEf3rBARETlIiUMHTK6u0CBQIiIiKHHokEnV5bxVv5+d+3RlhYiI5DclDh0weVhwZcVqXVkhIiJ5TolDBxy4JFP9HEREJM8pceiA0YP607+oQFdWiIhI3lPi0AGxmDFxWDmrtqjGQURE8psShw6aVK1LMkVERJQ4dNCkYRVsrm/QlRUiIpLXlDh0kIaeFhERUeLQYfErK9RBUkRE8pkShw4aNTB+ZYVqHEREJH8pceigWMyYVF2uQaBERCSvKXHohEnDKlTjICIieU2JQydMri5ny64Gdu7VlRUiIpKflDh0woEOkhoISkRE8lRGJA5mNsfMVprZajO7LsX6SjP7k5ktMrNlZnZ5uHyKmS1MeNSb2bXhuuvNbEPCunO6G+fEYcElmWquEBGRfFUYdQBmVgDcDJwB1ALzzexBd1+esNlVwHJ3P9fMqoCVZnanu68EZiTsZwNwf0K5H7j7d3sq1lED+1NaXMAqXZIpIiJ5KhNqHGYCq919jbs3AncDc5O2caDCzAwoB+qA5qRtTgded/c3eivQWMyYNExDT4uISP7KhMRhFLA+Yb42XJboJuBIYCOwBLjG3VuTtrkQuCtp2dVmttjMbjOzQale3MyuMLMFZrZg69at7QY7qbpCg0CJiEjeyoTEwVIs86T5s4CFwEiCpombzGzAgR2YFQPvB36fUOZnwIRw+03A91K9uLvf6u417l5TVVXVbrCTq8vZtruB7Xsa291WREQk12RC4lALjEmYH01Qs5DocuA+D6wG1gJHJKw/G3jZ3TfHF7j7ZndvCWsmfk7QJNJtk8IrK1ZpICgREclDmZA4zAcmmdn4sObgQuDBpG3eJOjDgJlVA1OANQnrLyKpmcLMRiTMng8s7YlgD96zQv0cREQk/0R+VYW7N5vZ1cAjQAFwm7svM7Mrw/W3AF8HfmVmSwiaNr7k7tsAzKyU4IqMTyTt+jtmNoOg2WNdivVdMrKyhLLiAt0lU0RE8lLkiQOAu88D5iUtuyXh+UbgzDRl9wJDUiy/uIfDBMDMmKgOkiIikqcyoaki6xxRXcGKt+pxT+7DKSIiktuUOHTBMWMq2bG3ifV1+6IORUREpE8pceiC6aMHArCwdkekcYiIiPQ1JQ5dMGV4BcWFMRav3xF1KCIiIn1KiUMXFBXEOGrkABbX7ow6FBERkT6lxKGLpo8eyJINO2luSR75WkREJHcpceii6WMq2dfUwuqtuixTRETyhxKHLjom7CC5SP0cREQkjyhx6KLxQ8qoKClkkfo5iIhIHlHi0EWxmHHM6EoW65JMERHJI0ocumH66IG8umkX+5taog5FRESkTyhx6IZjRg+kudVZvqk+6lBERET6hBKHbpg+phJQB0kREckfShy6YfiAEoZV9NNAUCIikjeUOHSDmXHM6IEsUgdJERHJE0ocumnGmErWbN3Dzn1NUYciIiLS65Q4dFN8IKilG9RcISIiuU+JQzcdMzroILlQHSRFRCQPKHHopoGlxYwbUqqBoEREJC8ocegBx4weqCsrREQkLyhx6AHTxwxk0879bKnfH3UoIiIivUqJQw+YHvZz0A2vREQk1ylx6AFHjaykIGYaQVJERHKeEoce0L+4gMnVFRoISkREcp4Shx4yfXQli2t34u5RhyIiItJrlDj0kOljBrJzXxNvvL036lBERER6jRKHHnLMgQ6SO6INREREpBdlROJgZnPMbKWZrTaz61KsrzSzP5nZIjNbZmaXJ6xbZ2ZLzGyhmS1IWD7YzB4zs1XhdFBvHsPk6gpKimIsWq8rK0REJHdFnjiYWQFwM3A2MBW4yMymJm12FbDc3acDs4HvmVlxwvpT3X2Gu9ckLLsOeNzdJwGPh/O9pqggxlEjKzWCpIiI5LTIEwdgJrDa3de4eyNwNzA3aRsHKszMgHKgDmhuZ79zgdvD57cD5/VYxGkcM7qSpRt30tzS2tsvJSIiEolMSBxGAesT5mvDZYluAo4ENgJLgGvcPf7t7MCjZvaSmV2RUKba3TcBhNNhvRF8ohljBrK/qZXXNu/u7ZcSERGJRCYkDpZiWfI1jWcBC4GRwAzgJjMbEK472d2PI2jquMrM3tOpFze7wswWmNmCrVu3dirwZPFbbKu5QkREclUmJA61wJiE+dEENQuJLgfu88BqYC1wBIC7bwynW4D7CZo+ADab2QiAcLol1Yu7+63uXuPuNVVVVd06kHFDShlQUqgrK0REJGdlQuIwH5hkZuPDDo8XAg8mbfMmcDqAmVUDU4A1ZlZmZhXh8jLgTGBpWOZB4NLw+aXAA716FEEMTB8zUFdWiIhIzoo8cXD3ZuBq4BFgBXCPuy8zsyvN7Mpws68Ds8xsCcEVEl9y921ANfCMmS0CXgT+4u4Ph2VuAM4ws1XAGeF8rztmdCUrN+9iX2NLX7yciIhInyqMOgAAd58HzEtadkvC840EtQnJ5dYA09Ps823CWoq+NH30QFpaneWbdnL82MF9/fIiIiK9KvIah1wzfcxAADVXiIhITlLi0MOqB5QwfECJOkiKiEhOUuLQC44J75QpIiKSa5Q49ILpYwaydtsedu5tijoUERGRHqXEoRdMjw8EtWFHpHGIiIj0NCUOveDo8Bbbaq4QEZFco8ShF1T2L+LwoWUsXL8j6lBERER6lBKHXhJ0kNwRdRgiIiI9SolDL5k+ZiCb6xt4a+f+qEMRERHpMUocekn8Tpkaz0FERHKJEodectTIARTGTM0VIiKSU5Q49JKSogKmDK/Q0NMiIpJTlDj0omNGD2Rx7Q5aWz3qUERERHqEEodeNGNMJfX7m1n39p6oQxEREekRShx6UbyDpAaCEhGRXKHEoRdNGlZOSVFMV1aIiEjOUOLQiwoLYhw9qpJFGkFSRERyhBKHXnbM6IEs21hPY3Nr1KGIiIh0mxKHXnbCuME0NLfqvhUiIpITlDj0spMOH0LM4NnV26IORUREpNuUOPSyytIipo2q5LnXlTiIiEj2U+LQB2ZNGMorb+5gT0Nz1KGIiIh0ixKHPnDyxCE0tzovrquLOhQREZFuUeLQB2rGDqa4IMZz6ucgIiJZTolDH+hfXMBxYwfy7Oq3ow5FRESkW5Q49JGTJwxl+aZ66vY0Rh2KiIhIlylx6COzJg4F4O+vq9ZBRESylxKHPjJ9dCXl/Qp5VpdliohIFsuIxMHM5pjZSjNbbWbXpVhfaWZ/MrNFZrbMzC4Pl48xsyfNbEW4/JqEMteb2QYzWxg+zunLY0pWWBDjxPGD1UFSRESyWuSJg5kVADcDZwNTgYvMbGrSZlcBy919OjAb+J6ZFQPNwOfc/UjgXcBVSWV/4O4zwse83j6W9syaOJR1b+9lw459UYciIiLSJZEnDsBMYLW7r3H3RuBuYG7SNg5UmJkB5UAd0Ozum9z9ZQB33wWsAEb1Xeidc/LEIQCqdRARkayVCYnDKGB9wnwt7/zyvwk4EtgILAGucfdDbjdpZuOAY4EXEhZfbWaLzew2MxuU6sXN7AozW2BmC7Zu3dq9I2nHlOoKhpYX85w6SIqISJbKhMTBUizzpPmzgIXASGAGcJOZDTiwA7Ny4F7gWnevDxf/DJgQbr8J+F6qF3f3W929xt1rqqqqun4UHWBmnDRhKM+u3oZ78iGKiIhkvkxIHGqBMQnzowlqFhJdDtzngdXAWuAIADMrIkga7nT3++IF3H2zu7eENRM/J2gSidysCUPYsquB17fujjoUERGRTsuExGE+MMnMxocdHi8EHkza5k3gdAAzqwamAGvCPg//C6xw9+8nFjCzEQmz5wNLeyn+Tjl5QjCeg0aRFBGRbBR54uDuzcDVwCMEnRvvcfdlZnalmV0ZbvZ1YJaZLQEeB77k7tuAk4GLgdNSXHb5HTNbYmaLgVOBz/blcaVz2JBSRg/qz7PqICkiIlmoMOoAAMJLJeclLbsl4flG4MwU5Z4hdR8J3P3iHg6zx5w8YSgPLd1ES6tTEEsZvoiISEaKvMYhH82aOIT6/c0s3bAz6lBEREQ6RYlDBGbF+zlo+GkREckyShwiUFXRjynVFTynDpIiIpJllDhEZNbEIcxfV8f+ppaoQxEREekwJQ4ROXnCUBqaW3n5ze1RhyIiItJhShwicuLhgymImZorREQkqyhxiEhFSRHHjK5UB0kREckqShwidPKEoSyu3cmu/U1RhyIiItIhShwiNGviEFpanRfX1kUdioiISIcocYjQcYcNol9hTPetEBGRrKHEIUIlRQWcMG4wz6mfg4iIZAklDhGbNXEIr761i227G6IORUREpF1KHCIWv832c6+ruUJERDKfEoeITRtVyYCSQp7TbbZFRCQLKHGIWEHMeNfhQzSeg4iIZAUlDhlg1oQhrK/bx/q6vVGHIiIi0iYlDhng5InhbbbVXCEiIhmu3cTBzIaZ2bfM7L/NbERfBJVvJg4rZ1hFP55VB0kREclwhW2tNLMY8ChwDODACcCZfRBXXjEzZk0YwjOrt+HumFnUIYmIiKTUXo3DKcDrwKcBA97s9Yjy1KyJQ9m2u5GVm3dFHYqIiEha7SUOJwK/cPebgUHAx3s/pPx0sJ+DmitERCRztZc4HAEsAnD3ne7u8RVm9mxvBpZvRg3sz7ghpRrPQUREMlp7icMEIN032WE9HEvemzVxKC+sraO5pTXqUERERFJqL3GoBErSrPM0y6WL3j1xKLsbmnnpje1RhyIiIpJSe4lDCfCwmX3EzMb2RUD57D2Tq+hXGOOhpW9FHYqIiEhK7SUOMYIOkj8H1pjZajO7xcw+1Puh5Z/yfoWcMrmKh5ZuorVVFToiIpJ52kscdhJchkk4PZzgyorfAqPM7AUz+4qZHdWLMeaVfzxmBJvrG3hlvZorREQk87SXONQCXwdKgdOB7wIrCJIIIxgQ6uvAYjNbYWafN7OyzgZhZnPMbGVYo3FdivWVZvYnM1tkZsvM7PL2yprZYDN7zMxWhdNBnY0rCqcdMYzighjzlqi5QkREMk97icOzwHZ3b3D3J939i+4+DRgLfBL4E7CXIImYAnwbWGJm4zoagJkVADcDZwNTgYvMbGrSZlcBy919OjAb+J6ZFbdT9jrgcXefBDwezme8ipIi3jN5KA8t2UTC1a8iIiIZob3E4ffAzOSF7r7e3f/H3ecCgwmGof4hsAYYB3y/EzHMBFa7+xp3bwTuBuYmvyRQYcFYzOVAHdDcTtm5wO3h89uB8zoRU6TOnjaCjTv3s3D9jqhDEREROUSbiYO7rwXeTFEDkLhNk7v/n7v/W/jrfi7wrk7EMApYnzBfGy5LdBNwJLARWAJc4+6t7ZStdvdNYYybgGGdiClS751aTVGB6eoKERHJOB25rfZXgausg3decvc/Af/diRhS7Te5jv4sYCEwEpgB3GRmAzpYtu0XN7vCzBaY2YKtW7d2pmivqexfxLsnDmWemitERCTDtJs4hDUKV3knvsHCe1t0VC0wJmF+NEHNQqLLgfs8sBpYSzAcdltlN8dvAx5Ot6SJ9VZ3r3H3mqqqqk6E3bvOPnoEtdv3sWTDzqhDEREROaAjNQ69bT4wyczGm1kxcCHwYNI2bxJc1YGZVRN0xFzTTtkHgUvD55cCD/TqUfSwM6dWUxgzXV0hIiIZJfLEwd2bgauBRwgu9bzH3ZeZ2ZVmdmW42deBWWa2hOAKiS+5+7Z0ZcMyNwBnmNkq4IxwPmsMLC1m1sShPLRUzRUiIpI5CqMOAMDd5wHzkpbdkvB8I8GVGx0qGy5/m7CWIludM2041923hOWb6jlqZGXU4YiIiERf4yDpnXnUcApixrwlm6IORUREBFDikNEGlxVz0uFDmLfkLTVXiIhIRlDikOHOPno4a7ftYeXmXVGHIiIiosQh0505dTgxQ1dXiIhIRlDikOGqKvoxc/xg9XMQEZGMoMQhC/zj0SNYvWU3q9RcISIiEVPikAXOOmo4puYKERHJAEocssCwASWcMFbNFSIiEj0lDlninKOHs3LzLlZv2R11KCIikseUOGSJOdNGAPDwUtU6iIhIdJQ4ZInhlSUcP3aQ+jmIiEiklDhkkbOnDWf5pnrWbdsTdSgiIpKnlDhkkbOPDpor5qm5QkREIqLEIYuMGtifGWMG8pCaK0REJCJKHLLMOUcPZ8mGnbz59t6oQxERkTykxCHLnB1eXfGQmitERCQCShyyzJjBpRwzupJ5S9VcISIifU+JQxY6e9oIFq3fQe12NVeIiEjfUuKQhc45ejgAD6vWQURE+pgShyw0dkgZR40coHtXiIhIn1PikKXOOXoEL7+5g00790UdioiI5BElDlnqnHAwqPte3hBxJCIikk+UOGSp8UPLOOnwIfz2hTdpafWowxERkTyhxCGLXXLSWDbs2MeTr26JOhQREckTShyy2HunVlM9oB93PP9G1KGIiEieUOKQxYoKYnx45liefm2r7pgpIiJ9QolDlrtw5hgKY8adL6jWQUREep8ShyxXPaCEs44azj0Latnf1BJ1OCIikuMyInEwszlmttLMVpvZdSnWf8HMFoaPpWbWYmaDzWxKwvKFZlZvZteGZa43sw0J687p8wPrIxefNJad+5p4cNHGqEMREZEcF3niYGYFwM3A2cBU4CIzm5q4jbvf6O4z3H0G8GXgaXevc/eVCcuPB/YC9ycU/UF8vbvP64vjicKJ4wczubqc36iTpIiI9LLIEwdgJrDa3de4eyNwNzC3je0vAu5Ksfx04HV3z7tvTzPj4neNZXHtThau3xF1OCIiksMyIXEYBaxPmK8Nl72DmZUCc4B7U6y+kHcmFFeb2WIzu83MBqXZ5xVmtsDMFmzdurXz0WeI844dRVlxAXf8Pe/yJhER6UOZkDhYimXphkI8F3jW3esO2YFZMfB+4PcJi38GTABmAJuA76Xaobvf6u417l5TVVXVydAzR0VJEecfN4o/Ld5I3Z7GqMMREZEclQmJQy0wJmF+NJCul1+qWgUI+ke87O6b4wvcfbO7t7h7K/BzgiaRnHbxu8bR2NzK7xesb39jERGRLsiExGE+MMnMxoc1BxcCDyZvZGaVwCnAAyn28Y5+D2Y2ImH2fGBpj0WcoaYMr2Dm+MH85oU3aNX9K0REpBdEnji4ezNwNfAIsAK4x92XmdmVZnZlwqbnA4+6+yFDJIb9Hs4A7kva9XfMbImZLQZOBT7baweRQS45aSzr6/bx9GvZ219DREQyl7nrl2lcTU2NL1iwIOowuqWxuZWTv/0ER4+q5LbLTog6HBERyWBm9pK713SmTOQ1DtKzigtjXHTCGJ5cuYX1dXujDkdERHKMEoccdNGJhxEz4ze6f4WIiPQwJQ45aERlf844spp75q/X/StERKRHKXHIUZecNJbte5v4y+JNUYciIiI5RIlDjjppwhAOryrjDt2/QkREepAShxwVv3/FwvU7WFK7M+pwREQkRyhxyGH/dPxo+hcVcMfz66IORUREcoQShxw2oKSI844dxQMLN7Jzb1PU4YiISA5Q4pDjLn7XWBqaW/n9S7p/hYiIdJ8Shxw3deQAasYO4jfP6/4VIiLSfUoc8sDFJ41l3dt7+dvqbVGHIiIiWU6JQx6YM204wyr6cdMTq9C9SUREpDuUOOSBfoUFfPr0Scxft52ndNdMERHpBiUOeeJDNWM4bHApNz68Un0dRESky5Q45IniwhifPWMSyzfVM2+phqEWEZGuUeKQR94/fRRTqiv4/qOv0dzSGnU4IiKShZQ45JGCmPG5MyezZtse7n25NupwREQkCylxyDNnTK1mxpiB/PD/VumW2yIi0mlKHPKMmfHFs6awaed+7nzhzajDERGRLKPEIQ/NmjiUkycO4eYnV7O7oTnqcEREJIsocchTXzjrCOr2NHLbM2ujDkVERLKIEoc8NWPMQM6cWs3P/7qG7Xsaow5HRESyhBKHPPb5s6awu7GZW55+PepQREQkSyhxyGOTqys4f8YofvXcOjbX7486HBERyQJKHPLcZ8+YTKs7P358VdShiIhIFlDikOfGDC7lwhMO43fz1/PG23uiDkdERDKcEgfh06dNpLDA+MFjr0UdioiIZLiMSBzMbI6ZrTSz1WZ2XYr1XzCzheFjqZm1mNngcN06M1sSrluQUGawmT1mZqvC6aC+PKZsMmxACZfNGs8Dizby6lv1UYcjIiIZLPLEwcwKgJuBs4GpwEVmNjVxG3e/0d1nuPsM4MvA0+5el7DJqeH6moRl1wGPu/sk4PFwXtK48pTDKe9XyHcfUa2DiIikF3niAMwEVrv7GndvBO4G5rax/UXAXR3Y71zg9vD57cB53Qky1w0sLeYT7zmc/1uxmZff3B51OCIikqEyIXEYBaxPmK8Nl72DmZUCc4B7ExY78KiZvWRmVyQsr3b3TQDhdFiPRp2DLj95PEPLi7nx4ZW4e9ThiIhIBsqExMFSLEv3rXUu8GxSM8XJ7n4cQVPHVWb2nk69uNkVZrbAzBZs3bq1M0VzTlm/Qq46dSJ/X/M2z65+O+pwREQkA2VC4lALjEmYHw1sTLPthSQ1U7j7xnC6BbifoOkDYLOZjQAIp1tS7dDdb3X3Gnevqaqq6vJB5IoPn3gYowb257/+tIyGZt12W0REDpUJicN8YJKZjTezYoLk4MHkjcysEjgFeCBhWZmZVcSfA2cCS8PVDwKXhs8vTSwn6fUrLOAb509j1ZbdGhRKRETeIfLEwd2bgauBR4AVwD3uvszMrjSzKxM2PR941N0TRymqBp4xs0XAi8Bf3P3hcN0NwBlmtgo4I5yXDjh1yjA+ePxobnl6DYtrd0QdjoiIZBBTJ7iDampqfMGCBe1vmAd27mvirB/8lcr+RTz46ZPpV1gQdUgiItLDzOylpKEM2hV5jYNkpsr+RXzrgqNZuXkXNz2xOupwREQkQyhxkLROPWIYHzh+ND996nWW1O6MOhwREckAShykTV/9x6kMLS/m879fRGNza9ThiIhIxJQ4SJsqSxObLHSVhYhIvlPiIO067YhqLjhuFDc/9TpLN6jJQkQknylxkA752vuOYkiZmixERPKdEgfpkMrSIr55/tG8+tYubnpSV1mIiOQrJQ7SYe+dWs0Fx47ip0+uVpOFiEieUuIgnfKf505lUFkxX/jDYjVZiIjkISUO0ikDS4v55vlHs2JTPT99Sk0WIiL5RomDdNoZU6s5b8ZIbnpiNcs31kcdjoiI9CElDtIlXzv3KAaWBldZNLWoyUJEJF8ocZAuGVRWzDfPn8byTfW6l4WISB5R4iBdduZRwzn/2FH8+IlVPL5ic9ThiIhIH1DiIN3y3+dPY9rISj5z1yus2KT+DiIiuU6Jg3RLaXEhP7+khvKSQj52+wK27mqIOiQREelFShyk24ZXlvCLS07g7T0NXHHHAvY3tUQdkoiI9BIlDtIjjh5dyQ8/NINX3tzBF/+wGHePOiQREekFShykx8yZNoIvnDWFBxdt5Ce60kJEJCcVRh2A5JZPzZ7A61t38/3HXuPwqjLed8zIqEMSEZEepBoH6VFmxrcuOJqasYP43D2LWLh+R9QhiYhID1LiID2uX2EB/3Px8VRV9OPjv17Axh37og5JRER6iBIH6RVDyvtx22UnsK+xhY/dvoA9Dc1RhyQiIj1AiYP0msnVFdz04WN59a16Pvu7hbS26koLEZFsp8RBetXsKcP46vum8ujyzXznkZVRhyMiIt2kqyqk1102axyrt+zmlqdf5/CqMv65ZkzUIYmISBcpcZBeZ2Zc//6jeOPtvXz5viX0K4wxd8aoqMMSEZEuUFOF9Imighg/+9fjqBk7iGt/t5A7X3gj6pBERKQLMiJxMLM5ZrbSzFab2XUp1n/BzBaGj6Vm1mJmg81sjJk9aWYrzGyZmV2TUOZ6M9uQUO6cvj0qSVZRUsTtH5nJqVOG8e/3L+WWp1+POiQREemkyBMHMysAbgbOBqYCF5nZ1MRt3P1Gd5/h7jOALwNPu3sd0Ax8zt2PBN4FXJVU9gfxcu4+ry+OR9pWUlTALf96PO87ZgQ3PPQqNz7yqu5rISKSRTKhj8NMYLW7rwEws7uBucDyNNtfBNwF4O6bgE3h811mtgIY1UZZyQDFhTF+dOGxlPcr5OYnX2f3/ma+du5RxGIWdWgiItKOyGscCL7o1yfM14bL3sHMSoE5wL0p1o0DjgVeSFh8tZktNrPbzGxQmn1eYWYLzGzB1q1bu3gI0lkFsWBo6o//w3hu//sbfP4Pi2huaY06LBERaUcmJA6pfmamq7s+F3g2bKY4uAOzcoJk4lp3rw8X/wyYAMwgqJX4Xqoduvut7l7j7jVVVVVdCF+6ysz4yjlH8m9nTOa+lzdw1W9fpqG5JeqwRESkDZmQONQCiRf2jwY2ptn2QsJmijgzKyJIGu509/viy919s7u3uHsr8HOCJhHJMGbGZ06fxH++byqPLNvMx25fwN5GDU8tIpKpMiFxmA9MMrPxZlZMkBw8mLyRmVUCpwAPJCwz4H+BFe7+/aTtRyTMng8s7YXYpYd85N3jufEDx/Ds6m1c/L8vsnNfU9QhiYhICpEnDu7eDFwNPAKsAO5x92VmdqWZXZmw6fnAo+6+J2HZycDFwGkpLrv8jpktMbPFwKnAZ3v/aKQ7Plgzhps/fByLa3dw0a3Ps213Q9QhiYhIEtOlcAfV1NT4ggULog4j7z392lY+cccCRlb259ZLapg4rDzqkEREcpKZveTuNZ0pE3mNg0iyUyZXccdHT2THvibO/ckz3PtSbdQhiYhISImDZKQTxg1m3mf+gaNHV/K53y/i879fpE6TIiIZQImDZKzhlSX89mMn8unTJnLvy7XMvelZXtu8K+qwRETymhIHyWiFBTE+d+YU7vjIiWzf28T7b3qGe+av1zDVIiIRUeIgWeHdk4Yy75p3c9xhg/jivYv57O8WsqdBTRciIn1NiYNkjWEVJdzx0RP5tzMm8+CijZz7k2dYvrG+/YIiItJjlDhIVimIBSNN3vmxd7G7oZnzfvosd77whpouRET6iBIHyUonTRjCvGv+gRPHD+bf71/Kp+96hR17G6MOS0Qk5ylxkKw1tLwft18+ky/OmcJDS99i9nef4jfPv0FLq2ofRER6ixIHyWqxmPGp2RP5y2fezZTqCv7jj0t5/03PsGBdXfuFRUSk05Q4SE44YvgA7r7iXfzkomOp29PIB275O//2u4Vsqd8fdWgiIjlFiYPkDDPj3Okjefxzp3DVqRP48+JNnPa9p7n1r6/T2NwadXgiIjlBiYPknNLiQr5w1hE8+tn3MHP8YL4571Xm/Oiv/PW1rVGHJiKS9ZQ4SM4aN7SM2y47gdsuq6Gl1bnkthe54tcLWF+3N+rQRESylhIHyXmnHVHNI9e+hy+cNYW/rdrGe7//NF//83I27dwXdWgiIlnHNHDOQTU1Nb5gwYKow5BetHHHPr77yEoeWLSRmMF5M0bxiVMmMHFYedShiYj0OTN7yd1rOlVGicNBShzyx/q6vfzib2u4e/56GltaOWvqcD45ewLTxwyMOjQRkT6jxKGblDjkn227G7j9uXXc/tw66vc3M2vCED45ewLvnjgUM4s6PBGRXqXEoZuUOOSv3Q3N3PXCm/zimTVsrm9g2qgBfPKUicyZNpyCmBIIEclNShy6SYmDNDS38MdXNnDL02tYu20P44eWcclJY5k7YxSDy4qjDk9EpEcpcegmJQ4S19LqPLrsLW55+nUW1e6kqMA4dcowPnD8aGZPGUZxoS5IEpHs15XEobC3ghHJZgUx4+yjR3D20SN49a167n2plvtf2cijyzczuKyY908fyQeOH81RIweoL4SI5BXVOCRQjYO0pbmllb+u2sq9L23gseWbaWxp5YjhFfzTcaOZe+xIhlWURB2iiEinqKmim5Q4SEft2NvInxZv4g8v1bJo/Q4KYsYpk6uYO2MksycPo7K0KOoQRUTapcShm5Q4SFes3rKLP7y0gftfqWVzfQMFMeP4sYM4/YhhnH7kMCZUlas5Q0QykhKHblLiIN3R0uosqt3BEyu28PirW1ixqR6AwwaXclqYRMwcP5h+hQURRyoiElDi0E1KHKQnbdixjydf3cITr27h2dXbaGhupay4gH+YVMVpRwxj9pQqhg1QvwgRiU7WJg5mNgf4EVAA/MLdb0ha/wXgX8LZQuBIoMrd69KVNbPBwO+AccA64J/dfXtbcShxkN6yr7GF517fxuOvbuGJFVt4q34/AOOGlHLCuMHBY/xgxg0pVbOGiPSZrEwczKwAeA04A6gF5gMXufvyNNufC3zW3U9rq6yZfQeoc/cbzOw6YJC7f6mtWJQ4SF9wd5ZtrOe517fx4trtLHijjh17mwAYWt6PE8YNombcYGaOG8yRIyooLNCYESLSO7J1HIeZwGp3XwNgZncDc4GUiQNwEXBXB8rOBWaH290OPAW0mTiI9AUzY9qoSqaNquSK90Brq/P61t3MX7ed+evqmL+ujoeWvgVAWXEBx40dxHGHDWLaqEqOGjmAEZUlqpUQkchkQuIwClifMF8LnJhqQzMrBeYAV3egbLW7bwJw901mNqwngxbpKbGYMam6gknVFXz4xMMA2LRzH/PXbWfBujpeXFvHj59YRbxycGBpEVNHDGDqiAEcNWoAU0dUcnhVGUWqmRCRPpAJiUOqn07p2k/OBZ5197oulE394mZXAFcAHHbYYZ0pKtJrRlT25/3T+/P+6SMB2NPQzKtv1bN8Yz3LNwXTO55/g4bmVgCKC2NMqa7gqJEDOHLEACYOK2f80DKGDyghppt0iUgPyoTEoRYYkzA/GtiYZtsLOdhM0V7ZzWY2IqxtGAFsSbVDd78VuBWCPg6dD1+k95X1K+T4sYM5fuzgA8uaW1pZs20PyzfWs2zjTpZvqufhZW9x9/yDlXD9iwoYP7SM8VVlTAinhw8tZ3xVGQNKNEiViHReJnSOLCTo4Hg6sIGgg+OH3X1Z0naVwFpgjLvvaa+smd0IvJ3QOXKwu3+xrVjUOVKynbuzub6BNVt3s2bbHtZs3cPabcHz9XV7aU34dx9a3o/Dq8oYM6iUUQNLGDWoP6MGljJqUH9GVJZQUqTxJkRyXVZ2jnT3ZjO7GniE4JLK28Iv/ivD9beEm54PPBpPGtoqG66+AbjHzD4KvAl8sG+OSCQ6ZsbwyhKGV5Ywa+LQQ9Y1NrfyZt0eXt+6h7Xb9rBm627WbtvDc69vY3P9/kOSCggSi1GD+jN6YH9GDerPyMoShlf2p6qiH8Mq+lFV0U/JhUgeirzGIZOoxkHyVVNLK2/t3M+GHfvYsH3fodPw0Rj2p0g0oKSQYQNKDiQSwyr6MayihKqKfgwt78egsiIGlxUzqLRYSYZIBsrKGgcRiV5RQYwxg0sZM7g05Xp3Z9vuRjbX72frrga27IpPG9hSH8y//OZ2ttQ3HOiwmay0uIBBpcUMKitiUGnxgYQivmxASRED+heG02C+oqSQ0uICXX4qkkGUOIhIu8yMqrBWoS3uTv3+Zrbu2s/buxvZvreRuj1NbN/byPY9jdSF0+17m3izbi91exrZtb+5zX0WxIwBJYWHJBNl/QopKy6grF8h5f2C+dLiggPPy8P5+PL+xQX0LyqgpKiAfoUxJSIi3aDEQUR6jJlR2b+Iyv5FTOzgyCmNza3s3NfErv1N1O9vDqb7mqnf30T9vqZwGszv2t9M/b4m6vbsZW9jC3samtnd0Jy2liOVmAVXm/QvDhKJ/kUFlIbP+xUVUFIYo1+YYPQrjB1INvoVFtCvKHZgfXFBjKLCGMUFwXZFBTGKC4NHUYEdsqyoIEZRLEZRoVEYC9YreZFspcRBRCJVXBjrUG1GW5paWtnb0MLuxmb2hsnEnoaWMKloYW9jC/saW9jX1ML+pnC+qYX94XRfuGznvia2NLXQ0NxKQ3za3EpDcwtNLT3bH6wwZhQWWJBUFMQojMWfGwXh84KYURgL5gvDbZLXxeLbWLCuIGFZzA6Wj4XbHJhaMPhYQcLymAU1PDELHgWxIBmMP49ZkPDEy1v4mjEL1hFO4/NGvDwH9g+GJawP9knwwIjFgmmwzcHtD9mWhDIHXidheVDs0HneuS3hPsLND1kfvvKB5ySWO/D84H4P7uPQZblIiYOIZL2ighiVpTEqS3tvbIrmllYaW1ppaGplf3MLjc2tNLUEiUXw3A9d1tJKU3zaEqxvammlOfF5q4frWmlucRrDaUur09zaSkur05Qw39TSyt7G+LzT3NJKizut4fyBqR/cJnlZ8tUz0jcSE5Rg3rAU64NtDplJ9fSQ5CZ5WXm/Ql789/d2N+S0dFVFAjPbBayMOo5eNBTYFnUQvSiXjy+Xjw10fNlOx5e9prh7RWcKqMbhUCs7e1lKNjGzBTq+7JTLxwY6vmyn48teZtbpMQh0VxwRERHpMCUOIiIi0mFKHA51a9QB9DIdX/bK5WMDHV+20/Flr04fmzpHioiISIepxkFEREQ6TIkDYGZzzGylma0Ob8GdU8xsnZktMbOFXelBm2nM7DYz22JmSxOWDTazx8xsVTgdFGWM3ZHm+K43sw3hOVxoZudEGWN3mNkYM3vSzFaY2TIzuyZcnvXnsI1jy4nzZ2YlZvaimS0Kj++/wuVZf+6gzePLifMHYGYFZvaKmf05nO/0ucv7pgozKwBeA84AaoH5wEXuvjzSwHqQma0Datw9J65DNrP3ALuBX7v7tHDZd4A6d78hTP4GufuXooyzq9Ic3/XAbnf/bpSx9QQzGwGMcPeXzawCeAk4D7iMLD+HbRzbP5MD58+C4RDL3H23mRUBzwDXABeQ5ecO2jy+OeTA+QMws38DaoAB7v6+rnx2qsYBZgKr3X2NuzcCdwNzI45J2uDufwXqkhbPBW4Pn99O8GGdldIcX85w903u/nL4fBewAhhFDpzDNo4tJ3hgdzhbFD6cHDh30Obx5QQzGw38I/CLhMWdPndKHIJ/6vUJ87Xk0D96yIFHzewlM7si6mB6SbW7b4Lgwxvo4C2WssrVZrY4bMrIyqrgZGY2DjgWeIEcO4dJxwY5cv7Cqu6FwBbgMXfPqXOX5vggN87fD4EvAol3hev0uVPicOjw33E5k2GGTnb344CzgavCqnDJLj8DJgAzgE3A9yKNpgeYWTlwL3Ctu9dHHU9PSnFsOXP+3L3F3WcAo4GZZjYt4pB6VJrjy/rzZ2bvA7a4+0vd3ZcSh6CGYUzC/GhgY0Sx9Ap33xhOtwD3EzTP5JrNYftyvJ15S8Tx9Ch33xx+oLUCPyfLz2HYfnwvcKe73xcuzolzmOrYcu38Abj7DuApgvb/nDh3iRKPL0fO38nA+8M+b3cDp5nZb+jCuVPiEHSGnGRm482sGLgQeDDimHqMmZWFnbQwszLgTGBp26Wy0oPApeHzS4EHIoylx8X/sUPnk8XnMOyA9r/ACnf/fsKqrD+H6Y4tV86fmVWZ2cDweX/gvcCr5MC5g/THlwvnz92/7O6j3X0cwffcE+7+r3Th3OX9Ta7cvdnMrgYeAQqA29x9WcRh9aRq4P7g84xC4Lfu/nC0IXWPmd0FzAaGmlkt8DXgBuAeM/so8Cbwwegi7J40xzfbzGYQNKOtAz4RVXw94GTgYmBJ2JYM8BVy4xymO7aLcuT8jQBuD69GiwH3uPufzezvZP+5g/THd0eOnL9UOv1/l/eXY4qIiEjHqalCREREOkyJg4iIiHSYEgcRERHpMCUOIiIi0mFKHERERKTDlDiI5CAL7ojqZjY76lh6k5mNC49zXdSxiOQLJQ4ieSK8NbCHd9rMCmb2VD4kQCLZJO8HgBKRrLYBOBJoijoQkXyhxEFEspa7NxEMeSwifURNFSJ5wMycYOhqgK+F1f+equkivL/JF81svpnVm9k+M1sWNnWUp9j3gSYQMxtrZr80s1ozazazH4bbFJnZxWZ2l5mtNLNdZrbXzJab2bfNbHDSPmeHMZ8SLnoyKebZ4XZt9nEI4/mpma0xswYz225mT5rZh9Nsn3gs1Wb2P+GxNJjZWjO7wcxKOvi2i+Qk1TiI5IfbCW4JPB1YBCxMWHfguZmNJrhvy1RgK/B3YD9wAkHicb6ZzXb37SleYxLwSrj9swSfLzvCddXAr4HtBDUEC4EBQA3wReADZnaiu28Lt38rjHlOWPaRcBkJ69tkZicCDwMDgbUEd4YdQpCMzDazOcClnnrc/THAS4ABz4Wxvhv4UvjevL+91xfJWe6uhx565NiD4EY8DsxOWHZ9uOz6NGXiX5IO/AQoTVjXH7gjXPerpHLx/TrwS6A4xb4rgHOBoqTl/YHbwrI/S1HuqeTjSFo/Lly/Lml5CcENexz4AVCQsG4asDlc94k2juXnicdC0JdiV7ju5KjPsR56RPVQU4WIxM0BTgKeB65x973xFe6+D7gS2AL8i5kNSlG+DviMuzcmr3D3Xe7+Jw/6JCQu3wdcDTQD/9RjRxLc4W8M8AbwRXdvSXjNpQQJAsDn05RfT9KxuPsKguQJ4PQejFUkq6ipQkTizgmn97p7a/JKd99jZgvC7U4AHk3a5DF339XWC5jZsQRfuuOAMoJaDoBGoMrMBnnqZpDOiveNuDM5WQn9ErgZmGhmo9x9Q9L6J8KkJlm8I+bIHohRJCspcRCRuMPD6Y1mdmM721alWPZGuo3DTpV30n7fgAEE/SC6a1Q4XZtqpbvvN7ON4XajCC7rTPRmmv3Wh1N1kJS8pcRBROIKwunTBH0k2pIqSUj1Cz3uWwRJw3LgOmABsC1eGxB+iY/gYA1Ed8X3k6rjY/I2qbyjxkVEAkocRCRufTj9vbvf3MP7/mA4/VDYx+AAMysDhvfw69WG08NTrQwvqRwRzibXNohIG9Q5UiR/xDv6pfvB8FA4/WCa9d0RH6dhfYp1Hyb9r//2Yk7n6XB6kZmlKntp+JqrU/RvEJE2KHEQyR/xL8gj06z/I8HYBaeY2S3JgzIBmNnhZnZVF1473qnwkLJmVkPQjJFOezGn83uCJGU88C0zO/BZZ2ZTgf8KZ7/byf2K5D0lDiL54xFgL3CBmf01HOHxF2b2foDwSorzgCXAJ4B1Zva3cLTHx8xsJfA68NUuvPb/C6f/bWYLw30+DbwQxpWuY+X94fRGM3swjPcXZjalrRdz9/3APxMMQPV54LXwNR8hGKSqmuDSylu7cCwieU2Jg0iecPe3gPcRDKp0DEF1/UeB4xK2qQVmEoyt8ApwFMH4CtMIBj/6LnBBF177D8CpwJME4yucS3AFxbXAxW2UexD4FEGNxXvDeD/Kwf4Jbb3m8wSjZd5C0PHzAuBEgnEq/pX0o0aKSBtM/zciIiLSUapxEBERkQ5T4iAiIiIdpsRBREREOkyJg4iIiHSYEgcRERHpMCUOIiIi0mFKHERERKTDlDiIiIhIhylxEBERkQ5T4iAiIiId9v8B2x4QpoJhQcAAAAAASUVORK5CYII=\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"fig = plt.figure(figsize=(8,6))\\n\",\n \"plt.plot(vfe_hist)\\n\",\n \"plt.ylabel('$\\\\\\\\mathcal{F}$', fontsize = 22)\\n\",\n \"plt.xlabel(\\\"Iteration\\\", fontsize = 22)\\n\",\n \"plt.xlim(0, n_iter)\\n\",\n \"plt.ylim(vfe_hist[-1], vfe_hist[0])\\n\",\n \"plt.title('Gradient descent on VFE', fontsize = 24)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 17,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/latex\": [\n \"$\\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln \\\\frac{Q(s)}{P(o, s)}] = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(o, s)]:$\"\n ],\n \"text/plain\": [\n \"\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Initial F = 0.916\\n\",\n \"==================\\n\",\n \"Final posterior:\\n\",\n \"[0.8 0.2]\\n\",\n \"==================\\n\",\n \"Final F = 0.693\\n\",\n \"==================\\n\"\n ]\n }\n ],\n \"source\": [\n \"final_qs, initial_F, final_F = qs_hist[-1,:], vfe_hist[0], vfe_hist[-1]\\n\",\n \"\\n\",\n \"display(Latex('$\\\\mathcal{F} = \\\\mathbb{E}_{Q(s)}[\\\\ln \\\\\\\\frac{Q(s)}{P(o, s)}] = \\\\mathbb{E}_{Q(s)}[\\\\ln Q(s) - \\\\ln P(o, s)]:$'))\\n\",\n \"print(f'Initial F = {initial_F.round(3)}')\\n\",\n \"print('==================')\\n\",\n \"\\n\",\n \"print('Final posterior:')\\n\",\n \"print(f'{final_qs.round(1)}') # note that because of numerical imprecision in the gradient descent (constant learning rate, etc.), the approximate posterior will not exactly be the optimal posterior\\n\",\n \"print('==================')\\n\",\n \"print(f'Final F = {vfe_qs(final_qs).round(3)}')\\n\",\n \"print('==================')\\n\"\n ]\n }\n ],\n \"metadata\": {\n \"interpreter\": {\n \"hash\": \"24ee14d9f6452059a99d44b6cbd71d1bb479b0539b0360a6a17428ecea9f0810\"\n },\n \"kernelspec\": {\n \"display_name\": \"Python 3.8.10 64-bit ('pymdp_env2': conda)\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.7.10\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/legacy/gridworld_tutorial_1.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Tutorial on Active Inference with `pymdp`\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"This set of 3 tutorial notebooks aims to be an accessible introduction to discrete-state-space active inference modelling with the `pymdp` package. We assume no prerequisites other than a good grasp of Python and some basic mathematical knowledge (specifically some familiarity with probability and linear algebra). We assume no prior knowledge of active inference. Hopefully, by the end of this series of notebooks, you will understand active inference well enough to understand the recent literature, as well as implement your own agents!\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"These tutorials will walk you through the specification, and construction of an active inference agent which can solve a simple navigation task in a 2-dimensional grid-world environment. The goal here is to implement the agent 'from scratch'. Specifically, instead of just using magical library functions, we will show you an example of how these functions could be implemented from pure Python and numpy code. The goal at the end of these tutorials is that you understand at a fairly detailed level how active inference works in discrete state spaces and how to apply it, as well as how you could implement a simple agent without using the `pymdp` package. Once you understand what the `pymdp` package aims to abstract, we will go through the structure and functionality offered by the package, and show how you can construct complex agents in a simple and straightforward way.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# What is Active Inference?\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Fundamentally, the core contention of active inference is that the brain (and agents in general) can be thought of as fundamentally performing (Bayesian) inference about the world. Specifically, an agent performs two functions.\\n\",\n \"\\n\",\n \"\\n\",\n \"1.) **Perception**. An agent does not necessarily know the true state of the world, but instead must infer it from a limited set of (potentially ambiguous) observations.\\n\",\n \"\\n\",\n \"\\n\",\n \"2.) **Action**. Typically, the agent can also perform the actions which change the state of the world. The agent can use these actions to drive the world towards a set of states that it desires. \\n\",\n \"\\n\",\n \"The theory of Active Inference argues that **both** perception and action can be represented and solved as Bayesian inference problems. \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# What is Bayesian Inference?\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Bayesian inference provides a recipe for performing *optimal* inference. That is, if you have some set of Hypotheses $H$ and some set of data $D$, then Bayesian inference allows you to compute the *best possible* update to your hypotheses given the data that you have. In other words, the best explanation $H$ that accounts for your actual data $D$.\\n\",\n \"\\n\",\n \"For instance, suppose you are a trader and you want to know whether some stock will go up tomorrow. And you have a set of information about that stock (for instance earnings reports, sales data, rumours a friend of a friend told you etc). Then Bayesian inference provides the *optimal way* to estimate the probability that the stock will go up. In this scenario, our \\\"hypotheses\\\" $H$ is that the stock will go up, or it will go down and our \\\"data\\\" $D$ is the various pieces of information we hold.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The fundamental equation in Bayesian inference is **Bayes Rule**. Which is \\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"p(H | D) = \\\\frac{p(D | H)p(H)}{p(D)}\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"Here $p(H)$ etc are *probability distributions*. All a probability distribution is is a function that assigns a probability value (between 0 and 1) to a specific outcome. A probability distribution then represents the probability of that outcome for every possible outcome. For instance, take p(H). This is the probability distribution over our *hypothesis space*, which you can think of as our baseline assumptions about whether the stock tends to go up or down i.e. $p(H) = [p(stock\\\\_goes\\\\_up), p(stock\\\\_goes\\\\_down)]$, before we've encountered any data that provides evidence for/against either hypothesis.\\n\",\n \"\\n\",\n \"If we assume we have no idea whether the stock will go up or down, we can say that the probability in each case is 0.5 so that $p(H) = [0.5, 0.5]$. When there is a discrete set of possible outcomes or states, probability distributions can be simply represented as vectors with one element for each outcome - where the element itself is simply the probability of seeing that outcome. The sum of all the elements of a probability distribution must equal 1. The vector's elements encode the probabilities of *all possible events*, so one of them *must* occur -- i.e. the probability of seeing *some* outcome is 100%.\\n\",\n \"\\n\",\n \"There are three fundamental quantities in Bayesian inference: the **posterior**, the **likelihood** and the **prior**. The posterior is ultimately the goal of inference, it is $p(H | D)$. What this represents is the probability of each hypothesis in the hypothesis space *given the data $D$*. You can think of as you best guesses at the truth of each hypothesis after optimally integrating the data. Next is the **prior** $p(H)$ which represents your assumptions about how likely each hypothesis is *prior to seeing the data*. Finally, there is the likelihood $p(D | H)$ which quantifies how likely each outcome you see is, given the different hypotheses. The likelihood distribution can also be thought of as a *model* for how the data relates to the hypotheses. \\n\",\n \"\\n\",\n \"The key insight of Bayes rule is simply that the posterior probability -- how likely the hypothesis is, given the data -- is simply the likelihood times the prior. This multiplication can be expressed as computing the following: how likely is the data you actually saw, given the different hypotheses ($P(D = d | H)$), multiplied by the prior probability you assign to each hypothesis ($P(H)$). So the full posterior is a distribution over the different hypotheses - in the case of discrete / Categorical distributions, your posterior $p(H |D)$ will also be a vector of probabilities, e.g. $p(H | D) = [0.75, 0.25]$.\\n\",\n \"\\n\",\n \"Effectively, hypotheses are more likely if they can predict the data well, but are also weighted by their a-priori probability. The marginal likelihood $p(D)$ is basically just there to normalize the posterior (i.e. make sure it equals 1).\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Generative Models\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"In Active Inference we typically talk about *generative models* as a core component. But what are generative models? Technically a generative model is simply the product of a likelihood and a prior, for all the possible data points $D$ and hypotheses $H$. This is also known as a *joint distribution* $p(H,D) = p(D | H)p(H)$. The generative model, then, is simply the numerator of Bayes rule, and if we normalize it we can compute posterior probabilities. It is called a generative model because it allows you to *generate* samples of the data. To do so, we follow the following steps:\\n\",\n \"\\n\",\n \"1.) Sample a hypothesis $h_i$ from the prior -- i.e. $p(H)$\\n\",\n \"\\n\",\n \"2.) Sample a datum $d_i$ from the likelihood distribution, given the particular hypothesis $h_i$ that you sampled i.e. sample $d_i$ from $p(D | H = h_i)$.\\n\",\n \"\\n\",\n \"Another way to think about a generative model is that it is simply a model, or set of beliefs/assumptions, of how observed data are generated. This is often a very helpful way to think about inference problems, since it aligns with our notion of causality -- i.e. there are unknown processes in the world which generate data. If we can imagine a process and then imagine the data generated by this process, then we are imagining a generative model. Inference of the posterior, on the other hand, is more difficult because it goes in the *reverse* direction -- i.e. you have some set of observations and want to reconstruct the process that gave rise to them. Fundamentally, all of Bayesian statistics can be broken down into two steps:\\n\",\n \"\\n\",\n \"1.) Make a mathematical model of the data-generating process - the sort of environmental / world structures you think could give rise to the sort of data you have (i.e. come up with a generative model). Generative models are classically written down using a set of unknown parameters (e.g. parameters that describe probability distributions, like sufficient statistics). You want to \\\"fit\\\" (read: infer the values of) these parameters, given some data.\\n\",\n \"\\n\",\n \"2.) Given your generative model and some data, compute the posterior distribution over the unknown parameters using Bayes rule, or some approximation of Bayes rule.\\n\",\n \"\\n\",\n \"3.) Be happy!\\n\",\n \"\\n\",\n \"All the methods in Bayesian statistics essentially fall into two classes. Coming up with more expressive and powerful generative models and then figuring out algorithms to perform inference on them.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Why is Bayesian Inference hard?\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"At this point, you may be wondering: Bayesian inference seems pretty easy. We known Bayes rule. We can invent generative models easily enough. Computing the posterior is just taking the generative model and dividing it by $p(D)$. Why all this fuss? Why do we need to make a whole academic field out of this anyway? Luckily this has a straightforward answer. Bayesian inference is hard for essentially just one reason: that computing $p(D)$, the normalizing constant, is hard.\\n\",\n \"\\n\",\n \"Let's think about why. $p(D)$, which is known as the **marginal likelihood**, is fundamentally just the probability of the data. What does that mean? How is there just some free-floating probability of the data? Fundamentally there isn't. $p(D)$ is the probability of the data *averaged over all possible hypotheses*. We can write this as,\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"p(D) = \\\\sum_h p(D | H)p(H)\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"\\n\",\n \"Effectively, $p(D)$ is the sum over all possible hypotheses of the probability of the data given that hypothesis, weighted by the prior probability of that hypothesis. This is challenging to compute in practice because you are often using really large (or indeed often infinite) hypothesis spaces. For instance, suppose your trader doesn't just want to know whether the stock will go up or down but *how much* it will go up or down. Now, with this simple change, you have an *infinite* amount of hypotheses: $p(H) = [p(stock\\\\_goes\\\\_up\\\\_0.00001), p(stock\\\\_goes\\\\_up\\\\_0.00002), p(stock\\\\_goes\\\\_up\\\\_0.00003) ...]$. Then, if we want to compute the posterior in this case, we need to sum over every one of this infinite amount of hypotheses. You can see why this ends up being quite challenging in practice.\\n\",\n \"\\n\",\n \"Because of this intrinsic difficulty, there are a large number of special case algorithms which can solve (or usually approximate) the Bayesian posterior in various cases, and a large amount of work in statistics goes into inventing new ones or improving existing methods. Active Inference agents use one special class of approximate Bayesian inference methods called *variational methods* or *variational inference*. This will be discussed in much more detail in notebook 2.\\n\",\n \"\\n\",\n \"Beyond merely the difficulty of performing inference, another reason why Bayesian statistics is hard is that you often *don't know* the generative model. Or at least you are uncertain about some aspects of it. There is also a wide class of methods which let you perform inference and *learning* simultaneously, including for active inference, although they won't be covered in this tutorial.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# A Generative Model for an Agent\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"In Active Inference, we typically go a step beyond the simple cases of Bayesian inference described above, where we have a static set of hypotheses and some static data. We are instead interested in the case of an *agent* interacting with a *dynamic environment*. The key thing we need to add to the formalism to accomodate this is a notion of *time*. We consider an environment consisting of a set of *states* $[x_1, x_2, \\\\dots x_t]$ evolving over time. Moreover, there is an agent which is in the environment over time. This agent receives a set of *observations* $[o_1, o_2 \\\\dots o_t]$, which are a function of the state of the environment, and it can emit *actions* $[a_1, a_2 \\\\dots a_t]$ which can change the state of the environment. The key step to get a handle on this situation mathematically is to define a *generative model* of it. \\n\",\n \"\\n\",\n \"To start, we must make some assumptions to simplify the problem. Specifically, we assume that the *state* of the environment $x_t$ only depends on the state at the previous timestep $x_{t-1}$ and the action emitted by the agent at the previous timestep $a_{t-1}$. Then, we assume that the observation $o_t$ at a given time-step is only a function of the environmental state at the current timestep $x_t$. Together, these assumptions are often called the **Markov Assumptions** and if the environment adheres to them it is often called a **Markov Decision Process**. \\n\",\n \"\\n\",\n \"The general computational \\\"flow\\\" of a Markov decision process can be thought of as following a sequence of steps.\\n\",\n \"\\n\",\n \"1.) The state of the environment is $x_t$. \\n\",\n \"\\n\",\n \"2.) The environment state $x_t$ generates an observation $o_t$.\\n\",\n \"\\n\",\n \"3.) The agent receives an observation $o_t$, and based on it (or inferences derived thereof) decides to take some action $a_t$, which it executes in the environment.\\n\",\n \"\\n\",\n \"4.) Given the current state $x_t$ and the agent's action $a_t$, the environment updates its own state to produce $x_{t+1}$\\n\",\n \"\\n\",\n \"5.) Go back to step 1.\\n\",\n \"\\n\",\n \"Now that we have this series of steps, we can try to define what it means mathematically. Specifically, we need to define two quantities. \\n\",\n \"\\n\",\n \"a.) We need to know how the state of the environment $x_t$ is reflected in the observation sent to the agent $o_t$. In Bayesian terms from the agent's perspective, the true state of the environment is unknown, and its various possible states can be thought of as \\\"hypotheses\\\", while the observations it receives are \\\"data\\\". The agent's generative model encodes some prior assumptions about each possible state $x_t$ (i.e. each hypothesis) relates to the probability of seeing each possible outcome $o_t$. This relationship (from the agent's perspective) is a function known as the **likelihood distribution** $p(D | H)$ or, in our new notation $p(o_t | x_t)$. \\n\",\n \"\\n\",\n \"b.) We need to know how the environment updates itself to form its new state $x_{t+1}$, given the old one $x_t$ and the action $a_t$. This can be thought of (from the perspective of the agent who does not observe it) as the **prior** since it can be thought of as the default expectation the agent can have about the state of the environment prior to receiving any observations. It can be written as $p(x_t | x_{t-1}, a_{t-1})$. This distribution is also known as the **transition distribution** since it specifies (the agent's assumptions about) how the environment transitions from one state to another.\\n\",\n \"\\n\",\n \"These two distributions $p(o_t | x_t)$ and $p(x_t | x_{t-1}, a_{t-1})$ are all that is needed to specify the evolution of the environment. At this point, it is necessary to make a distinction between the *actual* evolution of the environment -- known as the **generative process** -- and the *agent's model* of the evolution of the environment, which is known as the **generative model**. These are not necessarily the same, although in some sense the goal of the agent is to figure out a generative model that is as close to the true generative process as possible. In this example, we will consider a scenario in which the agent knows the true model, so the generative model and the generative process are the same, although this is not always the case.\\n\",\n \"\\n\",\n \"To make this concrete, all that is necessary to do is to specify precisely what the **likelihood** and **transition** distributions actually are.\\n\",\n \"\\n\",\n \"In the case of discrete state spaces, where it is possible to explicitly enumerate all states, a very generic way of representing these distributions is as *matrices*. Specifically, we can represent the likelihood distribution as a matrix denoted $\\\\textbf{A}$, which is of shape $dimension\\\\_of\\\\_observation \\\\times dimension\\\\_of\\\\_state$. The element $A_{i,j}$ of $\\\\textbf{A}$ represents the probability that observation $i$ is generated by state $j$.\\n\",\n \"\\n\",\n \"Secondly, we can represent the transition distribution by a matrix $\\\\textbf{B}$ of shape $state\\\\_dim \\\\times state\\\\_dim \\\\times action\\\\_dim$ where element $\\\\textbf{B}_{i,j,k}$ represents the probability of the environment moving to state $i$ given that it was previously in state $j$ and that action $k$ was taken.\\n\",\n \"\\n\",\n \"In the rest of this notebook, we will explicitly write down the generative process / generative model for a simple grid-world environment in code, to get a better handle on how the environment and the agent's model is specified. In the next notebook, we will turn to inference and action selection and discuss how active inference solves these two tricky problems.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import numpy as np\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import seaborn as sns\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Constructing a Generative Model \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For the rest of this notebook, we will construct a simple generative model for an active inference agent navigating a 3x3 grid world environment. The agent can perform one of 5 movement actions at each time step: `LEFT, RIGHT, UP, DOWN, STAY`. The goal of the agent is to navigate to its preferred position. \\n\",\n \"\\n\",\n \"We will create matrices for both the environment as well as the agent itself. As we go up levels of abstraction, these environment and generative model matrices will be imported from classes - but this notebook is the lowest level representation of construction, to show how everything is built from the ground up. \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Understanding the state space\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The first thing to note is that we are in a 3x3 grid world which means we have 9 states in total. We can define the following mapping to better understand the space.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"state_mapping = {0: (0,0), 1: (1,0), 2: (2,0), 3: (0,1), 4: (1,1), 5:(2,1), 6: (0,2), 7:(1,2), 8:(2,2)}\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"All we're doing with this mapping dictionary is assigning a particular index (`0`, `1`, `2`, ..., `8`) to each grid position, which is defined as a pair of `(x, y)` coordinates ( `(0, 0), (1, 0)`, ..., `(2, 2)`). We will use the linear indices to refer to the grid positions in our probability distributions (e.g. `P(o_t | x_t = 5)`), so this `state_mapping` will allow us to easily move between these linear indices and the grid world indices. These kinds of mappings are very handy for intuition and visualization.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"And the following heatmap just represents how the coordinates map to the real grid space\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"grid = np.zeros((3,3))\\n\",\n \"for linear_index, xy_coordinates in state_mapping.items():\\n\",\n \" x, y = xy_coordinates\\n\",\n \" grid[y,x] = linear_index # rows are the y-coordinate, columns are the x-coordinate -- so we index into the grid we'll be visualizing using '[y, x]'\\n\",\n \"fig = plt.figure(figsize = (3,3))\\n\",\n \"sns.set(font_scale=1.5)\\n\",\n \"sns.heatmap(grid, annot=True, cbar = False, fmt='.0f', cmap='crest')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Likelihood Matrix: A\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The likelihood matrix represents $P(o_t | x_t)$ , the probability of an observation given a state. In a grid world environment, the likelihood matrix of the agent is identical to that of the environment. It is simply the identity matrix over all states (in this case 9 states, for a 3x3 grid world) which represents the fact that the agent has probability 1 of observing that it is occupying any state x, given that it is in state x. This just means that the agent has full transparency over its own location in the grid. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"A = np.eye(9)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"A\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can also plot the likelihood matrix as follows:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"labels = [state_mapping[i] for i in range(A.shape[1])]\\n\",\n \"def plot_likelihood(A):\\n\",\n \" plt.figure(figsize = (6,6))\\n\",\n \" sns.heatmap(A, xticklabels = labels, yticklabels = labels, cbar = False)\\n\",\n \" plt.title(\\\"Likelihood distribution (A)\\\")\\n\",\n \" plt.show()\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"plot_likelihood(A)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Transition matrix: B\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The transition matrix determines how the agent can move around the gridworld given each of the 5 available actions (UP, DOWN, LEFT, RIGHT, STAY). \\n\",\n \"So the transition matrix will be a 9x9x5 matrix, where each entry corresponds to an end state, a starting state, and the action that defines that specific transition. \\n\",\n \"\\n\",\n \"To construct this matrix, we have to understand that when the agent is at the edges of the grid, it cannot move outward, so trying to move right at the right wall will cause the agent to stay still. \\n\",\n \"\\n\",\n \"We will start by constructing a dictionary which we call P, which maps each state to its next state given an action\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"state_mapping\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"P = {}\\n\",\n \"dim = 3\\n\",\n \"actions = {'UP':0, 'RIGHT':1, 'DOWN':2, 'LEFT':3, 'STAY':4}\\n\",\n \"\\n\",\n \"for state_index, xy_coordinates in state_mapping.items():\\n\",\n \" P[state_index] = {a : [] for a in range(len(actions))}\\n\",\n \" x, y = xy_coordinates\\n\",\n \"\\n\",\n \" '''if your y-coordinate is all the way at the top (i.e. y == 0), you stay in the same place -- otherwise you move one upwards (achieved by subtracting 3 from your linear state index'''\\n\",\n \" P[state_index][actions['UP']] = state_index if y == 0 else state_index - dim \\n\",\n \"\\n\",\n \" '''f your x-coordinate is all the way to the right (i.e. x == 2), you stay in the same place -- otherwise you move one to the right (achieved by adding 1 to your linear state index)'''\\n\",\n \" P[state_index][actions[\\\"RIGHT\\\"]] = state_index if x == (dim -1) else state_index+1 \\n\",\n \"\\n\",\n \" '''if your y-coordinate is all the way at the bottom (i.e. y == 2), you stay in the same place -- otherwise you move one down (achieved by adding 3 to your linear state index)'''\\n\",\n \" P[state_index][actions['DOWN']] = state_index if y == (dim -1) else state_index + dim \\n\",\n \"\\n\",\n \" ''' if your x-coordinate is all the way at the left (i.e. x == 0), you stay at the same place -- otherwise, you move one to the left (achieved by subtracting 1 from your linear state index)'''\\n\",\n \" P[state_index][actions['LEFT']] = state_index if x == 0 else state_index -1 \\n\",\n \"\\n\",\n \" ''' Stay in the same place (self explanatory) '''\\n\",\n \" P[state_index][actions['STAY']] = state_index\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"P\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"From here, we can easily construct the transition matrix\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"num_states = 9\\n\",\n \"B = np.zeros([num_states, num_states, len(actions)])\\n\",\n \"for s in range(num_states):\\n\",\n \" for a in range(len(actions)):\\n\",\n \" ns = int(P[s][a])\\n\",\n \" B[ns, s, a] = 1\\n\",\n \" \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"B is a very large matrix, we can see its shape below, which is as expected:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"B.shape\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"We can also visualize B on the plots below. The x axis is the starting state, and the y axis is the ending state, and each plot corresponds to an action given by the title.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"fig, axes = plt.subplots(2,3, figsize = (15,8))\\n\",\n \"a = list(actions.keys())\\n\",\n \"count = 0\\n\",\n \"for i in range(dim-1):\\n\",\n \" for j in range(dim):\\n\",\n \" if count >= 5:\\n\",\n \" break \\n\",\n \" g = sns.heatmap(B[:,:,count], cmap = \\\"OrRd\\\", linewidth = 2.5, cbar = False, ax = axes[i,j], xticklabels=labels, yticklabels=labels)\\n\",\n \" g.set_title(a[count])\\n\",\n \" count +=1 \\n\",\n \"fig.delaxes(axes.flatten()[5])\\n\",\n \"plt.tight_layout()\\n\",\n \"plt.show()\\n\",\n \" \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now our generative model and environment are set up, and we can move on to Notebook 2, where we go through the core mechanics of how to perform inference and planning on this environment with this generative model.\"\n ]\n }\n ],\n \"metadata\": {\n \"interpreter\": {\n \"hash\": \"24ee14d9f6452059a99d44b6cbd71d1bb479b0539b0360a6a17428ecea9f0810\"\n },\n \"kernelspec\": {\n \"display_name\": \"Python 3.8.10 64-bit ('pymdp_env2': conda)\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.8.10\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/legacy/gridworld_tutorial_2.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Tutorial Notebook 2. Inference and Planning\\n\",\n \"\\n\",\n \"\\n\",\n \"In this notebook, we will continue on from the last notebook to build a fully fledged active inference agent capable of performing inference and planning using Active Inference in the simple grid-world environment. We will also begin to use some aspects of `pymdp`, although this will mostly be helpful functions for building and sampling from discrete distributions while we will implement the core functionality of the agent ourselves.\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"First, we simply start out by defining our generative model as we did last time.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Add `pymdp` module\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# This is needed (on my machine at least) due to weird python import issues\\n\",\n \"import os\\n\",\n \"import sys\\n\",\n \"from pathlib import Path\\n\",\n \"\\n\",\n \"path = Path(os.getcwd())\\n\",\n \"print(path)\\n\",\n \"module_path = str(path.parent) + '/'\\n\",\n \"sys.path.append(module_path)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Imports\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import numpy as np\\n\",\n \"import seaborn as sns\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"from copy import deepcopy\\n\",\n \"\\n\",\n \"from pymdp import maths, utils\\n\",\n \"from pymdp.maths import spm_log_single as log_stable # @NOTE: we use the `spm_log_single` helper function from the `maths` sub-library of pymdp. This is a numerically stable version of np.log()\\n\",\n \"from pymdp import control\\n\",\n \"print(\\\"imports loaded\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Plotting\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"state_mapping = {0: (0,0), 1: (1,0), 2: (2,0), 3: (0,1), 4: (1,1), 5:(2,1), 6: (0,2), 7:(1,2), 8:(2,2)}\\n\",\n \"\\n\",\n \"A = np.eye(9)\\n\",\n \"def plot_beliefs(Qs, title=\\\"\\\"):\\n\",\n \" #values = Qs.values[:, 0]\\n\",\n \" plt.grid(zorder=0)\\n\",\n \" plt.bar(range(Qs.shape[0]), Qs, color='r', zorder=3)\\n\",\n \" plt.xticks(range(Qs.shape[0]))\\n\",\n \" plt.title(title)\\n\",\n \" plt.show()\\n\",\n \" \\n\",\n \"labels = [state_mapping[i] for i in range(A.shape[1])]\\n\",\n \"def plot_likelihood(A):\\n\",\n \" plt.figure(figsize = (6,6))\\n\",\n \" sns.heatmap(A, xticklabels = labels, yticklabels = labels, cbar = False)\\n\",\n \" plt.title(\\\"Likelihood distribution (A)\\\")\\n\",\n \" plt.show()\\n\",\n \" \\n\",\n \"def plot_empirical_prior(B):\\n\",\n \" fig, axes = plt.subplots(3,2, figsize=(8, 10))\\n\",\n \" actions = ['UP', 'RIGHT', 'DOWN', 'LEFT', 'STAY']\\n\",\n \" count = 0\\n\",\n \" for i in range(3):\\n\",\n \" for j in range(2):\\n\",\n \" if count >= 5:\\n\",\n \" break\\n\",\n \" \\n\",\n \" g = sns.heatmap(B[:,:,count], cmap=\\\"OrRd\\\", linewidth=2.5, cbar=False, ax=axes[i,j])\\n\",\n \"\\n\",\n \" g.set_title(actions[count])\\n\",\n \" count += 1\\n\",\n \" fig.delaxes(axes.flatten()[5])\\n\",\n \" plt.tight_layout()\\n\",\n \" plt.show()\\n\",\n \" \\n\",\n \"def plot_transition(B):\\n\",\n \" fig, axes = plt.subplots(2,3, figsize = (15,8))\\n\",\n \" a = list(actions.keys())\\n\",\n \" count = 0\\n\",\n \" for i in range(dim-1):\\n\",\n \" for j in range(dim):\\n\",\n \" if count >= 5:\\n\",\n \" break \\n\",\n \" g = sns.heatmap(B[:,:,count], cmap = \\\"OrRd\\\", linewidth = 2.5, cbar = False, ax = axes[i,j], xticklabels=labels, yticklabels=labels)\\n\",\n \" g.set_title(a[count])\\n\",\n \" count +=1 \\n\",\n \" fig.delaxes(axes.flatten()[5])\\n\",\n \" plt.tight_layout()\\n\",\n \" plt.show()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Generative model\\n\",\n \"\\n\",\n \"Here, we setup our generative model which is the same as in the last notebook. This is formed of a likelihood distribution $P(o_t|s_t)$, denoted `A`, and a empirical prior (transition) distribution $P(s_t|s_{t-1},a_{t-1})$, denoted `B`.\\n\",\n \"\\n\",\n \"Since this was covered in more detail in the previous tutorial, we quickly skip over the details here\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# A matrix\\n\",\n \"A = np.eye(9)\\n\",\n \"plot_likelihood(A)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# construct B matrix\\n\",\n \"\\n\",\n \"P = {}\\n\",\n \"dim = 3\\n\",\n \"actions = {'UP':0, 'RIGHT':1, 'DOWN':2, 'LEFT':3, 'STAY':4}\\n\",\n \"\\n\",\n \"for state_index, xy_coordinates in state_mapping.items():\\n\",\n \" P[state_index] = {a : [] for a in range(len(actions))}\\n\",\n \" x, y = xy_coordinates\\n\",\n \"\\n\",\n \" '''if your y-coordinate is all the way at the top (i.e. y == 0), you stay in the same place -- otherwise you move one upwards (achieved by subtracting 3 from your linear state index'''\\n\",\n \" P[state_index][actions['UP']] = state_index if y == 0 else state_index - dim \\n\",\n \"\\n\",\n \" '''f your x-coordinate is all the way to the right (i.e. x == 2), you stay in the same place -- otherwise you move one to the right (achieved by adding 1 to your linear state index)'''\\n\",\n \" P[state_index][actions[\\\"RIGHT\\\"]] = state_index if x == (dim -1) else state_index+1 \\n\",\n \"\\n\",\n \" '''if your y-coordinate is all the way at the bottom (i.e. y == 2), you stay in the same place -- otherwise you move one down (achieved by adding 3 to your linear state index)'''\\n\",\n \" P[state_index][actions['DOWN']] = state_index if y == (dim -1) else state_index + dim \\n\",\n \"\\n\",\n \" ''' if your x-coordinate is all the way at the left (i.e. x == 0), you stay at the same place -- otherwise, you move one to the left (achieved by subtracting 1 from your linear state index)'''\\n\",\n \" P[state_index][actions['LEFT']] = state_index if x == 0 else state_index -1 \\n\",\n \"\\n\",\n \" ''' Stay in the same place (self explanatory) '''\\n\",\n \" P[state_index][actions['STAY']] = state_index\\n\",\n \"\\n\",\n \"\\n\",\n \"num_states = 9\\n\",\n \"B = np.zeros([num_states, num_states, len(actions)])\\n\",\n \"for s in range(num_states):\\n\",\n \" for a in range(len(actions)):\\n\",\n \" ns = int(P[s][a])\\n\",\n \" B[ns, s, a] = 1\\n\",\n \"\\n\",\n \"plot_transition(B)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Create Environment Class\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"To make things simple we will parcel up the $A$ and $B$ matrices into a class which represents the environment. The environment has two functions `step` which when given an action will update the environment a single step and `reset` which resets the environment back to its initial condition. The API of our simple environment class is similar to the `Env` base class used by `pymdp`, although the `pymdp` version has many more features than we use here.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"class GridWorldEnv():\\n\",\n \" \\n\",\n \" def __init__(self,A,B):\\n\",\n \" self.A = deepcopy(A)\\n\",\n \" self.B = deepcopy(B)\\n\",\n \" print(\\\"B:\\\", B.shape)\\n\",\n \" self.state = np.zeros(9)\\n\",\n \" # start at state 3\\n\",\n \" self.state[2] = 1\\n\",\n \" \\n\",\n \" def step(self,a):\\n\",\n \" self.state = np.dot(self.B[:,:,a], self.state)\\n\",\n \" obs = utils.sample(np.dot(self.A, self.state))\\n\",\n \" return obs\\n\",\n \"\\n\",\n \" def reset(self):\\n\",\n \" self.state =np.zeros(9)\\n\",\n \" self.state[2] =1 \\n\",\n \" obs = utils.sample(np.dot(self.A, self.state))\\n\",\n \" return obs\\n\",\n \" \\n\",\n \"env = GridWorldEnv(A,B)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Inference\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now that we have the generative model setup, we turn to the behaviour of the active inference agent itself. To recap, we assume that this agent receives observations from the environment and can emit actions. Moreover, we assume that this agent has some kind of goal or preferences over the state of the environment it wants to create, and will choose actions in order to increase the probability of observing itself in its preferred state. For the time being, we will not deal with the problem of action selection but only with inference.\\n\",\n \"\\n\",\n \"The agent receives observations $o_t$ from the environment but does not naturally know the environments true state $x_t$. Thus, the agent must *infer* this state by computing the posterior distribution $p(x_t | o_t)$. It can do this by Bayesian inference using Bayes rule but, as we discussed last time, explicitly computing Bayes rule is often intractable because the marginal likelihood requires the averaging over an infinite number of hypotheses. We therefore need some other way to compute or approximate this posterior. Active inference assumes that this posterior can be approximated through a family of methods called *variational inference* which only approximate the posterior, but are fast and computationally efficient.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Variational Inference\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Variational inference is a set of inference methods which can rapidly and efficiently compute *approximate* posteriors for Bayesian inference problems. The key idea behind variational inference is that instead of trying to compute the true posterior $p(x_t | o_t)$ which may be extremely complex, is that we instead optimize an *approximate posterior*. Specifically, we will define another distribution $q(x_t ; \\\\phi)$ which has some parameters $\\\\phi$ which we then optimize so as to make $q(x_t ; \\\\phi)$ as close as possible to the true distribution. Typically, we choose this $q$ distribution to be some simple distribution which is easy to work with mathematically. If the process works, then we can get the $q$ distribution very close to the true posterior, and as such get a good estimate of the posterior without ever explicitly computing it using Bayes rule. \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Mathematically, we can do this by setting up an optimization problem. We have the true posterior $p(x_t | o_t)$, which is unknown, and we have our $q$ distribution which we do know. We then want to optimize the $q$ distribution to make it as *close as possible* to the true posterior $p(x_t | o_t)$. To do this, we first need a way to quantify *how close* two probability distributions are. The way we do this is by using a quantity known as the *Kullback-Leibler (KL) divergence*. This is a metric derived from information theory which lets us quantify the distance (in bits) of two distributions. The KL divergence between two distributions $q(x)$ and $p(x)$ is defined as,\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"KL[q(x) || p(x)] = \\\\sum_x q(x) (\\\\ln q(x) - \\\\ln p(x))\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"Mathematically it can be thought of as the average of the difference of the logarithms of the probabilities assigned by $q$ and $p$ to the states $x$. The KL divergence is smallest when $q(x) = p(x)$ when it is equal to 0, and can grow to be infinitely large which happens wherever $q(x)$ assigns a nonzero probability but $p(x)$ doesn't. In code, we can compute the KL divergence as:\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"def KL_divergence(q,p):\\n\",\n \" return np.sum(q * (log_stable(q) - log_stable(p)))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now that we know about the KL divergence, we can express our variational problem of making our approximate posterior $q(x_t ; \\\\varphi)$ as close as possible to the true posterior as simply minimizing the KL divergence between the two distributions. That is, we can define the optimal approximate distribution as,\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"q^*(x_t ; \\\\varphi) = \\\\operatorname{argmin}_{\\\\varphi} \\\\, KL[q(x_t ; \\\\varphi) || p(x_t | o_t)]\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"\\n\",\n \"And then simply try to optimize this objective so as to find the setting of the variational parameters $\\\\varphi$ that make $q(x_t ; \\\\varphi)$ as close to $p(x_t |o_t)$ as possible. The trouble with this is that our objective actually explicitly contains the true posterior in it and so, since we can't conpute the true posterior, we can't compute this objective either -- so we are stuck!\\n\",\n \"\\n\",\n \"Variational inference provides a clever way to get around this problem by instead minimizing an *upper bound* on this divergence called the *variational free energy*. Importantly this bound is computable so we can actually optimize it and moreover since it is an upper bound, if we minimize it, we can make $q$ as close as possible to the real bound, thus still managing to obtain a good approximate posterior distribution. Deriving the variational free energy is very simple, we first take our initial objective and apply Bayes rule to the true posterior, and then take out the marginal likelihood term separately\\n\",\n \"\\n\",\n \"\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \" KL[q(x_t ; \\\\varphi) || p(x_t | o_t)] &= KL[q(x_t ; \\\\varphi) || \\\\frac{p(o_t,x_t)}{p(o_t)}] \\\\\\\\\\n\",\n \" &= KL[q(x_t ; \\\\varphi) || p(o_t, x_t)] + \\\\sum_x q(x_t ; \\\\varphi) \\\\ln p(o_t) \\\\\\\\\\n\",\n \" &= KL[q(x_t ; \\\\varphi) || p(o_t, x_t)] + \\\\ln p(o_t) \\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"\\n\",\n \"\\n\",\n \"Where in the final line we have used the fact that the sum is over a different variable than the distribution, and the sum of a probability distribution is $1$ -- i.e $\\\\sum_x q(x_t ; \\\\varphi) \\\\ln p(o_t) = \\\\ln p(o_t) * \\\\sum_x q(x_t ; \\\\varphi)$ and $\\\\sum_x q(x_t ; \\\\varphi) = 1$. Specifically, since $ \\\\ln p(o_t)$ is the log of a probability distribution it is always negative, since the probability of a state is always between 0 and 1. This means that we know that this term we have devised $KL[q(x_t ; \\\\varphi) || p(o_t, x_t)]$ is always necessarily greater than our original divergence between the approximate posterior and the true posterior, so it is an *upper bound*. We call this term the *variational free energy* and denote it by $\\\\mathcal{F}$.\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"\\\\mathcal{F} = KL[q(x_t ; \\\\varphi) || p(o_t, x_t)]\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"\\n\",\n \"The free energy here is simply the divergence between the approximate posterior and the *generative model* of the agent. Since we know both the approximate posterior (as we defined it in the first place!) and the generative model, then both terms of this divergence are computable. We thus have our algorithm to approximate the posterior! Since the free energy is an upper bound, if we minimize the free energy, we also implicitly minimize the true divergence between the true and approximate posteriors, which will force the approximate posterior to be close to the true posterior and thus a good approximation! Moreover, since we can compute the free energy, we can actually perform this optimization! \\n\",\n \"\\n\",\n \"In many cases, we typically perform variational inference by taking the gradients of the free energy with respect to the variational parameteres $\\\\varphi$ and then doing gradient descent on the parameters $\\\\varphi$ that define $q(x_t ; \\\\varphi)$. However, when the distributions are discrete (i.e. Categorical distributions), the parameters of the approximate distribution are simply the probability values for each state (the elements of the vector $q(x)$. For some simple generative models (e.g. the grid-world described here), we can actually solve this optimization problem directly to obtain $q(x)$ in a single step, instead of as a gradient descent.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Directly solving variational inference in the case of a simple discrete model\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"To recap, remember that we have turned the problem of computing the posterior distribution $p(x_t | o_t)$ into that of minimizing the variational free energy: $\\\\mathcal{F} = KL[q(x_t) || p(o_t, x_t)]$ with respect to an approximate posterior distribution $q(x_t)$. From now on, we will leave out the variational parameters $\\\\varphi$ when referring to $q(x_t)$, since we are dealing with a single Categorical distribution $q(x_t)$ whose vector elements are identical to the variational parameters, i.e. $\\\\forall_{i} \\\\varphi_i = q(x_t = i)$.\\n\",\n \"\\n\",\n \"The optimal distribution is simply that particular $q^*(x_t)$ that minimizes the KL divergence. Now, remember from high-school calculus that we can explicitly compute the minimum of a function by taking its derivative and setting it to 0 (i.e. at the minimum the first derivative of the function is 0) (if you don't remember this from calculus, trust me on this). This means that to solve this problem all we need to do is take the derivative of the free energy and set it to 0 and rearrange. First, let's write out the free energy explicitly.\\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"\\\\mathcal{F} &= KL[q(x_t) || p(o_t, x_t)] \\\\\\\\\\n\",\n \"&= \\\\sum_x q(x_t)(\\\\ln q(x_t) - \\\\ln p(o_t,x_t))\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"If we then split the generative model up into a likelihood and a prior, we can write it as,\\n\",\n \"\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"\\\\mathcal{F} = \\\\sum_x q(x_t) \\\\big[ \\\\ln q(x_t) - \\\\ln p(o_t | x_t) - \\\\ln p(x_t) \\\\big]\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"Recall that we have explicitly defined the observation and transition likelihood distributions as the $\\\\textbf{A}$ and $\\\\textbf{B}$ matrices, which play the role of the likelihood and prior distributions, respectively. In particular, we can define the prior over the current timestep $p(x_t)$ to be the \\\"expected prior\\\", given the beliefs about the state at the last timesep $q(x_{t-1})$ the beliefs about the transition dynamics and the past action, i.e.:\\n\",\n \"\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"p(x_t) = \\\\mathcal{E}_{q(x_{t-1})}\\\\big[p(x_t | x_{t-1}, a_t) \\\\big]\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"\\n\",\n \"which can be expressed as a simple matrix vector product\\n\",\n \"\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"p(x_t) = \\\\textbf{B}_{a_t}q(x_{t-1})\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"\\n\",\n \"where $\\\\textbf{B}_{a_t}$ is the component of the $\\\\textbf{B}$ matrix that is conditioned on action $a_t$. In other words, for this simple Markovian model, we assume that \\\"yesterday's posterior is today's prior.\\\" For simplicity, we refer to this entire prior term as $\\\\textbf{B}$ below, i.e. we temporarily define $\\\\textbf{B} \\\\equiv \\\\textbf{B}_{a_t}q(x_{t-1})$.\\n\",\n \"\\n\",\n \"As mentioned above, the posterior beliefs $q(x_t)$ are a vector of probabilities (the variational parameters) which we denote $\\\\textbf{q} = [q_1, q_2, q_3 \\\\dots]$. With this all defined, we can write out the free energy as,\\n\",\n \"\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"\\\\mathcal{F} = \\\\sum_x \\\\textbf{q} * \\\\big[ \\\\ln \\\\textbf{q} - \\\\ln \\\\textbf{A} - \\\\ln \\\\textbf{B} \\\\big]\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"\\n\",\n \"\\n\",\n \"And for fun, we can explicitly compute it in code:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"def compute_free_energy(q,A, B):\\n\",\n \" return np.sum(q * (log_stable(q) - log_stable(A) - log_stable(B)))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Then, all we need to do is take the derivative of the free energy with respect to the approximate posterior distribution $\\\\textbf{q}$ as follows,\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"\\\\frac{\\\\partial \\\\mathcal{F}}{\\\\partial \\\\textbf{q}} = \\\\ln \\\\textbf{q} - \\\\ln \\\\textbf{A} - \\\\ln \\\\textbf{B} - \\\\textbf{1}\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"\\n\",\n \"Where $\\\\textbf{1}$ is just a vector of ones of equal length to $\\\\textbf{q}$ and comes from the $q \\\\frac{\\\\partial \\\\ln q}{\\\\partial q} = q * \\\\frac{1}{q} = 1$. Thus, if we set this derivative to 0 and rearrange, we can get,\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"0 &= \\\\ln \\\\textbf{q} - \\\\ln \\\\textbf{A} - \\\\ln \\\\textbf{B} - \\\\textbf{1} \\\\\\\\\\n\",\n \"&\\\\implies \\\\textbf{q}^* = \\\\sigma(\\\\ln \\\\textbf{A} + \\\\ln \\\\textbf{B})\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"\\n\",\n \"Where $\\\\sigma$ is a softmax function $\\\\sigma(x) = \\\\frac{e^x}{\\\\sum_x e^x}$ which ensures that the resulting probability distribution is normalized. This expression lets us compute the optimal approximate posterior instantly as a straightforward function of the current observation $o_t$, $\\\\textbf{A}$, and $\\\\textbf{B}$. We can thus quickly right the code for inference:\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"def softmax(x):\\n\",\n \" return np.exp(x) / np.sum(np.exp(x))\\n\",\n \"\\n\",\n \"def perform_inference(likelihood, prior):\\n\",\n \" return softmax(log_stable(likelihood) + log_stable(prior))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Note that the likelihood term is not the entire $\\\\textbf{A}$ matrix, but just the 'row' of the $\\\\textbf{A}$ matrix corresponding to the current observation, i.e. $P(o_t = o \\\\mid x_t)$. \\n\",\n \"\\n\",\n \"Inference for simple discrete state-space models like these is therefore very simple. All we need to do is have some initial set of beliefs $\\\\textbf{q}_0$ and then update them according to these rules for every observation we get, using the $\\\\textbf{A}$, $\\\\textbf{B}$, the past action $a_t$ and the past posterior $q(x_{t-1})$ to provide the likelihood and prior terms.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Planning through Active Inference\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"So far we just have an agent that can perform perform inference in the discrete state space, but inference by itself isn't really that useful. Instead what we really want to do is *planning*. That is, the agent needs to be able to figure out how to emit a series of actions which will take it to a certain goal state. A key part of Active Inference is that this process of planning, or more broadly action selection, can also be solved as a process of variational inference. This is why it is called *Active* Inference, after all. \\n\",\n \"\\n\",\n \"\\n\",\n \"\\n\",\n \"However, when starting to think about this, it is not immediately obvious how to turn planning into an inference problem. What are the hypotheses? What are the observations? To turn the problem of planning into an inference problem, we need to introduce two additional concepts. The first is the idea of a *preferred observations*. To make planning useful, the agent has to *want something*. This is different from just performing objective inference about the state of the world in which there is no goal except to infer correctly. In Active Inference, we define the preferred observations as a separate goal vector denoted $\\\\textbf{C}$. When performing planning we then modify the generative model of the agent so that it no longer reflects the true distribution of observations in the environment, but rather includes the goal vector, which is a *prior over observations*. We denote this new generative model $\\\\tilde{p}(o_t, x_t) = p(x_t | o_t)\\\\tilde{p}(o_t)$ where we use $\\\\tilde{p}$ to say that this distribution is not a true distribution describing the agent's model of the world, but is instead a *preference distribution*. Here, we set the preference distribution to be over the state of the environment $o_t$ such that $\\\\tilde{p}(o_t) = \\\\textbf{C}$.\\n\",\n \"\\n\",\n \"By changing the generative model in this way, we have effectively changed the inference problem from: *infer the most likely states and actions given the true generative model of the world* to *infer the most likely states and actions given a false model of the world, in which I achieve my goals*. Perhaps more intuitively, we can think of this inference problem as answering the question: *Given that I have achieved my goals, what actions must have I taken to get there?*.\\n\",\n \"\\n\",\n \"The second thing we need to do to perform planning is to also extend the inference problem to *actions in the future*, since these are the fundamental things that the agent controls which it can use to adjust the environment. We call a sequence of future actions from now (time $t$) until some set future time $T$ a *policy* and denote it $\\\\pi = [a_t, a_{t+1}, a_{t+2} \\\\dots a_T]$. The goal is then to infer the optimal policy $\\\\pi^*$ given the preferences $\\\\textbf{C}$. \\n\",\n \"\\n\",\n \"However here there is a problem. Typically we would perform variational inference to solve this inference problem, but the variational free energy is not defined over future trajectories of observations, which are not yet known. Instead, we define a new objective which can handle this -- the *Expected Free Energy (EFE)*, which is defined over policies and which we denote as $\\\\mathcal{G}(\\\\pi)$. We define the EFE for a particular timepoint $\\\\tau$ and policy $\\\\pi$ as:\\n\",\n \"\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"\\\\mathcal{G}(\\\\pi)_{\\\\tau} = \\\\sum_{o_{\\\\tau}, x_{\\\\tau}} q(x_{\\\\tau} | \\\\pi)q(o_{\\\\tau} | \\\\pi) \\\\big[ \\\\ln q(x_{\\\\tau} | \\\\pi) - \\\\ln \\\\tilde{p}(o_{\\\\tau}, x_{\\\\tau}) \\\\big]\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"\\n\",\n \"The expected free energy is defined for a single time-step of a trajectory *in the future*, i.e. prior to receiving any observations. The key difference between the standard variational free energy and the expected free energy is that the expected free energy also averages over the *expected observations* $q(o_{\\\\tau} | pi)$ and *expected states* $q(x_{\\\\tau} | \\\\pi)$, where the expectations are conditioned on some policy $\\\\pi$. This is necessary because with the expected free energy, we are evaluating possible future trajectories without a given observation, unlike the variational free energy where we can assume that we have already received the observation.\\n\",\n \"\\n\",\n \"To get an intuitive handle on what the expected free energy *means* we can decompose it into two more intuitive quantities.\\n\",\n \"\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"\\\\mathcal{G}(\\\\pi)_{\\\\tau}&= \\\\sum_{o_{\\\\tau}, x_{\\\\tau}} q(x_{\\\\tau} | \\\\pi)q(o_{\\\\tau} | \\\\pi) \\\\big[ \\\\ln q(x_{\\\\tau} | \\\\pi) - \\\\ln \\\\tilde{p}(o_{\\\\tau}, x_{\\\\tau}) \\\\big] \\\\\\\\\\n\",\n \"&= -\\\\underbrace{\\\\sum_{o_{\\\\tau}, x_{\\\\tau}} q(x_{\\\\tau} | \\\\pi)q(o_{\\\\tau} | \\\\pi) \\\\big[ \\\\ln p(o_{\\\\tau} | x_{\\\\tau}) \\\\big]}_{\\\\text{Uncertainty}} + \\\\underbrace{KL[q(x_{\\\\tau} | \\\\pi) || \\\\tilde{p}(x_{\\\\tau}) ]}_{\\\\text{Divergence}}\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"\\n\",\n \"The first term is called *expected uncertainty* or sometimes *novelty* and represents essentially the spread of the observations expected in the future. Since we are choosing actions that *minimize* the whole quantity, we want to take actions that *maximize* novelty. We can think of this as a bonus to aid exploration since active inference agents will preferentially pursue resolveable uncertainty. The second term is the *divergence* term which is the KL divergence between the states expected under a given policy (also known as the posterior predictive density $q(x_\\\\tau | \\\\pi)$) and the goal distribution of the generative model, $\\\\tilde{p}(x)$. This term scores how far away (in an informational sense) the agent expects it will be from the goal, if it were to pursue that policy. Since we are minimizing the expected free energy this term is positive and so is also minimized -- that is by minimizing the expected free energy, we are trying to choose trajectories which will bring the expected states in the future close to the desired states.\\n\",\n \"\\n\",\n \"Now that we have the expected free energy to score possible trajectories, we now need to infer the optimal policy. A simple approach (which can be derived explicitly although it is somewhat complex) is to say that the posterior probability of a policy is proportional to the (exponentiated) sum of the expected free energy accumulated along the trajectory through the environment created by that policy. While this sounds complex, mathematically we can express it very simply as,\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"q(\\\\pi) = \\\\sigma( \\\\sum_{\\\\tau}^T \\\\mathcal{G}(\\\\pi)_{\\\\tau})\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"\\n\",\n \"We can then choose which action we choose for the next timestep by computing the marginal probability of each action $P(a)$, given the posterior over actions $q(\\\\pi)$ and some mapping between policies and actions $P(a | \\\\pi)$:\\n\",\n \"\\n\",\n \"$$\\n\",\n \"\\\\begin{align}\\n\",\n \"P(a) = \\\\sum_{\\\\pi}P(a | \\\\pi)q(\\\\pi)\\n\",\n \"\\\\end{align}\\n\",\n \"$$\\n\",\n \"\\n\",\n \"We can sample from this distribution over actions to choose our action for the next timestep.\\n\",\n \"\\n\",\n \"In our simple grid world environment, policies are identical to actions since we are only planning ahead 1-step in the future, so $\\\\forall_{i} P(a = i | \\\\pi = i) = 1$, which implies $P(a) == q(\\\\pi)$.\\n\",\n \"\\n\",\n \"While all this may seem exceptionally long and complex, it results in an algorithm which is actually remarkably simple. The algorithm is:\\n\",\n \"\\n\",\n \"1.) There is an agent with a generative model of the environment ($\\\\textbf{A}$ and $\\\\textbf{B}$ matrices), some initial set of approximate posterior beliefs $q(x_t | o_t)$ and a desired state vector $\\\\textbf{C}$. \\n\",\n \"\\n\",\n \"2.) The agent receives an observation $o_t$ and computes its posterior beliefs as we did earlier by minimizing the free energy.\\n\",\n \"\\n\",\n \"3.) The agent now needs to choose what action to make to achieve its goals. It does this by:\\n\",\n \"\\n\",\n \" 3.1.) First creating a set of potential policies to evaluate.\\n\",\n \" \\n\",\n \" 3.2.) For each policy in this set, use the generative model to simulate the agent's trajectory in the environment *as if* it had emitted the actions prescribed by the policy\\n\",\n \" \\n\",\n \" 3.3.) For each future timestep of each future trajectory, compute the expected free energy of that time-step\\n\",\n \" \\n\",\n \" 3.4.) Sum the expected free energies for each timestep of each trajectory to get a total expected free energy for each possible policy.\\n\",\n \" \\n\",\n \" 3.5.) Use these total expected free energies to compute the posterior distribution $q(\\\\pi)$ as done above.\\n\",\n \"\\n\",\n \" 3.6 ) Compute the marginal probability of each action, expected under the policies that include them, and then sample from this \\\"action marginal\\\" to generate an action at the current timestep.\\n\",\n \" \\n\",\n \"4.) Execute the sampled action to 'step forward' the environmental dynamics and get a new observation. Go back to step 1.\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"And that's it! We're done. We have the full algorithm to create an active inference agent. Now all we do is show how to translate this algorithm into code for our specific case.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Beliefs\\n\",\n \"\\n\",\n \"First we need to setup an initial belief distribution which we will then update according to the observations we will receive.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# setup initial prior beliefs -- uncertain -- completely unknown which state it is in\\n\",\n \"Qs = np.ones(9) * 1/9\\n\",\n \"plot_beliefs(Qs)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Preferences\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we have to encode the agent's preferences, so that it can learn to go to its reward state. In the current context, the agent wants (i.e. expects) to be in the reward location 7.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# C matrix -- desires\\n\",\n \"\\n\",\n \"REWARD_LOCATION = 7\\n\",\n \"reward_state = state_mapping[REWARD_LOCATION]\\n\",\n \"print(reward_state)\\n\",\n \"\\n\",\n \"C = np.zeros(num_states)\\n\",\n \"C[REWARD_LOCATION] = 1. \\n\",\n \"print(C)\\n\",\n \"plot_beliefs(C)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The C matrix is a 1x9 matrix, where each value represents the preference to occupy a given state. We will create a one-hot C matrix, so that the agent only has a preference to be in state 7. \"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Implementing the Active Inference Agent\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Evaluate policy \\n\",\n \"\\n\",\n \"This helper function we evaluate the negative expected free energy for a given policy $-\\\\mathcal{G}(\\\\pi)$. To do this we need to calculate the cumulative expected free energy for that policy. All that entails is looping through the timesteps of the policy, simulate what the environment would do, using our generative model, evolving posterior beliefs and the actions entailed by the policy, and then compute the expected free energy of our (policy-dependent) expectations about the hidden states and observations.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"def evaluate_policy(policy, Qs, A, B, C):\\n\",\n \" # initialize expected free energy at 0\\n\",\n \" G = 0\\n\",\n \"\\n\",\n \" # loop over policy\\n\",\n \" for t in range(len(policy)):\\n\",\n \"\\n\",\n \" # get action entailed by the policy at timestep `t`\\n\",\n \" u = int(policy[t])\\n\",\n \"\\n\",\n \" # work out expected state, given the action\\n\",\n \" Qs_pi = B[:,:,u].dot(Qs)\\n\",\n \"\\n\",\n \" # work out expected observations, given the action\\n\",\n \" Qo_pi = A.dot(Qs_pi)\\n\",\n \"\\n\",\n \" # get entropy\\n\",\n \" H = - (A * log_stable(A)).sum(axis = 0)\\n\",\n \"\\n\",\n \" # get predicted divergence\\n\",\n \" # divergence = np.sum(Qo_pi * (log_stable(Qo_pi) - log_stable(C)), axis=0)\\n\",\n \" divergence = KL_divergence(Qo_pi, C)\\n\",\n \" \\n\",\n \" # compute the expected uncertainty or ambiguity \\n\",\n \" uncertainty = H.dot(Qs_pi)\\n\",\n \"\\n\",\n \" # increment the expected free energy counter for the policy, using the expected free energy at this timestep\\n\",\n \" G += (divergence + uncertainty)\\n\",\n \"\\n\",\n \" return -G\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Infer action\\n\",\n \"\\n\",\n \"This helper function will infer the most likely action. Specifically, it computes steps 3.1 to 3.5 in the active inference algorithm. First, it constructs all possible policies for a given policy length and set of actions. Then it loops through every possible policy and computes the expected free energy of that policy using our previous function, and then computing the policy distribution $q(\\\\pi)$ using the softmax over the expected free energies.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"def infer_action(Qs, A, B, C, n_actions, policies):\\n\",\n \" \\n\",\n \" # initialize the negative expected free energy\\n\",\n \" neg_G = np.zeros(len(policies))\\n\",\n \"\\n\",\n \" # loop over every possible policy and compute the EFE of each policy\\n\",\n \" for i, policy in enumerate(policies):\\n\",\n \" neg_G[i] = evaluate_policy(policy, Qs, A, B, C)\\n\",\n \"\\n\",\n \" # get distribution over policies\\n\",\n \" Q_pi = maths.softmax(neg_G)\\n\",\n \"\\n\",\n \" # initialize probabilites of control states (convert from policies to actions)\\n\",\n \" Qu = np.zeros(n_actions)\\n\",\n \"\\n\",\n \" # sum probabilites of control states or actions \\n\",\n \" for i, policy in enumerate(policies):\\n\",\n \" # control state specified by policy\\n\",\n \" u = int(policy[0])\\n\",\n \" # add probability of policy\\n\",\n \" Qu[u] += Q_pi[i]\\n\",\n \"\\n\",\n \" # normalize action marginal\\n\",\n \" utils.norm_dist(Qu)\\n\",\n \"\\n\",\n \" # sample control from action marginal\\n\",\n \" u = utils.sample(Qu)\\n\",\n \"\\n\",\n \" return u\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Main loop\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Here we simply implement the main loop of the active inference agent interacting with the environment. Specifically, this essentially implements steps 1-5 of the MDP \\\"program\\\" we discussed in notebook 1. Specifically, for each timestep, the agent infers an action, it emits that action to the environment, the environment is updated and returns an observation to the agent. The agent then infers the new state of the environment given that observation.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"# number of time steps\\n\",\n \"T = 10\\n\",\n \"\\n\",\n \"#n_actions = env.n_control\\n\",\n \"n_actions = 5\\n\",\n \"\\n\",\n \"# length of policies we consider\\n\",\n \"policy_len = 4\\n\",\n \"\\n\",\n \"# this function generates all possible combinations of policies\\n\",\n \"policies = control.construct_policies([B.shape[0]], [n_actions], policy_len)\\n\",\n \"\\n\",\n \"# reset environment\\n\",\n \"o = env.reset()\\n\",\n \"\\n\",\n \"# loop over time\\n\",\n \"for t in range(T):\\n\",\n \"\\n\",\n \" # infer which action to take\\n\",\n \" a = infer_action(Qs, A, B, C, n_actions, policies)\\n\",\n \" \\n\",\n \" # perform action in the environment and update the environment\\n\",\n \" o = env.step(int(a))\\n\",\n \" \\n\",\n \" # infer new hidden state (this is the same equation as above but with PyMDP functions)\\n\",\n \" likelihood = A[o,:]\\n\",\n \" prior = B[:,:,int(a)].dot(Qs)\\n\",\n \"\\n\",\n \" Qs = maths.softmax(log_stable(likelihood) + log_stable(prior))\\n\",\n \" \\n\",\n \" print(Qs.round(3))\\n\",\n \" plot_beliefs(Qs, \\\"Beliefs (Qs) at time {}\\\".format(t))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"And that's it! In the last two notebooks, we have implemented a basic active inference agent which can successfully navigate around a 3x3 gridworld using active inference. Moreover, we have implemented this all from scratch using mostly basic numpy functions and not using much of the functionality of `pymdp`. \\n\",\n \"\\n\",\n \"Hopefully after going through this you now understand roughly what active inference is and how it works, as well as ideally have some intuitions about how inference as well as policy selection work \\\"under the hood\\\", as well as learnt a lot about Bayesian and specifically variational inference. In the next notebook, we will focus more on the `pymdp` library itself and demonstrate how `pymdp` provides a useful set of abstractions that allows us to easily create active inference agents, as well as perform inference and policy selection in considerably more complex environments than the one described here.\\n\",\n \"\\n\",\n \"We will discuss the high level structure of the library and show how its possible to replicate these notebooks in a much smaller amount of code using the `pymdp` abstractions.\"\n ]\n }\n ],\n \"metadata\": {\n \"interpreter\": {\n \"hash\": \"24ee14d9f6452059a99d44b6cbd71d1bb479b0539b0360a6a17428ecea9f0810\"\n },\n \"kernelspec\": {\n \"display_name\": \"Python 3.8.10 64-bit ('pymdp_env2': conda)\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.8.10\"\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/legacy/tmaze_demo.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Active Inference Demo: T-Maze Environment\\n\",\n \"This demo notebook provides a full walk-through of active inference using the `Agent()` class of `pymdp`. The canonical example used here is the 'T-maze' task, often used in the active inference literature in discussions of epistemic behavior (see, for example, [\\\"Active Inference and Epistemic Value\\\"](https://pubmed.ncbi.nlm.nih.gov/25689102/))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Imports\\n\",\n \"\\n\",\n \"First, import `pymdp` and the modules we'll need.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import os\\n\",\n \"import sys\\n\",\n \"import pathlib\\n\",\n \"import copy\\n\",\n \"\\n\",\n \"path = pathlib.Path(os.getcwd())\\n\",\n \"module_path = str(path.parent) + '/'\\n\",\n \"sys.path.append(module_path)\\n\",\n \"\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp.utils import plot_beliefs, plot_likelihood\\n\",\n \"from pymdp import utils\\n\",\n \"from pymdp.envs import TMazeEnv\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Environment\\n\",\n \"\\n\",\n \"Here we consider an agent navigating a three-armed 'T-maze,' with the agent starting in a central location of the maze. The bottom arm of the maze contains an informative cue, which signals in which of the two top arms ('Left' or 'Right', the ends of the 'T') a reward is likely to be found. \\n\",\n \"\\n\",\n \"At each timestep, the environment is described by the joint occurrence of two qualitatively-different 'kinds' of states (hereafter referred to as _hidden state factors_). These hidden state factors are independent of one another.\\n\",\n \"\\n\",\n \"We represent the first hidden state factor (`Location`) as a $ 1 \\\\ x \\\\ 4 $ vector that encodes the current position of the agent, and can take the following values: {`CENTER`, `RIGHT ARM`, `LEFT ARM`, or `CUE LOCATION`}. For example, if the agent is in the `CUE LOCATION`, the current state of this factor would be $s_1 = [0 \\\\ 0 \\\\ 0 \\\\ 1]$.\\n\",\n \"\\n\",\n \"We represent the second hidden state factor (`Reward Condition`) as a $ 1 \\\\ x \\\\ 2 $ vector that encodes the reward condition of the trial: {`Reward on Right`, or `Reward on Left`}. A trial where the condition is reward is `Reward on Left` is thus encoded as the state $s_2 = [0 \\\\ 1]$.\\n\",\n \"\\n\",\n \"The environment is designed such that when the agent is located in the `RIGHT ARM` and the reward condition is `Reward on Right`, the agent has a specified probability $a$ (where $a > 0.5$) of receiving a reward, and a low probability $b = 1 - a$ of receiving a 'loss' (we can think of this as an aversive or unpreferred stimulus). If the agent is in the `LEFT ARM` for the same reward condition, the reward probabilities are swapped, and the agent experiences loss with probability $a$, and reward with lower probability $b = 1 - a$. These reward contingencies are intuitively swapped for the `Reward on Left` condition. \\n\",\n \"\\n\",\n \"For instance, we can encode the state of the environment at the first time step in a `Reward on Right` trial with the following pair of hidden state vectors: $s_1 = [1 \\\\ 0 \\\\ 0 \\\\ 0]$, $s_2 = [1 \\\\ 0]$, where we assume the agent starts sitting in the central location. If the agent moved to the right arm, then the corresponding hidden state vectors would now be $s_1 = [0 \\\\ 1 \\\\ 0 \\\\ 0]$, $s_2 = [1 \\\\ 0]$. This highlights the _independence_ of the two hidden state factors -- the location of the agent ($s_1$) can change without affecting the identity of the reward condition ($s_2$).\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### 1. Initialize environment\\n\",\n \"Now we can initialize the T-maze environment using the built-in `TMazeEnv` class from the `pymdp.envs` module.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Choose reward probabilities $a$ and $b$, where $a$ and $b$ are the probabilities of reward / loss in the 'correct' arm, and the probabilities of loss / reward in the 'incorrect' arm. Which arm counts as 'correct' vs. 'incorrect' depends on the reward condition (state of the 2nd hidden state factor).\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"reward_probabilities = [0.98, 0.02] # probabilities used in the original SPM T-maze demo\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Initialize an instance of the T-maze environment\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"env = TMazeEnv(reward_probs = reward_probabilities)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Structure of the state --> outcome mapping\\n\",\n \"We can 'peer into' the rules encoded by the environment (also known as the _generative process_ ) by looking at the probability distributions that map from hidden states to observations. Following the SPM version of active inference, we refer to this collection of probabilistic relationships as the `A` array. In the case of the true rules of the environment, we refer to this array as `A_gp` (where the suffix `_gp` denotes the generative process). \\n\",\n \"\\n\",\n \"It is worth outlining what constitute the agent's observations in this task. In this T-maze demo, we have three sensory channels or observation modalities: `Location`, `Reward`, and `Cue`. \\n\",\n \"\\n\",\n \">The `Location` observation values are identical to the `Location` hidden state values. In this case, the agent always unambiguously observes its own state - if the agent is in `RIGHT ARM`, it receives a `RIGHT ARM` observation in the corresponding modality. This might be analogized to a 'proprioceptive' sense of one's own place.\\n\",\n \"\\n\",\n \">The `Reward` observation modality assumes the values `No Reward`, `Reward` or `Loss`. The `No Reward` (index 0) observation is observed whenever the agent isn't occupying one of the two T-maze arms (the right or left arms). The `Reward` (index 1) and `Loss` (index 2) observations are observed in the right and left arms of the T-maze, with associated probabilities that depend on the reward condition (i.e. on the value of the second hidden state factor).\\n\",\n \"\\n\",\n \"> The `Cue` observation modality assumes the values `Cue Right`, `Cue Left`. This observation unambiguously signals the reward condition of the trial, and therefore in which arm the `Reward` observation is more probable. When the agent occupies the other arms, the `Cue` observation will be `Cue Right` or `Cue Left` with equal probability. However (as we'll see below when we intialise the agent), the agent's beliefs about the likelihood mapping render these observations uninformative and irrelevant to state inference.\\n\",\n \"\\n\",\n \"In `pymdp`, we store the set of probability distributions encoding the conditional probabilities of observations, under different configurations of hidden states, as a set of matrices referred to as the likelihood mapping or `A` array (this is a convention borrowed from SPM). The likelihood mapping _for a single modality_ is stored as a single matrix `A[i]` with the larger likelihood array, where `i` is the index of the corresponding modality. Each modality-specific A matrix has `n_observations[i]` rows, and as many lagging dimensions (e.g. columns, 'slices' and higher-order dimensions) as there are hidden state factors. `n_observations[i]` tells you the number of observation values for observation modality `i`, and is usually stored as a property of the `Env` class (e.g. `env.n_observations`).\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"A_gp = env.get_likelihood_dist()\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A_gp[1][:,:,0],'Reward Right')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {\n \"scrolled\": false\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A_gp[1][:,:,1],'Reward Left')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A_gp[2][:,3,:],'Cue Mapping')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Transition Dynamics\\n\",\n \"\\n\",\n \"We represent the dynamics of the environment (e.g. changes in the location of the agent and changes to the reward condition) as conditional probability distributions that encode the likelihood of transitions between the states of a given hidden state factor. These distributions are collected into the so-called `B` array, also known as _transition likelihoods_ or _transition distribution_ . As with the `A` array, we denote the true probabilities describing the environmental dynamics as `B_gp`. Each sub-matrix `B_gp[f]` of the larger array encodes the transition probabilities between state-values of a given hidden state factor with index `f`. These matrices encode dynamics as Markovian transition probabilities, such that the entry $i,j$ of a given matrix encodes the probability of transition to state $i$ at time $t+1$, given state $j$ at $t$. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"B_gp = env.get_transition_dist()\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"For example, we can inspect the 'dynamics' of the `Reward Condition` factor by indexing into the appropriate sub-matrix of `B_gp`\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(B_gp[1][:,:,0],'Reward Condition Transitions')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The above transition array is the 'trivial' identity matrix, meaning that the reward condition doesn't change over time (it's mapped from whatever it's current value is to the same value at the next timestep).\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### (Controllable-) Transition Dynamics\\n\",\n \"\\n\",\n \"Importantly, some hidden state factors are _controllable_ by the agent, meaning that the probability of being in state $i$ at $t+1$ isn't merely a function of the state at $t$, but also of actions (or from the agent's perspective, _control states_ ). So now each transition likelihood encodes conditional probability distributions over states at $t+1$, where the conditioning variables are both the states at $t-1$ _and_ the actions at $t-1$. This extra conditioning on actions is encoded via an optional third dimension to each factor-specific `B` matrix.\\n\",\n \"\\n\",\n \"For example, in our case the first hidden state factor (`Location`) is under the control of the agent, which means the corresponding transition likelihoods `B[0]` are index-able by both previous state and action.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {\n \"scrolled\": false\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(B_gp[0][:,:,0],'Transition likelihood for \\\"Move to Center\\\"')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(B_gp[0][:,:,1],'Transition likelihood for \\\"Move to Right Arm\\\"')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(B_gp[0][:,:,2],'Transition likelihood for \\\"Move to Left Arm\\\"')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(B_gp[0][:,:,3],'Transition likelihood for \\\"Move to Cue Location\\\"')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## The generative model\\n\",\n \"Now we can move onto setting up the generative model of the agent - namely, the agent's beliefs about how hidden states give rise to observations, and how hidden states transition among eachother.\\n\",\n \"\\n\",\n \"In almost all MDPs, the critical building blocks of this generative model are the agent's representation of the observation likelihood, which we'll refer to as `A_gm`, and its representation of the transition likelihood, or `B_gm`. \\n\",\n \"\\n\",\n \"Here, we assume the agent has a veridical representation of the rules of the T-maze (namely, how hidden states cause observations) as well as its ability to control its own movements with certain consequences (i.e. 'noiseless' transitions).\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 14,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"A_gm = copy.deepcopy(A_gp) # make a copy of the true observation likelihood to initialize the observation model\\n\",\n \"B_gm = copy.deepcopy(B_gp) # make a copy of the true transition likelihood to initialize the transition model\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Note !\\n\",\n \"It is not necessary, or even in many cases _important_ , that the generative model is a veridical representation of the generative process. This distinction between generative model (essentially, beliefs entertained by the agent and its interaction with the world) and the generative process (the actual dynamical system 'out there' generating sensations) is of crucial importance to the active inference formalism and (in our experience) often overlooked in code.\\n\",\n \"\\n\",\n \"It is for notational and computational convenience that we encode the generative process using `A` and `B` matrices. By doing so, it simply puts the rules of the environment in a data structure that can easily be converted into the Markovian-style conditional distributions useful for encoding the agent's generative model.\\n\",\n \"\\n\",\n \"Strictly speaking, however, all the generative process needs to do is generate observations and be 'perturbable' by actions. The way in which it does so can be arbitrarily complex, non-linear, and unaccessible by the agent.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Introducing the `Agent()` class\\n\",\n \"\\n\",\n \"In `pymdp`, we have abstracted much of the computations required for active inference into the `Agent()` class, a flexible object that can be used to store necessary aspects of the generative model, the agent's instantaneous observations and actions, and perform action / perception using functions like `Agent.infer_states` and `Agent.infer_policies`. \\n\",\n \"\\n\",\n \"An instance of `Agent` is straightforwardly initialized with a call to `Agent()` with a list of optional arguments.\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"In our call to `Agent()`, we need to constrain the default behavior with some of our T-Maze-specific needs. For example, we want to make sure that the agent's beliefs about transitions are constrained by the fact that it can only control the `Location` factor - _not_ the `Reward Condition` (which we assumed stationary across an epoch of time). Therefore we specify this using a list of indices that will be passed as the `control_fac_idx` argument of the `Agent()` constructor. \\n\",\n \"\\n\",\n \"Each element in the list specifies a hidden state factor (in terms of its index) that is controllable by the agent. Hidden state factors whose indices are _not_ in this list are assumed to be uncontrollable.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 15,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"controllable_indices = [0] # this is a list of the indices of the hidden state factors that are controllable\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can construct our agent...\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 16,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"agent = Agent(A=A_gm, B=B_gm, control_fac_idx=controllable_indices)\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can inspect properties (and change) of the agent as we see fit. Let's look at the initial beliefs the agent has about its starting location and reward condition, encoded in the prior over hidden states $P(s)$, known in SPM-lingo as the `D` array.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 17,\n \"metadata\": {\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_beliefs(agent.D[0],\\\"Beliefs about initial location\\\")\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 18,\n \"metadata\": {\n \"scrolled\": false\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_beliefs(agent.D[1],\\\"Beliefs about reward condition\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Let's make it so that agent starts with precise and accurate prior beliefs about its starting location.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 19,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"agent.D[0] = utils.onehot(0, agent.num_states[0])\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"And now confirm that our agent knows (i.e. has accurate beliefs about) its initial state by visualizing its priors again.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 20,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": \"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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_beliefs(agent.D[0],\\\"Beliefs about initial location\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Another thing we want to do in this case is make sure the agent has a 'sense' of reward / loss and thus a motivation to be in the 'correct' arm (the arm that maximizes the probability of getting the reward outcome).\\n\",\n \"\\n\",\n \"We can do this by changing the prior beliefs about observations, the `C` array (also known as the _prior preferences_ ). This is represented as a collection of distributions over observations for each modality. It is initialized by default to be all 0s. This means agent has no preference for particular outcomes. Since the second modality (index `1` of the `C` array) is the `Reward` modality, with the index of the `Reward` outcome being `1`, and that of the `Loss` outcome being `2`, we populate the corresponding entries with values whose relative magnitudes encode the preference for one outcome over another (technically, this is encoded directly in terms of relative log-probabilities). \\n\",\n \"\\n\",\n \"Our ability to make the agent's prior beliefs that it tends to observe the outcome with index `1` in the `Reward` modality, more often than the outcome with index `2`, is what makes this modality a Reward modality in the first place -- otherwise, it would just be an arbitrary observation with no extrinsic value _per se_. \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 21,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"agent.C[1][1] = 3.0\\n\",\n \"agent.C[1][2] = -3.0\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 22,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_beliefs(agent.C[1],\\\"Prior beliefs about observations\\\")\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"## Active Inference\\n\",\n \"Now we can start off the T-maze with an initial observation and run active inference via a loop over a desired time interval.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 23,\n \"metadata\": {\n \"scrolled\": false\n },\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \" === Starting experiment === \\n\",\n \" Reward condition: Left, Observation: [CENTER, No reward, Cue Left]\\n\",\n \"[Step 0] Action: [Move to CUE LOCATION]\\n\",\n \"[Step 0] Observation: [CUE LOCATION, No reward, Cue Left]\\n\",\n \"[Step 1] Action: [Move to LEFT ARM]\\n\",\n \"[Step 1] Observation: [LEFT ARM, Reward!, Cue Left]\\n\",\n \"[Step 2] Action: [Move to LEFT ARM]\\n\",\n \"[Step 2] Observation: [LEFT ARM, Reward!, Cue Right]\\n\",\n \"[Step 3] Action: [Move to LEFT ARM]\\n\",\n \"[Step 3] Observation: [LEFT ARM, Reward!, Cue Right]\\n\",\n \"[Step 4] Action: [Move to LEFT ARM]\\n\",\n \"[Step 4] Observation: [LEFT ARM, Reward!, Cue Right]\\n\"\n ]\n }\n ],\n \"source\": [\n \"T = 5 # number of timesteps\\n\",\n \"\\n\",\n \"obs = env.reset() # reset the environment and get an initial observation\\n\",\n \"\\n\",\n \"# these are useful for displaying read-outs during the loop over time\\n\",\n \"reward_conditions = [\\\"Right\\\", \\\"Left\\\"]\\n\",\n \"location_observations = ['CENTER','RIGHT ARM','LEFT ARM','CUE LOCATION']\\n\",\n \"reward_observations = ['No reward','Reward!','Loss!']\\n\",\n \"cue_observations = ['Cue Right','Cue Left']\\n\",\n \"msg = \\\"\\\"\\\" === Starting experiment === \\\\n Reward condition: {}, Observation: [{}, {}, {}]\\\"\\\"\\\"\\n\",\n \"print(msg.format(reward_conditions[env.reward_condition], location_observations[obs[0]], reward_observations[obs[1]], cue_observations[obs[2]]))\\n\",\n \"\\n\",\n \"for t in range(T):\\n\",\n \" qx = agent.infer_states(obs)\\n\",\n \"\\n\",\n \" q_pi, efe = agent.infer_policies()\\n\",\n \"\\n\",\n \" action = agent.sample_action()\\n\",\n \"\\n\",\n \" msg = \\\"\\\"\\\"[Step {}] Action: [Move to {}]\\\"\\\"\\\"\\n\",\n \" print(msg.format(t, location_observations[int(action[0])]))\\n\",\n \"\\n\",\n \" obs = env.step(action)\\n\",\n \"\\n\",\n \" msg = \\\"\\\"\\\"[Step {}] Observation: [{}, {}, {}]\\\"\\\"\\\"\\n\",\n \" print(msg.format(t, location_observations[obs[0]], reward_observations[obs[1]], cue_observations[obs[2]]))\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": []\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The agent begins by moving to the `CUE LOCATION` to resolve its uncertainty about the reward condition - this is because it knows it will get an informative cue in this location, which will signal the true reward condition unambiguously. At the beginning of the next timestep, the agent then uses this observaiton to update its posterior beliefs about states `qx[1]` to reflect the true reward condition. Having resolved its uncertainty about the reward condition, the agent then moves to `RIGHT ARM` to maximize utility and continues to do so, given its (correct) beliefs about the reward condition and the mapping between hidden states and reward observations. \\n\",\n \"\\n\",\n \"Notice, perhaps confusingly, that the agent continues to receive observations in the 3rd modality (i.e. samples from `A_gp[2]`). These are observations of the form `Cue Right` or `Cue Left`. However, these 'cue' observations are random and totally umambiguous unless the agent is in the `CUE LOCATION` - this is reflected by totally entropic distributions in the corresponding columns of `A_gp[2]` (and the agents beliefs about this ambiguity, reflected in `A_gm[2]`. See below.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 24,\n \"metadata\": {\n \"scrolled\": false\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A_gp[2][:,:,0],'Cue Observations when condition is Reward on Right, for Different Locations')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 25,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A_gp[2][:,:,1],'Cue Observations when condition is Reward on Left, for Different Locations')\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"The final column on the right side of these matrices represents the distribution over cue observations, conditioned on the agent being in `CUE LOCATION` and the appropriate Reward Condition. This demonstrates that cue observations are uninformative / lacking epistemic value for the agent, _unless_ they are in `CUE LOCATION.`\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"Now we can inspect the agent's final beliefs about the reward condition characterizing the 'trial,' having undergone 10 timesteps of active inference.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 26,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_beliefs(qx[1],\\\"Final posterior beliefs about reward condition\\\")\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3.8.8 ('base')\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.8.8\"\n },\n \"vscode\": {\n \"interpreter\": {\n \"hash\": \"70b7ceca5df5387258d861d4588082cea9500e731be001548c95afd8cd8c3af8\"\n }\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/legacy/tmaze_learning_demo.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Demo: T-Maze Environment + Learning\\n\",\n \"This notebook gives a step-by-step demonstration of active inference and learning using the `Agent()` class of `pymdp` and the `TMazeEnv` environment.\\n\",\n \"\\n\",\n \"For a thorough introduction to the basic `TMazeEnv` used here and active inference _without learning_ in that environment, please see the main `tmaze_demo.ipynb` notebook.\\n\",\n \"\\n\",\n \"In this particular case, we assume that the contingencies describing the 'rules' of the T-Maze are unknown to the agent, and must be learned. This demo therefore requires understanding the distinction between the agent's _generative model_ and the _generative process_ (the actual rules governing world dynamics).\\n\",\n \"\\n\",\n \"'Learning' under active inference corresponds to updating posterior beliefs about the sufficient statistics of distributions that parameterize the so-called 'structure' of the generative model. In the case of the Categorical distributions used to represent beliefs about states and outcomes in the discrete space-and-time MDPs used in `pymdp`, these structural parameters correspond to prior beliefs about the sensory and transition likelihoods and priors (the `A`, `B`, `C`, and `D` arrays) of the generative model. \\n\",\n \"\\n\",\n \"In the following exercise, we consider the case when an active inference agent needs to learn how sensory cues (the equivalent of a 'conditioned stimulus' or CS in learning theory) indicate the probability of receiving a reward in the two arms of a T-Maze.\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Imports|\\n\",\n \"\\n\",\n \"First, import `pymdp` and the modules we'll need.\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import os\\n\",\n \"import sys\\n\",\n \"import pathlib\\n\",\n \"import numpy as np\\n\",\n \"import copy\\n\",\n \"\\n\",\n \"path = pathlib.Path(os.getcwd())\\n\",\n \"module_path = str(path.parent) + '/'\\n\",\n \"sys.path.append(module_path)\\n\",\n \"\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp.utils import plot_likelihood\\n\",\n \"from pymdp import utils\\n\",\n \"from pymdp.envs import TMazeEnvNullOutcome\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"reward_probabilities = [0.85, 0.15] # the 'true' reward probabilities \\n\",\n \"env = TMazeEnvNullOutcome(reward_probs = reward_probabilities)\\n\",\n \"A_gp = env.get_likelihood_dist()\\n\",\n \"B_gp = env.get_transition_dist()\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"pA = utils.dirichlet_like(A_gp, scale = 1e16)\\n\",\n \"\\n\",\n \"pA[1][1:,1:3,:] = 1.0\\n\",\n \"\\n\",\n \"A_gm = utils.norm_dist_obj_arr(pA) \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"metadata\": {\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A_gm[1][:,:,0],'Initial beliefs about reward mapping')\\n\",\n \"plot_likelihood(A_gp[1][:,:,0],'True reward mapping in RIGHT ARM (Condition 0)')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(A_gm[2][:,:,0],'Initial beliefs about cue mapping')\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"B_gm = copy.deepcopy(B_gp)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"controllable_indices = [0] # this is a list of the indices of the hidden state factors that are controllable\\n\",\n \"learnable_modalities = [1] # this is a list of the modalities that you want to be learn-able \"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"agent = Agent(A=A_gm,pA=pA,B=B_gm,\\n\",\n \" control_fac_idx=controllable_indices,\\n\",\n \" modalities_to_learn=learnable_modalities,\\n\",\n \" lr_pA = 0.25,\\n\",\n \" use_param_info_gain=True)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"agent.D[0] = utils.onehot(0, agent.num_states[0])\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"agent.C[1][1] = 2.0\\n\",\n \"agent.C[1][2] = -2.0\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \" === Starting experiment === \\n\",\n \" Reward condition: Left arm Better, Observation: [CENTER, No reward, Null]\\n\",\n \"[Step 0] Action: [Move to CUE LOCATION]\\n\",\n \"[Step 0] Observation: [CUE LOCATION, No reward, Cue Left]\\n\",\n \"[Step 1] Action: [Move to RIGHT ARM]\\n\",\n \"[Step 1] Observation: [RIGHT ARM, Loss!, Null]\\n\",\n \"[Step 2] Action: [Move to RIGHT ARM]\\n\",\n \"[Step 2] Observation: [RIGHT ARM, Loss!, Null]\\n\",\n \"[Step 3] Action: [Move to LEFT ARM]\\n\",\n \"[Step 3] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 4] Action: [Move to LEFT ARM]\\n\",\n \"[Step 4] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 5] Action: [Move to LEFT ARM]\\n\",\n \"[Step 5] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 6] Action: [Move to LEFT ARM]\\n\",\n \"[Step 6] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 7] Action: [Move to LEFT ARM]\\n\",\n \"[Step 7] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 8] Action: [Move to LEFT ARM]\\n\",\n \"[Step 8] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 9] Action: [Move to LEFT ARM]\\n\",\n \"[Step 9] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 10] Action: [Move to LEFT ARM]\\n\",\n \"[Step 10] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 11] Action: [Move to LEFT ARM]\\n\",\n \"[Step 11] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 12] Action: [Move to LEFT ARM]\\n\",\n \"[Step 12] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 13] Action: [Move to LEFT ARM]\\n\",\n \"[Step 13] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 14] Action: [Move to LEFT ARM]\\n\",\n \"[Step 14] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 15] Action: [Move to LEFT ARM]\\n\",\n \"[Step 15] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 16] Action: [Move to LEFT ARM]\\n\",\n \"[Step 16] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 17] Action: [Move to LEFT ARM]\\n\",\n \"[Step 17] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 18] Action: [Move to LEFT ARM]\\n\",\n \"[Step 18] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 19] Action: [Move to LEFT ARM]\\n\",\n \"[Step 19] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 20] Action: [Move to LEFT ARM]\\n\",\n \"[Step 20] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 21] Action: [Move to LEFT ARM]\\n\",\n \"[Step 21] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 22] Action: [Move to LEFT ARM]\\n\",\n \"[Step 22] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 23] Action: [Move to LEFT ARM]\\n\",\n \"[Step 23] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 24] Action: [Move to LEFT ARM]\\n\",\n \"[Step 24] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 25] Action: [Move to LEFT ARM]\\n\",\n \"[Step 25] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 26] Action: [Move to LEFT ARM]\\n\",\n \"[Step 26] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 27] Action: [Move to LEFT ARM]\\n\",\n \"[Step 27] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 28] Action: [Move to LEFT ARM]\\n\",\n \"[Step 28] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 29] Action: [Move to LEFT ARM]\\n\",\n \"[Step 29] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 30] Action: [Move to LEFT ARM]\\n\",\n \"[Step 30] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 31] Action: [Move to LEFT ARM]\\n\",\n \"[Step 31] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 32] Action: [Move to LEFT ARM]\\n\",\n \"[Step 32] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 33] Action: [Move to LEFT ARM]\\n\",\n \"[Step 33] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 34] Action: [Move to LEFT ARM]\\n\",\n \"[Step 34] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 35] Action: [Move to LEFT ARM]\\n\",\n \"[Step 35] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 36] Action: [Move to LEFT ARM]\\n\",\n \"[Step 36] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 37] Action: [Move to LEFT ARM]\\n\",\n \"[Step 37] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 38] Action: [Move to LEFT ARM]\\n\",\n \"[Step 38] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 39] Action: [Move to LEFT ARM]\\n\",\n \"[Step 39] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 40] Action: [Move to LEFT ARM]\\n\",\n \"[Step 40] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 41] Action: [Move to LEFT ARM]\\n\",\n \"[Step 41] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 42] Action: [Move to LEFT ARM]\\n\",\n \"[Step 42] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 43] Action: [Move to LEFT ARM]\\n\",\n \"[Step 43] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 44] Action: [Move to LEFT ARM]\\n\",\n \"[Step 44] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 45] Action: [Move to LEFT ARM]\\n\",\n \"[Step 45] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 46] Action: [Move to LEFT ARM]\\n\",\n \"[Step 46] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 47] Action: [Move to LEFT ARM]\\n\",\n \"[Step 47] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 48] Action: [Move to LEFT ARM]\\n\",\n \"[Step 48] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 49] Action: [Move to LEFT ARM]\\n\",\n \"[Step 49] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 50] Action: [Move to LEFT ARM]\\n\",\n \"[Step 50] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 51] Action: [Move to LEFT ARM]\\n\",\n \"[Step 51] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 52] Action: [Move to LEFT ARM]\\n\",\n \"[Step 52] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 53] Action: [Move to LEFT ARM]\\n\",\n \"[Step 53] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 54] Action: [Move to LEFT ARM]\\n\",\n \"[Step 54] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 55] Action: [Move to LEFT ARM]\\n\",\n \"[Step 55] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 56] Action: [Move to LEFT ARM]\\n\",\n \"[Step 56] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 57] Action: [Move to LEFT ARM]\\n\",\n \"[Step 57] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 58] Action: [Move to LEFT ARM]\\n\",\n \"[Step 58] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 59] Action: [Move to LEFT ARM]\\n\",\n \"[Step 59] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 60] Action: [Move to LEFT ARM]\\n\",\n \"[Step 60] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 61] Action: [Move to LEFT ARM]\\n\",\n \"[Step 61] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 62] Action: [Move to LEFT ARM]\\n\",\n \"[Step 62] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 63] Action: [Move to LEFT ARM]\\n\",\n \"[Step 63] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 64] Action: [Move to LEFT ARM]\\n\",\n \"[Step 64] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 65] Action: [Move to LEFT ARM]\\n\",\n \"[Step 65] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 66] Action: [Move to LEFT ARM]\\n\",\n \"[Step 66] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 67] Action: [Move to LEFT ARM]\\n\",\n \"[Step 67] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 68] Action: [Move to LEFT ARM]\\n\",\n \"[Step 68] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 69] Action: [Move to LEFT ARM]\\n\",\n \"[Step 69] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 70] Action: [Move to LEFT ARM]\\n\",\n \"[Step 70] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 71] Action: [Move to LEFT ARM]\\n\",\n \"[Step 71] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 72] Action: [Move to LEFT ARM]\\n\",\n \"[Step 72] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 73] Action: [Move to LEFT ARM]\\n\",\n \"[Step 73] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 74] Action: [Move to LEFT ARM]\\n\",\n \"[Step 74] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 75] Action: [Move to LEFT ARM]\\n\",\n \"[Step 75] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 76] Action: [Move to LEFT ARM]\\n\",\n \"[Step 76] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 77] Action: [Move to LEFT ARM]\\n\",\n \"[Step 77] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 78] Action: [Move to LEFT ARM]\\n\",\n \"[Step 78] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 79] Action: [Move to LEFT ARM]\\n\",\n \"[Step 79] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 80] Action: [Move to LEFT ARM]\\n\",\n \"[Step 80] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 81] Action: [Move to LEFT ARM]\\n\",\n \"[Step 81] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 82] Action: [Move to LEFT ARM]\\n\",\n \"[Step 82] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 83] Action: [Move to LEFT ARM]\\n\",\n \"[Step 83] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 84] Action: [Move to LEFT ARM]\\n\",\n \"[Step 84] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 85] Action: [Move to LEFT ARM]\\n\",\n \"[Step 85] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 86] Action: [Move to LEFT ARM]\\n\",\n \"[Step 86] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 87] Action: [Move to LEFT ARM]\\n\",\n \"[Step 87] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 88] Action: [Move to LEFT ARM]\\n\",\n \"[Step 88] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 89] Action: [Move to LEFT ARM]\\n\",\n \"[Step 89] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 90] Action: [Move to LEFT ARM]\\n\",\n \"[Step 90] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 91] Action: [Move to LEFT ARM]\\n\",\n \"[Step 91] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 92] Action: [Move to LEFT ARM]\\n\",\n \"[Step 92] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 93] Action: [Move to LEFT ARM]\\n\",\n \"[Step 93] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 94] Action: [Move to LEFT ARM]\\n\",\n \"[Step 94] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 95] Action: [Move to LEFT ARM]\\n\",\n \"[Step 95] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 96] Action: [Move to LEFT ARM]\\n\",\n \"[Step 96] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 97] Action: [Move to LEFT ARM]\\n\",\n \"[Step 97] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 98] Action: [Move to LEFT ARM]\\n\",\n \"[Step 98] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 99] Action: [Move to LEFT ARM]\\n\",\n \"[Step 99] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 100] Action: [Move to LEFT ARM]\\n\",\n \"[Step 100] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 101] Action: [Move to LEFT ARM]\\n\",\n \"[Step 101] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 102] Action: [Move to LEFT ARM]\\n\",\n \"[Step 102] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 103] Action: [Move to LEFT ARM]\\n\",\n \"[Step 103] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 104] Action: [Move to LEFT ARM]\\n\",\n \"[Step 104] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 105] Action: [Move to LEFT ARM]\\n\",\n \"[Step 105] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 106] Action: [Move to LEFT ARM]\\n\",\n \"[Step 106] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 107] Action: [Move to LEFT ARM]\\n\",\n \"[Step 107] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 108] Action: [Move to LEFT ARM]\\n\",\n \"[Step 108] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 109] Action: [Move to LEFT ARM]\\n\",\n \"[Step 109] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 110] Action: [Move to LEFT ARM]\\n\",\n \"[Step 110] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 111] Action: [Move to LEFT ARM]\\n\",\n \"[Step 111] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 112] Action: [Move to LEFT ARM]\\n\",\n \"[Step 112] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 113] Action: [Move to LEFT ARM]\\n\",\n \"[Step 113] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 114] Action: [Move to LEFT ARM]\\n\",\n \"[Step 114] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 115] Action: [Move to LEFT ARM]\\n\",\n \"[Step 115] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 116] Action: [Move to LEFT ARM]\\n\",\n \"[Step 116] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 117] Action: [Move to LEFT ARM]\\n\",\n \"[Step 117] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 118] Action: [Move to LEFT ARM]\\n\",\n \"[Step 118] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 119] Action: [Move to LEFT ARM]\\n\",\n \"[Step 119] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 120] Action: [Move to LEFT ARM]\\n\",\n \"[Step 120] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 121] Action: [Move to LEFT ARM]\\n\",\n \"[Step 121] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 122] Action: [Move to LEFT ARM]\\n\",\n \"[Step 122] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 123] Action: [Move to LEFT ARM]\\n\",\n \"[Step 123] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 124] Action: [Move to LEFT ARM]\\n\",\n \"[Step 124] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 125] Action: [Move to LEFT ARM]\\n\",\n \"[Step 125] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 126] Action: [Move to LEFT ARM]\\n\",\n \"[Step 126] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 127] Action: [Move to LEFT ARM]\\n\",\n \"[Step 127] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 128] Action: [Move to LEFT ARM]\\n\",\n \"[Step 128] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 129] Action: [Move to LEFT ARM]\\n\",\n \"[Step 129] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 130] Action: [Move to LEFT ARM]\\n\",\n \"[Step 130] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 131] Action: [Move to LEFT ARM]\\n\",\n \"[Step 131] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 132] Action: [Move to LEFT ARM]\\n\",\n \"[Step 132] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 133] Action: [Move to LEFT ARM]\\n\",\n \"[Step 133] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 134] Action: [Move to LEFT ARM]\\n\",\n \"[Step 134] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 135] Action: [Move to LEFT ARM]\\n\",\n \"[Step 135] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 136] Action: [Move to LEFT ARM]\\n\",\n \"[Step 136] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 137] Action: [Move to LEFT ARM]\\n\",\n \"[Step 137] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 138] Action: [Move to LEFT ARM]\\n\",\n \"[Step 138] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 139] Action: [Move to LEFT ARM]\\n\",\n \"[Step 139] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 140] Action: [Move to LEFT ARM]\\n\",\n \"[Step 140] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 141] Action: [Move to LEFT ARM]\\n\",\n \"[Step 141] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 142] Action: [Move to LEFT ARM]\\n\",\n \"[Step 142] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 143] Action: [Move to LEFT ARM]\\n\",\n \"[Step 143] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 144] Action: [Move to LEFT ARM]\\n\",\n \"[Step 144] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 145] Action: [Move to LEFT ARM]\\n\",\n \"[Step 145] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 146] Action: [Move to LEFT ARM]\\n\",\n \"[Step 146] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 147] Action: [Move to LEFT ARM]\\n\",\n \"[Step 147] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 148] Action: [Move to LEFT ARM]\\n\",\n \"[Step 148] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 149] Action: [Move to LEFT ARM]\\n\",\n \"[Step 149] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 150] Action: [Move to LEFT ARM]\\n\",\n \"[Step 150] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 151] Action: [Move to LEFT ARM]\\n\",\n \"[Step 151] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 152] Action: [Move to LEFT ARM]\\n\",\n \"[Step 152] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 153] Action: [Move to LEFT ARM]\\n\",\n \"[Step 153] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 154] Action: [Move to LEFT ARM]\\n\",\n \"[Step 154] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 155] Action: [Move to LEFT ARM]\\n\",\n \"[Step 155] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 156] Action: [Move to LEFT ARM]\\n\",\n \"[Step 156] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 157] Action: [Move to LEFT ARM]\\n\",\n \"[Step 157] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 158] Action: [Move to LEFT ARM]\\n\",\n \"[Step 158] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 159] Action: [Move to LEFT ARM]\\n\",\n \"[Step 159] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 160] Action: [Move to LEFT ARM]\\n\",\n \"[Step 160] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 161] Action: [Move to LEFT ARM]\\n\",\n \"[Step 161] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 162] Action: [Move to LEFT ARM]\\n\",\n \"[Step 162] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 163] Action: [Move to LEFT ARM]\\n\",\n \"[Step 163] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 164] Action: [Move to LEFT ARM]\\n\",\n \"[Step 164] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 165] Action: [Move to LEFT ARM]\\n\",\n \"[Step 165] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 166] Action: [Move to LEFT ARM]\\n\",\n \"[Step 166] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 167] Action: [Move to LEFT ARM]\\n\",\n \"[Step 167] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 168] Action: [Move to LEFT ARM]\\n\",\n \"[Step 168] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 169] Action: [Move to LEFT ARM]\\n\",\n \"[Step 169] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 170] Action: [Move to LEFT ARM]\\n\",\n \"[Step 170] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 171] Action: [Move to LEFT ARM]\\n\",\n \"[Step 171] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 172] Action: [Move to LEFT ARM]\\n\",\n \"[Step 172] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 173] Action: [Move to LEFT ARM]\\n\",\n \"[Step 173] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 174] Action: [Move to LEFT ARM]\\n\",\n \"[Step 174] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 175] Action: [Move to LEFT ARM]\\n\",\n \"[Step 175] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 176] Action: [Move to LEFT ARM]\\n\",\n \"[Step 176] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 177] Action: [Move to LEFT ARM]\\n\",\n \"[Step 177] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 178] Action: [Move to LEFT ARM]\\n\",\n \"[Step 178] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 179] Action: [Move to LEFT ARM]\\n\",\n \"[Step 179] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 180] Action: [Move to LEFT ARM]\\n\",\n \"[Step 180] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 181] Action: [Move to LEFT ARM]\\n\",\n \"[Step 181] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 182] Action: [Move to LEFT ARM]\\n\",\n \"[Step 182] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 183] Action: [Move to LEFT ARM]\\n\",\n \"[Step 183] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 184] Action: [Move to LEFT ARM]\\n\",\n \"[Step 184] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 185] Action: [Move to LEFT ARM]\\n\",\n \"[Step 185] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 186] Action: [Move to LEFT ARM]\\n\",\n \"[Step 186] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 187] Action: [Move to LEFT ARM]\\n\",\n \"[Step 187] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 188] Action: [Move to LEFT ARM]\\n\",\n \"[Step 188] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 189] Action: [Move to LEFT ARM]\\n\",\n \"[Step 189] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 190] Action: [Move to LEFT ARM]\\n\",\n \"[Step 190] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 191] Action: [Move to LEFT ARM]\\n\",\n \"[Step 191] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 192] Action: [Move to LEFT ARM]\\n\",\n \"[Step 192] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 193] Action: [Move to LEFT ARM]\\n\",\n \"[Step 193] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 194] Action: [Move to LEFT ARM]\\n\",\n \"[Step 194] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 195] Action: [Move to LEFT ARM]\\n\",\n \"[Step 195] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 196] Action: [Move to LEFT ARM]\\n\",\n \"[Step 196] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 197] Action: [Move to LEFT ARM]\\n\",\n \"[Step 197] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 198] Action: [Move to LEFT ARM]\\n\",\n \"[Step 198] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 199] Action: [Move to LEFT ARM]\\n\",\n \"[Step 199] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 200] Action: [Move to LEFT ARM]\\n\",\n \"[Step 200] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 201] Action: [Move to LEFT ARM]\\n\",\n \"[Step 201] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 202] Action: [Move to LEFT ARM]\\n\",\n \"[Step 202] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 203] Action: [Move to LEFT ARM]\\n\",\n \"[Step 203] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 204] Action: [Move to LEFT ARM]\\n\",\n \"[Step 204] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 205] Action: [Move to LEFT ARM]\\n\",\n \"[Step 205] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 206] Action: [Move to LEFT ARM]\\n\",\n \"[Step 206] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 207] Action: [Move to LEFT ARM]\\n\",\n \"[Step 207] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 208] Action: [Move to LEFT ARM]\\n\",\n \"[Step 208] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 209] Action: [Move to LEFT ARM]\\n\",\n \"[Step 209] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 210] Action: [Move to LEFT ARM]\\n\",\n \"[Step 210] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 211] Action: [Move to LEFT ARM]\\n\",\n \"[Step 211] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 212] Action: [Move to LEFT ARM]\\n\",\n \"[Step 212] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 213] Action: [Move to LEFT ARM]\\n\",\n \"[Step 213] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 214] Action: [Move to LEFT ARM]\\n\",\n \"[Step 214] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 215] Action: [Move to LEFT ARM]\\n\",\n \"[Step 215] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 216] Action: [Move to LEFT ARM]\\n\",\n \"[Step 216] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 217] Action: [Move to LEFT ARM]\\n\",\n \"[Step 217] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 218] Action: [Move to LEFT ARM]\\n\",\n \"[Step 218] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 219] Action: [Move to LEFT ARM]\\n\",\n \"[Step 219] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 220] Action: [Move to LEFT ARM]\\n\",\n \"[Step 220] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 221] Action: [Move to LEFT ARM]\\n\",\n \"[Step 221] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 222] Action: [Move to LEFT ARM]\\n\",\n \"[Step 222] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 223] Action: [Move to LEFT ARM]\\n\",\n \"[Step 223] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 224] Action: [Move to LEFT ARM]\\n\",\n \"[Step 224] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 225] Action: [Move to LEFT ARM]\\n\",\n \"[Step 225] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 226] Action: [Move to LEFT ARM]\\n\",\n \"[Step 226] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 227] Action: [Move to LEFT ARM]\\n\",\n \"[Step 227] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 228] Action: [Move to LEFT ARM]\\n\",\n \"[Step 228] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 229] Action: [Move to LEFT ARM]\\n\",\n \"[Step 229] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 230] Action: [Move to LEFT ARM]\\n\",\n \"[Step 230] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 231] Action: [Move to LEFT ARM]\\n\",\n \"[Step 231] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 232] Action: [Move to LEFT ARM]\\n\",\n \"[Step 232] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 233] Action: [Move to LEFT ARM]\\n\",\n \"[Step 233] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 234] Action: [Move to LEFT ARM]\\n\",\n \"[Step 234] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 235] Action: [Move to LEFT ARM]\\n\",\n \"[Step 235] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 236] Action: [Move to LEFT ARM]\\n\",\n \"[Step 236] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 237] Action: [Move to LEFT ARM]\\n\",\n \"[Step 237] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 238] Action: [Move to LEFT ARM]\\n\",\n \"[Step 238] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 239] Action: [Move to LEFT ARM]\\n\",\n \"[Step 239] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 240] Action: [Move to LEFT ARM]\\n\",\n \"[Step 240] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 241] Action: [Move to LEFT ARM]\\n\",\n \"[Step 241] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 242] Action: [Move to LEFT ARM]\\n\",\n \"[Step 242] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 243] Action: [Move to LEFT ARM]\\n\",\n \"[Step 243] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 244] Action: [Move to LEFT ARM]\\n\",\n \"[Step 244] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 245] Action: [Move to LEFT ARM]\\n\",\n \"[Step 245] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 246] Action: [Move to LEFT ARM]\\n\",\n \"[Step 246] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 247] Action: [Move to LEFT ARM]\\n\",\n \"[Step 247] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 248] Action: [Move to LEFT ARM]\\n\",\n \"[Step 248] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 249] Action: [Move to LEFT ARM]\\n\",\n \"[Step 249] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 250] Action: [Move to LEFT ARM]\\n\",\n \"[Step 250] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 251] Action: [Move to LEFT ARM]\\n\",\n \"[Step 251] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 252] Action: [Move to LEFT ARM]\\n\",\n \"[Step 252] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 253] Action: [Move to LEFT ARM]\\n\",\n \"[Step 253] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 254] Action: [Move to LEFT ARM]\\n\",\n \"[Step 254] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 255] Action: [Move to LEFT ARM]\\n\",\n \"[Step 255] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 256] Action: [Move to LEFT ARM]\\n\",\n \"[Step 256] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 257] Action: [Move to LEFT ARM]\\n\",\n \"[Step 257] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 258] Action: [Move to LEFT ARM]\\n\",\n \"[Step 258] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 259] Action: [Move to LEFT ARM]\\n\",\n \"[Step 259] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 260] Action: [Move to LEFT ARM]\\n\",\n \"[Step 260] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 261] Action: [Move to LEFT ARM]\\n\",\n \"[Step 261] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 262] Action: [Move to LEFT ARM]\\n\",\n \"[Step 262] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 263] Action: [Move to LEFT ARM]\\n\",\n \"[Step 263] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 264] Action: [Move to LEFT ARM]\\n\",\n \"[Step 264] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 265] Action: [Move to LEFT ARM]\\n\",\n \"[Step 265] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 266] Action: [Move to LEFT ARM]\\n\",\n \"[Step 266] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 267] Action: [Move to LEFT ARM]\\n\",\n \"[Step 267] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 268] Action: [Move to LEFT ARM]\\n\",\n \"[Step 268] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 269] Action: [Move to LEFT ARM]\\n\",\n \"[Step 269] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 270] Action: [Move to LEFT ARM]\\n\",\n \"[Step 270] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 271] Action: [Move to LEFT ARM]\\n\",\n \"[Step 271] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 272] Action: [Move to LEFT ARM]\\n\",\n \"[Step 272] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 273] Action: [Move to LEFT ARM]\\n\",\n \"[Step 273] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 274] Action: [Move to LEFT ARM]\\n\",\n \"[Step 274] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 275] Action: [Move to LEFT ARM]\\n\",\n \"[Step 275] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 276] Action: [Move to LEFT ARM]\\n\",\n \"[Step 276] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 277] Action: [Move to LEFT ARM]\\n\",\n \"[Step 277] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 278] Action: [Move to LEFT ARM]\\n\",\n \"[Step 278] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 279] Action: [Move to LEFT ARM]\\n\",\n \"[Step 279] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 280] Action: [Move to LEFT ARM]\\n\",\n \"[Step 280] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 281] Action: [Move to LEFT ARM]\\n\",\n \"[Step 281] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 282] Action: [Move to LEFT ARM]\\n\",\n \"[Step 282] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 283] Action: [Move to LEFT ARM]\\n\",\n \"[Step 283] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 284] Action: [Move to LEFT ARM]\\n\",\n \"[Step 284] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 285] Action: [Move to LEFT ARM]\\n\",\n \"[Step 285] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 286] Action: [Move to LEFT ARM]\\n\",\n \"[Step 286] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 287] Action: [Move to LEFT ARM]\\n\",\n \"[Step 287] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 288] Action: [Move to LEFT ARM]\\n\",\n \"[Step 288] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 289] Action: [Move to LEFT ARM]\\n\",\n \"[Step 289] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 290] Action: [Move to LEFT ARM]\\n\",\n \"[Step 290] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 291] Action: [Move to LEFT ARM]\\n\",\n \"[Step 291] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 292] Action: [Move to LEFT ARM]\\n\",\n \"[Step 292] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 293] Action: [Move to LEFT ARM]\\n\",\n \"[Step 293] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 294] Action: [Move to LEFT ARM]\\n\",\n \"[Step 294] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 295] Action: [Move to LEFT ARM]\\n\",\n \"[Step 295] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 296] Action: [Move to LEFT ARM]\\n\",\n \"[Step 296] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 297] Action: [Move to LEFT ARM]\\n\",\n \"[Step 297] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 298] Action: [Move to LEFT ARM]\\n\",\n \"[Step 298] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 299] Action: [Move to LEFT ARM]\\n\",\n \"[Step 299] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 300] Action: [Move to LEFT ARM]\\n\",\n \"[Step 300] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 301] Action: [Move to LEFT ARM]\\n\",\n \"[Step 301] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 302] Action: [Move to LEFT ARM]\\n\",\n \"[Step 302] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 303] Action: [Move to LEFT ARM]\\n\",\n \"[Step 303] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 304] Action: [Move to LEFT ARM]\\n\",\n \"[Step 304] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 305] Action: [Move to LEFT ARM]\\n\",\n \"[Step 305] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 306] Action: [Move to LEFT ARM]\\n\",\n \"[Step 306] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 307] Action: [Move to LEFT ARM]\\n\",\n \"[Step 307] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 308] Action: [Move to LEFT ARM]\\n\",\n \"[Step 308] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 309] Action: [Move to LEFT ARM]\\n\",\n \"[Step 309] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 310] Action: [Move to LEFT ARM]\\n\",\n \"[Step 310] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 311] Action: [Move to LEFT ARM]\\n\",\n \"[Step 311] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 312] Action: [Move to LEFT ARM]\\n\",\n \"[Step 312] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 313] Action: [Move to LEFT ARM]\\n\",\n \"[Step 313] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 314] Action: [Move to LEFT ARM]\\n\",\n \"[Step 314] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 315] Action: [Move to LEFT ARM]\\n\",\n \"[Step 315] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 316] Action: [Move to LEFT ARM]\\n\",\n \"[Step 316] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 317] Action: [Move to LEFT ARM]\\n\",\n \"[Step 317] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 318] Action: [Move to LEFT ARM]\\n\",\n \"[Step 318] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 319] Action: [Move to LEFT ARM]\\n\",\n \"[Step 319] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 320] Action: [Move to LEFT ARM]\\n\",\n \"[Step 320] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 321] Action: [Move to LEFT ARM]\\n\",\n \"[Step 321] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 322] Action: [Move to LEFT ARM]\\n\",\n \"[Step 322] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 323] Action: [Move to LEFT ARM]\\n\",\n \"[Step 323] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 324] Action: [Move to LEFT ARM]\\n\",\n \"[Step 324] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 325] Action: [Move to LEFT ARM]\\n\",\n \"[Step 325] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 326] Action: [Move to LEFT ARM]\\n\",\n \"[Step 326] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 327] Action: [Move to LEFT ARM]\\n\",\n \"[Step 327] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 328] Action: [Move to LEFT ARM]\\n\",\n \"[Step 328] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 329] Action: [Move to LEFT ARM]\\n\",\n \"[Step 329] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 330] Action: [Move to LEFT ARM]\\n\",\n \"[Step 330] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 331] Action: [Move to LEFT ARM]\\n\",\n \"[Step 331] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 332] Action: [Move to LEFT ARM]\\n\",\n \"[Step 332] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 333] Action: [Move to LEFT ARM]\\n\",\n \"[Step 333] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 334] Action: [Move to LEFT ARM]\\n\",\n \"[Step 334] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 335] Action: [Move to LEFT ARM]\\n\",\n \"[Step 335] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 336] Action: [Move to LEFT ARM]\\n\",\n \"[Step 336] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 337] Action: [Move to LEFT ARM]\\n\",\n \"[Step 337] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 338] Action: [Move to LEFT ARM]\\n\",\n \"[Step 338] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 339] Action: [Move to LEFT ARM]\\n\",\n \"[Step 339] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 340] Action: [Move to LEFT ARM]\\n\",\n \"[Step 340] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 341] Action: [Move to LEFT ARM]\\n\",\n \"[Step 341] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 342] Action: [Move to LEFT ARM]\\n\",\n \"[Step 342] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 343] Action: [Move to LEFT ARM]\\n\",\n \"[Step 343] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 344] Action: [Move to LEFT ARM]\\n\",\n \"[Step 344] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 345] Action: [Move to LEFT ARM]\\n\",\n \"[Step 345] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 346] Action: [Move to LEFT ARM]\\n\",\n \"[Step 346] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 347] Action: [Move to LEFT ARM]\\n\",\n \"[Step 347] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 348] Action: [Move to LEFT ARM]\\n\",\n \"[Step 348] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 349] Action: [Move to LEFT ARM]\\n\",\n \"[Step 349] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 350] Action: [Move to LEFT ARM]\\n\",\n \"[Step 350] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 351] Action: [Move to LEFT ARM]\\n\",\n \"[Step 351] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 352] Action: [Move to LEFT ARM]\\n\",\n \"[Step 352] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 353] Action: [Move to LEFT ARM]\\n\",\n \"[Step 353] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 354] Action: [Move to LEFT ARM]\\n\",\n \"[Step 354] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 355] Action: [Move to LEFT ARM]\\n\",\n \"[Step 355] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 356] Action: [Move to LEFT ARM]\\n\",\n \"[Step 356] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 357] Action: [Move to LEFT ARM]\\n\",\n \"[Step 357] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 358] Action: [Move to LEFT ARM]\\n\",\n \"[Step 358] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 359] Action: [Move to LEFT ARM]\\n\",\n \"[Step 359] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 360] Action: [Move to LEFT ARM]\\n\",\n \"[Step 360] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 361] Action: [Move to LEFT ARM]\\n\",\n \"[Step 361] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 362] Action: [Move to LEFT ARM]\\n\",\n \"[Step 362] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 363] Action: [Move to LEFT ARM]\\n\",\n \"[Step 363] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 364] Action: [Move to LEFT ARM]\\n\",\n \"[Step 364] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 365] Action: [Move to LEFT ARM]\\n\",\n \"[Step 365] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 366] Action: [Move to LEFT ARM]\\n\",\n \"[Step 366] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 367] Action: [Move to LEFT ARM]\\n\",\n \"[Step 367] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 368] Action: [Move to LEFT ARM]\\n\",\n \"[Step 368] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 369] Action: [Move to LEFT ARM]\\n\",\n \"[Step 369] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 370] Action: [Move to LEFT ARM]\\n\",\n \"[Step 370] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 371] Action: [Move to LEFT ARM]\\n\",\n \"[Step 371] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 372] Action: [Move to LEFT ARM]\\n\",\n \"[Step 372] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 373] Action: [Move to LEFT ARM]\\n\",\n \"[Step 373] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 374] Action: [Move to LEFT ARM]\\n\",\n \"[Step 374] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 375] Action: [Move to LEFT ARM]\\n\",\n \"[Step 375] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 376] Action: [Move to LEFT ARM]\\n\",\n \"[Step 376] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 377] Action: [Move to LEFT ARM]\\n\",\n \"[Step 377] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 378] Action: [Move to LEFT ARM]\\n\",\n \"[Step 378] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 379] Action: [Move to LEFT ARM]\\n\",\n \"[Step 379] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 380] Action: [Move to LEFT ARM]\\n\",\n \"[Step 380] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 381] Action: [Move to LEFT ARM]\\n\",\n \"[Step 381] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 382] Action: [Move to LEFT ARM]\\n\",\n \"[Step 382] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 383] Action: [Move to LEFT ARM]\\n\",\n \"[Step 383] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 384] Action: [Move to LEFT ARM]\\n\",\n \"[Step 384] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 385] Action: [Move to LEFT ARM]\\n\",\n \"[Step 385] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 386] Action: [Move to LEFT ARM]\\n\",\n \"[Step 386] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 387] Action: [Move to LEFT ARM]\\n\",\n \"[Step 387] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 388] Action: [Move to LEFT ARM]\\n\",\n \"[Step 388] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 389] Action: [Move to LEFT ARM]\\n\",\n \"[Step 389] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 390] Action: [Move to LEFT ARM]\\n\",\n \"[Step 390] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 391] Action: [Move to LEFT ARM]\\n\",\n \"[Step 391] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 392] Action: [Move to LEFT ARM]\\n\",\n \"[Step 392] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 393] Action: [Move to LEFT ARM]\\n\",\n \"[Step 393] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 394] Action: [Move to LEFT ARM]\\n\",\n \"[Step 394] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 395] Action: [Move to LEFT ARM]\\n\",\n \"[Step 395] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 396] Action: [Move to LEFT ARM]\\n\",\n \"[Step 396] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 397] Action: [Move to LEFT ARM]\\n\",\n \"[Step 397] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 398] Action: [Move to LEFT ARM]\\n\",\n \"[Step 398] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 399] Action: [Move to LEFT ARM]\\n\",\n \"[Step 399] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 400] Action: [Move to LEFT ARM]\\n\",\n \"[Step 400] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 401] Action: [Move to LEFT ARM]\\n\",\n \"[Step 401] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 402] Action: [Move to LEFT ARM]\\n\",\n \"[Step 402] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 403] Action: [Move to LEFT ARM]\\n\",\n \"[Step 403] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 404] Action: [Move to LEFT ARM]\\n\",\n \"[Step 404] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 405] Action: [Move to LEFT ARM]\\n\",\n \"[Step 405] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 406] Action: [Move to LEFT ARM]\\n\",\n \"[Step 406] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 407] Action: [Move to LEFT ARM]\\n\",\n \"[Step 407] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 408] Action: [Move to LEFT ARM]\\n\",\n \"[Step 408] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 409] Action: [Move to LEFT ARM]\\n\",\n \"[Step 409] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 410] Action: [Move to LEFT ARM]\\n\",\n \"[Step 410] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 411] Action: [Move to LEFT ARM]\\n\",\n \"[Step 411] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 412] Action: [Move to LEFT ARM]\\n\",\n \"[Step 412] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 413] Action: [Move to LEFT ARM]\\n\",\n \"[Step 413] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 414] Action: [Move to LEFT ARM]\\n\",\n \"[Step 414] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 415] Action: [Move to LEFT ARM]\\n\",\n \"[Step 415] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 416] Action: [Move to LEFT ARM]\\n\",\n \"[Step 416] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 417] Action: [Move to LEFT ARM]\\n\",\n \"[Step 417] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 418] Action: [Move to LEFT ARM]\\n\",\n \"[Step 418] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 419] Action: [Move to LEFT ARM]\\n\",\n \"[Step 419] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 420] Action: [Move to LEFT ARM]\\n\",\n \"[Step 420] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 421] Action: [Move to LEFT ARM]\\n\",\n \"[Step 421] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 422] Action: [Move to LEFT ARM]\\n\",\n \"[Step 422] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 423] Action: [Move to LEFT ARM]\\n\",\n \"[Step 423] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 424] Action: [Move to LEFT ARM]\\n\",\n \"[Step 424] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 425] Action: [Move to LEFT ARM]\\n\",\n \"[Step 425] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 426] Action: [Move to LEFT ARM]\\n\",\n \"[Step 426] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 427] Action: [Move to LEFT ARM]\\n\",\n \"[Step 427] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 428] Action: [Move to LEFT ARM]\\n\",\n \"[Step 428] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 429] Action: [Move to LEFT ARM]\\n\",\n \"[Step 429] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 430] Action: [Move to LEFT ARM]\\n\",\n \"[Step 430] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 431] Action: [Move to LEFT ARM]\\n\",\n \"[Step 431] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 432] Action: [Move to LEFT ARM]\\n\",\n \"[Step 432] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 433] Action: [Move to LEFT ARM]\\n\",\n \"[Step 433] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 434] Action: [Move to LEFT ARM]\\n\",\n \"[Step 434] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 435] Action: [Move to LEFT ARM]\\n\",\n \"[Step 435] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 436] Action: [Move to LEFT ARM]\\n\",\n \"[Step 436] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 437] Action: [Move to LEFT ARM]\\n\",\n \"[Step 437] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 438] Action: [Move to LEFT ARM]\\n\",\n \"[Step 438] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 439] Action: [Move to LEFT ARM]\\n\",\n \"[Step 439] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 440] Action: [Move to LEFT ARM]\\n\",\n \"[Step 440] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 441] Action: [Move to LEFT ARM]\\n\",\n \"[Step 441] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 442] Action: [Move to LEFT ARM]\\n\",\n \"[Step 442] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 443] Action: [Move to LEFT ARM]\\n\",\n \"[Step 443] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 444] Action: [Move to LEFT ARM]\\n\",\n \"[Step 444] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 445] Action: [Move to LEFT ARM]\\n\",\n \"[Step 445] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 446] Action: [Move to LEFT ARM]\\n\",\n \"[Step 446] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 447] Action: [Move to LEFT ARM]\\n\",\n \"[Step 447] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 448] Action: [Move to LEFT ARM]\\n\",\n \"[Step 448] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 449] Action: [Move to LEFT ARM]\\n\",\n \"[Step 449] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 450] Action: [Move to LEFT ARM]\\n\",\n \"[Step 450] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 451] Action: [Move to LEFT ARM]\\n\",\n \"[Step 451] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 452] Action: [Move to LEFT ARM]\\n\",\n \"[Step 452] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 453] Action: [Move to LEFT ARM]\\n\",\n \"[Step 453] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 454] Action: [Move to LEFT ARM]\\n\",\n \"[Step 454] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 455] Action: [Move to LEFT ARM]\\n\",\n \"[Step 455] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 456] Action: [Move to LEFT ARM]\\n\",\n \"[Step 456] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 457] Action: [Move to LEFT ARM]\\n\",\n \"[Step 457] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 458] Action: [Move to LEFT ARM]\\n\",\n \"[Step 458] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 459] Action: [Move to LEFT ARM]\\n\",\n \"[Step 459] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 460] Action: [Move to LEFT ARM]\\n\",\n \"[Step 460] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 461] Action: [Move to LEFT ARM]\\n\",\n \"[Step 461] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 462] Action: [Move to LEFT ARM]\\n\",\n \"[Step 462] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 463] Action: [Move to LEFT ARM]\\n\",\n \"[Step 463] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 464] Action: [Move to LEFT ARM]\\n\",\n \"[Step 464] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 465] Action: [Move to LEFT ARM]\\n\",\n \"[Step 465] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 466] Action: [Move to LEFT ARM]\\n\",\n \"[Step 466] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 467] Action: [Move to LEFT ARM]\\n\",\n \"[Step 467] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 468] Action: [Move to LEFT ARM]\\n\",\n \"[Step 468] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 469] Action: [Move to LEFT ARM]\\n\",\n \"[Step 469] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 470] Action: [Move to LEFT ARM]\\n\",\n \"[Step 470] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 471] Action: [Move to LEFT ARM]\\n\",\n \"[Step 471] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 472] Action: [Move to LEFT ARM]\\n\",\n \"[Step 472] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 473] Action: [Move to LEFT ARM]\\n\",\n \"[Step 473] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 474] Action: [Move to LEFT ARM]\\n\",\n \"[Step 474] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 475] Action: [Move to LEFT ARM]\\n\",\n \"[Step 475] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 476] Action: [Move to LEFT ARM]\\n\",\n \"[Step 476] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 477] Action: [Move to LEFT ARM]\\n\",\n \"[Step 477] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 478] Action: [Move to LEFT ARM]\\n\",\n \"[Step 478] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 479] Action: [Move to LEFT ARM]\\n\",\n \"[Step 479] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 480] Action: [Move to LEFT ARM]\\n\",\n \"[Step 480] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 481] Action: [Move to LEFT ARM]\\n\",\n \"[Step 481] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 482] Action: [Move to LEFT ARM]\\n\",\n \"[Step 482] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 483] Action: [Move to LEFT ARM]\\n\",\n \"[Step 483] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 484] Action: [Move to LEFT ARM]\\n\",\n \"[Step 484] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 485] Action: [Move to LEFT ARM]\\n\",\n \"[Step 485] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 486] Action: [Move to LEFT ARM]\\n\",\n \"[Step 486] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 487] Action: [Move to LEFT ARM]\\n\",\n \"[Step 487] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 488] Action: [Move to LEFT ARM]\\n\",\n \"[Step 488] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 489] Action: [Move to LEFT ARM]\\n\",\n \"[Step 489] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 490] Action: [Move to LEFT ARM]\\n\",\n \"[Step 490] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 491] Action: [Move to LEFT ARM]\\n\",\n \"[Step 491] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 492] Action: [Move to LEFT ARM]\\n\",\n \"[Step 492] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 493] Action: [Move to LEFT ARM]\\n\",\n \"[Step 493] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 494] Action: [Move to LEFT ARM]\\n\",\n \"[Step 494] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 495] Action: [Move to LEFT ARM]\\n\",\n \"[Step 495] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 496] Action: [Move to LEFT ARM]\\n\",\n \"[Step 496] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 497] Action: [Move to LEFT ARM]\\n\",\n \"[Step 497] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 498] Action: [Move to LEFT ARM]\\n\",\n \"[Step 498] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 499] Action: [Move to LEFT ARM]\\n\",\n \"[Step 499] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 500] Action: [Move to LEFT ARM]\\n\",\n \"[Step 500] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 501] Action: [Move to LEFT ARM]\\n\",\n \"[Step 501] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 502] Action: [Move to LEFT ARM]\\n\",\n \"[Step 502] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 503] Action: [Move to LEFT ARM]\\n\",\n \"[Step 503] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 504] Action: [Move to LEFT ARM]\\n\",\n \"[Step 504] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 505] Action: [Move to LEFT ARM]\\n\",\n \"[Step 505] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 506] Action: [Move to LEFT ARM]\\n\",\n \"[Step 506] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 507] Action: [Move to LEFT ARM]\\n\",\n \"[Step 507] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 508] Action: [Move to LEFT ARM]\\n\",\n \"[Step 508] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 509] Action: [Move to LEFT ARM]\\n\",\n \"[Step 509] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 510] Action: [Move to LEFT ARM]\\n\",\n \"[Step 510] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 511] Action: [Move to LEFT ARM]\\n\",\n \"[Step 511] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 512] Action: [Move to LEFT ARM]\\n\",\n \"[Step 512] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 513] Action: [Move to LEFT ARM]\\n\",\n \"[Step 513] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 514] Action: [Move to LEFT ARM]\\n\",\n \"[Step 514] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 515] Action: [Move to LEFT ARM]\\n\",\n \"[Step 515] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 516] Action: [Move to LEFT ARM]\\n\",\n \"[Step 516] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 517] Action: [Move to LEFT ARM]\\n\",\n \"[Step 517] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 518] Action: [Move to LEFT ARM]\\n\",\n \"[Step 518] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 519] Action: [Move to LEFT ARM]\\n\",\n \"[Step 519] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 520] Action: [Move to LEFT ARM]\\n\",\n \"[Step 520] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 521] Action: [Move to LEFT ARM]\\n\",\n \"[Step 521] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 522] Action: [Move to LEFT ARM]\\n\",\n \"[Step 522] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 523] Action: [Move to LEFT ARM]\\n\",\n \"[Step 523] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 524] Action: [Move to LEFT ARM]\\n\",\n \"[Step 524] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 525] Action: [Move to LEFT ARM]\\n\",\n \"[Step 525] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 526] Action: [Move to LEFT ARM]\\n\",\n \"[Step 526] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 527] Action: [Move to LEFT ARM]\\n\",\n \"[Step 527] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 528] Action: [Move to LEFT ARM]\\n\",\n \"[Step 528] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 529] Action: [Move to LEFT ARM]\\n\",\n \"[Step 529] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 530] Action: [Move to LEFT ARM]\\n\",\n \"[Step 530] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 531] Action: [Move to LEFT ARM]\\n\",\n \"[Step 531] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 532] Action: [Move to LEFT ARM]\\n\",\n \"[Step 532] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 533] Action: [Move to LEFT ARM]\\n\",\n \"[Step 533] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 534] Action: [Move to LEFT ARM]\\n\",\n \"[Step 534] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 535] Action: [Move to LEFT ARM]\\n\",\n \"[Step 535] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 536] Action: [Move to LEFT ARM]\\n\",\n \"[Step 536] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 537] Action: [Move to LEFT ARM]\\n\",\n \"[Step 537] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 538] Action: [Move to LEFT ARM]\\n\",\n \"[Step 538] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 539] Action: [Move to LEFT ARM]\\n\",\n \"[Step 539] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 540] Action: [Move to LEFT ARM]\\n\",\n \"[Step 540] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 541] Action: [Move to LEFT ARM]\\n\",\n \"[Step 541] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 542] Action: [Move to LEFT ARM]\\n\",\n \"[Step 542] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 543] Action: [Move to LEFT ARM]\\n\",\n \"[Step 543] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 544] Action: [Move to LEFT ARM]\\n\",\n \"[Step 544] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 545] Action: [Move to LEFT ARM]\\n\",\n \"[Step 545] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 546] Action: [Move to LEFT ARM]\\n\",\n \"[Step 546] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 547] Action: [Move to LEFT ARM]\\n\",\n \"[Step 547] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 548] Action: [Move to LEFT ARM]\\n\",\n \"[Step 548] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 549] Action: [Move to LEFT ARM]\\n\",\n \"[Step 549] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 550] Action: [Move to LEFT ARM]\\n\",\n \"[Step 550] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 551] Action: [Move to LEFT ARM]\\n\",\n \"[Step 551] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 552] Action: [Move to LEFT ARM]\\n\",\n \"[Step 552] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 553] Action: [Move to LEFT ARM]\\n\",\n \"[Step 553] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 554] Action: [Move to LEFT ARM]\\n\",\n \"[Step 554] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 555] Action: [Move to LEFT ARM]\\n\",\n \"[Step 555] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 556] Action: [Move to LEFT ARM]\\n\",\n \"[Step 556] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 557] Action: [Move to LEFT ARM]\\n\",\n \"[Step 557] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 558] Action: [Move to LEFT ARM]\\n\",\n \"[Step 558] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 559] Action: [Move to LEFT ARM]\\n\",\n \"[Step 559] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 560] Action: [Move to LEFT ARM]\\n\",\n \"[Step 560] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 561] Action: [Move to LEFT ARM]\\n\",\n \"[Step 561] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 562] Action: [Move to LEFT ARM]\\n\",\n \"[Step 562] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 563] Action: [Move to LEFT ARM]\\n\",\n \"[Step 563] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 564] Action: [Move to LEFT ARM]\\n\",\n \"[Step 564] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 565] Action: [Move to LEFT ARM]\\n\",\n \"[Step 565] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 566] Action: [Move to LEFT ARM]\\n\",\n \"[Step 566] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 567] Action: [Move to LEFT ARM]\\n\",\n \"[Step 567] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 568] Action: [Move to LEFT ARM]\\n\",\n \"[Step 568] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 569] Action: [Move to LEFT ARM]\\n\",\n \"[Step 569] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 570] Action: [Move to LEFT ARM]\\n\",\n \"[Step 570] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 571] Action: [Move to LEFT ARM]\\n\",\n \"[Step 571] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 572] Action: [Move to LEFT ARM]\\n\",\n \"[Step 572] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 573] Action: [Move to LEFT ARM]\\n\",\n \"[Step 573] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 574] Action: [Move to LEFT ARM]\\n\",\n \"[Step 574] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 575] Action: [Move to LEFT ARM]\\n\",\n \"[Step 575] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 576] Action: [Move to LEFT ARM]\\n\",\n \"[Step 576] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 577] Action: [Move to LEFT ARM]\\n\",\n \"[Step 577] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 578] Action: [Move to LEFT ARM]\\n\",\n \"[Step 578] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 579] Action: [Move to LEFT ARM]\\n\",\n \"[Step 579] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 580] Action: [Move to LEFT ARM]\\n\",\n \"[Step 580] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 581] Action: [Move to LEFT ARM]\\n\",\n \"[Step 581] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 582] Action: [Move to LEFT ARM]\\n\",\n \"[Step 582] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 583] Action: [Move to LEFT ARM]\\n\",\n \"[Step 583] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 584] Action: [Move to LEFT ARM]\\n\",\n \"[Step 584] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 585] Action: [Move to LEFT ARM]\\n\",\n \"[Step 585] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 586] Action: [Move to LEFT ARM]\\n\",\n \"[Step 586] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 587] Action: [Move to LEFT ARM]\\n\",\n \"[Step 587] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 588] Action: [Move to LEFT ARM]\\n\",\n \"[Step 588] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 589] Action: [Move to LEFT ARM]\\n\",\n \"[Step 589] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 590] Action: [Move to LEFT ARM]\\n\",\n \"[Step 590] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 591] Action: [Move to LEFT ARM]\\n\",\n \"[Step 591] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 592] Action: [Move to LEFT ARM]\\n\",\n \"[Step 592] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 593] Action: [Move to LEFT ARM]\\n\",\n \"[Step 593] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 594] Action: [Move to LEFT ARM]\\n\",\n \"[Step 594] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 595] Action: [Move to LEFT ARM]\\n\",\n \"[Step 595] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 596] Action: [Move to LEFT ARM]\\n\",\n \"[Step 596] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 597] Action: [Move to LEFT ARM]\\n\",\n \"[Step 597] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 598] Action: [Move to LEFT ARM]\\n\",\n \"[Step 598] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 599] Action: [Move to LEFT ARM]\\n\",\n \"[Step 599] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 600] Action: [Move to LEFT ARM]\\n\",\n \"[Step 600] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 601] Action: [Move to LEFT ARM]\\n\",\n \"[Step 601] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 602] Action: [Move to LEFT ARM]\\n\",\n \"[Step 602] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 603] Action: [Move to LEFT ARM]\\n\",\n \"[Step 603] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 604] Action: [Move to LEFT ARM]\\n\",\n \"[Step 604] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 605] Action: [Move to LEFT ARM]\\n\",\n \"[Step 605] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 606] Action: [Move to LEFT ARM]\\n\",\n \"[Step 606] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 607] Action: [Move to LEFT ARM]\\n\",\n \"[Step 607] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 608] Action: [Move to LEFT ARM]\\n\",\n \"[Step 608] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 609] Action: [Move to LEFT ARM]\\n\",\n \"[Step 609] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 610] Action: [Move to LEFT ARM]\\n\",\n \"[Step 610] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 611] Action: [Move to LEFT ARM]\\n\",\n \"[Step 611] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 612] Action: [Move to LEFT ARM]\\n\",\n \"[Step 612] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 613] Action: [Move to LEFT ARM]\\n\",\n \"[Step 613] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 614] Action: [Move to LEFT ARM]\\n\",\n \"[Step 614] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 615] Action: [Move to LEFT ARM]\\n\",\n \"[Step 615] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 616] Action: [Move to LEFT ARM]\\n\",\n \"[Step 616] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 617] Action: [Move to LEFT ARM]\\n\",\n \"[Step 617] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 618] Action: [Move to LEFT ARM]\\n\",\n \"[Step 618] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 619] Action: [Move to LEFT ARM]\\n\",\n \"[Step 619] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 620] Action: [Move to LEFT ARM]\\n\",\n \"[Step 620] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 621] Action: [Move to LEFT ARM]\\n\",\n \"[Step 621] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 622] Action: [Move to LEFT ARM]\\n\",\n \"[Step 622] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 623] Action: [Move to LEFT ARM]\\n\",\n \"[Step 623] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 624] Action: [Move to LEFT ARM]\\n\",\n \"[Step 624] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 625] Action: [Move to LEFT ARM]\\n\",\n \"[Step 625] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 626] Action: [Move to LEFT ARM]\\n\",\n \"[Step 626] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 627] Action: [Move to LEFT ARM]\\n\",\n \"[Step 627] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 628] Action: [Move to LEFT ARM]\\n\",\n \"[Step 628] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 629] Action: [Move to LEFT ARM]\\n\",\n \"[Step 629] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 630] Action: [Move to LEFT ARM]\\n\",\n \"[Step 630] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 631] Action: [Move to LEFT ARM]\\n\",\n \"[Step 631] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 632] Action: [Move to LEFT ARM]\\n\",\n \"[Step 632] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 633] Action: [Move to LEFT ARM]\\n\",\n \"[Step 633] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 634] Action: [Move to LEFT ARM]\\n\",\n \"[Step 634] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 635] Action: [Move to LEFT ARM]\\n\",\n \"[Step 635] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 636] Action: [Move to LEFT ARM]\\n\",\n \"[Step 636] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 637] Action: [Move to LEFT ARM]\\n\",\n \"[Step 637] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 638] Action: [Move to LEFT ARM]\\n\",\n \"[Step 638] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 639] Action: [Move to LEFT ARM]\\n\",\n \"[Step 639] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 640] Action: [Move to LEFT ARM]\\n\",\n \"[Step 640] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 641] Action: [Move to LEFT ARM]\\n\",\n \"[Step 641] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 642] Action: [Move to LEFT ARM]\\n\",\n \"[Step 642] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 643] Action: [Move to LEFT ARM]\\n\",\n \"[Step 643] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 644] Action: [Move to LEFT ARM]\\n\",\n \"[Step 644] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 645] Action: [Move to LEFT ARM]\\n\",\n \"[Step 645] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 646] Action: [Move to LEFT ARM]\\n\",\n \"[Step 646] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 647] Action: [Move to LEFT ARM]\\n\",\n \"[Step 647] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 648] Action: [Move to LEFT ARM]\\n\",\n \"[Step 648] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 649] Action: [Move to LEFT ARM]\\n\",\n \"[Step 649] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 650] Action: [Move to LEFT ARM]\\n\",\n \"[Step 650] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 651] Action: [Move to LEFT ARM]\\n\",\n \"[Step 651] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 652] Action: [Move to LEFT ARM]\\n\",\n \"[Step 652] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 653] Action: [Move to LEFT ARM]\\n\",\n \"[Step 653] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 654] Action: [Move to LEFT ARM]\\n\",\n \"[Step 654] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 655] Action: [Move to LEFT ARM]\\n\",\n \"[Step 655] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 656] Action: [Move to LEFT ARM]\\n\",\n \"[Step 656] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 657] Action: [Move to LEFT ARM]\\n\",\n \"[Step 657] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 658] Action: [Move to LEFT ARM]\\n\",\n \"[Step 658] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 659] Action: [Move to LEFT ARM]\\n\",\n \"[Step 659] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 660] Action: [Move to LEFT ARM]\\n\",\n \"[Step 660] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 661] Action: [Move to LEFT ARM]\\n\",\n \"[Step 661] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 662] Action: [Move to LEFT ARM]\\n\",\n \"[Step 662] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 663] Action: [Move to LEFT ARM]\\n\",\n \"[Step 663] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 664] Action: [Move to LEFT ARM]\\n\",\n \"[Step 664] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 665] Action: [Move to LEFT ARM]\\n\",\n \"[Step 665] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 666] Action: [Move to LEFT ARM]\\n\",\n \"[Step 666] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 667] Action: [Move to LEFT ARM]\\n\",\n \"[Step 667] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 668] Action: [Move to LEFT ARM]\\n\",\n \"[Step 668] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 669] Action: [Move to LEFT ARM]\\n\",\n \"[Step 669] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 670] Action: [Move to LEFT ARM]\\n\",\n \"[Step 670] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 671] Action: [Move to LEFT ARM]\\n\",\n \"[Step 671] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 672] Action: [Move to LEFT ARM]\\n\",\n \"[Step 672] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 673] Action: [Move to LEFT ARM]\\n\",\n \"[Step 673] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 674] Action: [Move to LEFT ARM]\\n\",\n \"[Step 674] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 675] Action: [Move to LEFT ARM]\\n\",\n \"[Step 675] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 676] Action: [Move to LEFT ARM]\\n\",\n \"[Step 676] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 677] Action: [Move to LEFT ARM]\\n\",\n \"[Step 677] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 678] Action: [Move to LEFT ARM]\\n\",\n \"[Step 678] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 679] Action: [Move to LEFT ARM]\\n\",\n \"[Step 679] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 680] Action: [Move to LEFT ARM]\\n\",\n \"[Step 680] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 681] Action: [Move to LEFT ARM]\\n\",\n \"[Step 681] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 682] Action: [Move to LEFT ARM]\\n\",\n \"[Step 682] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 683] Action: [Move to LEFT ARM]\\n\",\n \"[Step 683] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 684] Action: [Move to LEFT ARM]\\n\",\n \"[Step 684] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 685] Action: [Move to LEFT ARM]\\n\",\n \"[Step 685] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 686] Action: [Move to LEFT ARM]\\n\",\n \"[Step 686] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 687] Action: [Move to LEFT ARM]\\n\",\n \"[Step 687] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 688] Action: [Move to LEFT ARM]\\n\",\n \"[Step 688] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 689] Action: [Move to LEFT ARM]\\n\",\n \"[Step 689] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 690] Action: [Move to LEFT ARM]\\n\",\n \"[Step 690] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 691] Action: [Move to LEFT ARM]\\n\",\n \"[Step 691] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 692] Action: [Move to LEFT ARM]\\n\",\n \"[Step 692] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 693] Action: [Move to LEFT ARM]\\n\",\n \"[Step 693] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 694] Action: [Move to LEFT ARM]\\n\",\n \"[Step 694] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 695] Action: [Move to LEFT ARM]\\n\",\n \"[Step 695] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 696] Action: [Move to LEFT ARM]\\n\",\n \"[Step 696] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 697] Action: [Move to LEFT ARM]\\n\",\n \"[Step 697] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 698] Action: [Move to LEFT ARM]\\n\",\n \"[Step 698] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 699] Action: [Move to LEFT ARM]\\n\",\n \"[Step 699] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 700] Action: [Move to LEFT ARM]\\n\",\n \"[Step 700] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 701] Action: [Move to LEFT ARM]\\n\",\n \"[Step 701] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 702] Action: [Move to LEFT ARM]\\n\",\n \"[Step 702] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 703] Action: [Move to LEFT ARM]\\n\",\n \"[Step 703] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 704] Action: [Move to LEFT ARM]\\n\",\n \"[Step 704] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 705] Action: [Move to LEFT ARM]\\n\",\n \"[Step 705] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 706] Action: [Move to LEFT ARM]\\n\",\n \"[Step 706] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 707] Action: [Move to LEFT ARM]\\n\",\n \"[Step 707] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 708] Action: [Move to LEFT ARM]\\n\",\n \"[Step 708] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 709] Action: [Move to LEFT ARM]\\n\",\n \"[Step 709] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 710] Action: [Move to LEFT ARM]\\n\",\n \"[Step 710] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 711] Action: [Move to LEFT ARM]\\n\",\n \"[Step 711] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 712] Action: [Move to LEFT ARM]\\n\",\n \"[Step 712] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 713] Action: [Move to LEFT ARM]\\n\",\n \"[Step 713] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 714] Action: [Move to LEFT ARM]\\n\",\n \"[Step 714] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 715] Action: [Move to LEFT ARM]\\n\",\n \"[Step 715] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 716] Action: [Move to LEFT ARM]\\n\",\n \"[Step 716] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 717] Action: [Move to LEFT ARM]\\n\",\n \"[Step 717] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 718] Action: [Move to LEFT ARM]\\n\",\n \"[Step 718] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 719] Action: [Move to LEFT ARM]\\n\",\n \"[Step 719] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 720] Action: [Move to LEFT ARM]\\n\",\n \"[Step 720] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 721] Action: [Move to LEFT ARM]\\n\",\n \"[Step 721] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 722] Action: [Move to LEFT ARM]\\n\",\n \"[Step 722] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 723] Action: [Move to LEFT ARM]\\n\",\n \"[Step 723] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 724] Action: [Move to LEFT ARM]\\n\",\n \"[Step 724] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 725] Action: [Move to LEFT ARM]\\n\",\n \"[Step 725] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 726] Action: [Move to LEFT ARM]\\n\",\n \"[Step 726] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 727] Action: [Move to LEFT ARM]\\n\",\n \"[Step 727] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 728] Action: [Move to LEFT ARM]\\n\",\n \"[Step 728] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 729] Action: [Move to LEFT ARM]\\n\",\n \"[Step 729] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 730] Action: [Move to LEFT ARM]\\n\",\n \"[Step 730] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 731] Action: [Move to LEFT ARM]\\n\",\n \"[Step 731] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 732] Action: [Move to LEFT ARM]\\n\",\n \"[Step 732] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 733] Action: [Move to LEFT ARM]\\n\",\n \"[Step 733] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 734] Action: [Move to LEFT ARM]\\n\",\n \"[Step 734] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 735] Action: [Move to LEFT ARM]\\n\",\n \"[Step 735] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 736] Action: [Move to LEFT ARM]\\n\",\n \"[Step 736] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 737] Action: [Move to LEFT ARM]\\n\",\n \"[Step 737] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 738] Action: [Move to LEFT ARM]\\n\",\n \"[Step 738] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 739] Action: [Move to LEFT ARM]\\n\",\n \"[Step 739] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 740] Action: [Move to LEFT ARM]\\n\",\n \"[Step 740] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 741] Action: [Move to LEFT ARM]\\n\",\n \"[Step 741] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 742] Action: [Move to LEFT ARM]\\n\",\n \"[Step 742] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 743] Action: [Move to LEFT ARM]\\n\",\n \"[Step 743] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 744] Action: [Move to LEFT ARM]\\n\",\n \"[Step 744] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 745] Action: [Move to LEFT ARM]\\n\",\n \"[Step 745] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 746] Action: [Move to LEFT ARM]\\n\",\n \"[Step 746] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 747] Action: [Move to LEFT ARM]\\n\",\n \"[Step 747] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 748] Action: [Move to LEFT ARM]\\n\",\n \"[Step 748] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 749] Action: [Move to LEFT ARM]\\n\",\n \"[Step 749] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 750] Action: [Move to LEFT ARM]\\n\",\n \"[Step 750] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 751] Action: [Move to LEFT ARM]\\n\",\n \"[Step 751] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 752] Action: [Move to LEFT ARM]\\n\",\n \"[Step 752] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 753] Action: [Move to LEFT ARM]\\n\",\n \"[Step 753] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 754] Action: [Move to LEFT ARM]\\n\",\n \"[Step 754] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 755] Action: [Move to LEFT ARM]\\n\",\n \"[Step 755] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 756] Action: [Move to LEFT ARM]\\n\",\n \"[Step 756] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 757] Action: [Move to LEFT ARM]\\n\",\n \"[Step 757] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 758] Action: [Move to LEFT ARM]\\n\",\n \"[Step 758] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 759] Action: [Move to LEFT ARM]\\n\",\n \"[Step 759] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 760] Action: [Move to LEFT ARM]\\n\",\n \"[Step 760] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 761] Action: [Move to LEFT ARM]\\n\",\n \"[Step 761] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 762] Action: [Move to LEFT ARM]\\n\",\n \"[Step 762] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 763] Action: [Move to LEFT ARM]\\n\",\n \"[Step 763] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 764] Action: [Move to LEFT ARM]\\n\",\n \"[Step 764] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 765] Action: [Move to LEFT ARM]\\n\",\n \"[Step 765] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 766] Action: [Move to LEFT ARM]\\n\",\n \"[Step 766] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 767] Action: [Move to LEFT ARM]\\n\",\n \"[Step 767] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 768] Action: [Move to LEFT ARM]\\n\",\n \"[Step 768] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 769] Action: [Move to LEFT ARM]\\n\",\n \"[Step 769] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 770] Action: [Move to LEFT ARM]\\n\",\n \"[Step 770] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 771] Action: [Move to LEFT ARM]\\n\",\n \"[Step 771] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 772] Action: [Move to LEFT ARM]\\n\",\n \"[Step 772] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 773] Action: [Move to LEFT ARM]\\n\",\n \"[Step 773] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 774] Action: [Move to LEFT ARM]\\n\",\n \"[Step 774] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 775] Action: [Move to LEFT ARM]\\n\",\n \"[Step 775] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 776] Action: [Move to LEFT ARM]\\n\",\n \"[Step 776] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 777] Action: [Move to LEFT ARM]\\n\",\n \"[Step 777] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 778] Action: [Move to LEFT ARM]\\n\",\n \"[Step 778] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 779] Action: [Move to LEFT ARM]\\n\",\n \"[Step 779] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 780] Action: [Move to LEFT ARM]\\n\",\n \"[Step 780] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 781] Action: [Move to LEFT ARM]\\n\",\n \"[Step 781] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 782] Action: [Move to LEFT ARM]\\n\",\n \"[Step 782] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 783] Action: [Move to LEFT ARM]\\n\",\n \"[Step 783] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 784] Action: [Move to LEFT ARM]\\n\",\n \"[Step 784] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 785] Action: [Move to LEFT ARM]\\n\",\n \"[Step 785] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 786] Action: [Move to LEFT ARM]\\n\",\n \"[Step 786] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 787] Action: [Move to LEFT ARM]\\n\",\n \"[Step 787] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 788] Action: [Move to LEFT ARM]\\n\",\n \"[Step 788] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 789] Action: [Move to LEFT ARM]\\n\",\n \"[Step 789] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 790] Action: [Move to LEFT ARM]\\n\",\n \"[Step 790] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 791] Action: [Move to LEFT ARM]\\n\",\n \"[Step 791] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 792] Action: [Move to LEFT ARM]\\n\",\n \"[Step 792] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 793] Action: [Move to LEFT ARM]\\n\",\n \"[Step 793] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 794] Action: [Move to LEFT ARM]\\n\",\n \"[Step 794] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 795] Action: [Move to LEFT ARM]\\n\",\n \"[Step 795] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 796] Action: [Move to LEFT ARM]\\n\",\n \"[Step 796] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 797] Action: [Move to LEFT ARM]\\n\",\n \"[Step 797] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 798] Action: [Move to LEFT ARM]\\n\",\n \"[Step 798] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 799] Action: [Move to LEFT ARM]\\n\",\n \"[Step 799] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 800] Action: [Move to LEFT ARM]\\n\",\n \"[Step 800] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 801] Action: [Move to LEFT ARM]\\n\",\n \"[Step 801] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 802] Action: [Move to LEFT ARM]\\n\",\n \"[Step 802] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 803] Action: [Move to LEFT ARM]\\n\",\n \"[Step 803] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 804] Action: [Move to LEFT ARM]\\n\",\n \"[Step 804] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 805] Action: [Move to LEFT ARM]\\n\",\n \"[Step 805] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 806] Action: [Move to LEFT ARM]\\n\",\n \"[Step 806] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 807] Action: [Move to LEFT ARM]\\n\",\n \"[Step 807] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 808] Action: [Move to LEFT ARM]\\n\",\n \"[Step 808] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 809] Action: [Move to LEFT ARM]\\n\",\n \"[Step 809] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 810] Action: [Move to LEFT ARM]\\n\",\n \"[Step 810] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 811] Action: [Move to LEFT ARM]\\n\",\n \"[Step 811] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 812] Action: [Move to LEFT ARM]\\n\",\n \"[Step 812] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 813] Action: [Move to LEFT ARM]\\n\",\n \"[Step 813] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 814] Action: [Move to LEFT ARM]\\n\",\n \"[Step 814] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 815] Action: [Move to LEFT ARM]\\n\",\n \"[Step 815] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 816] Action: [Move to LEFT ARM]\\n\",\n \"[Step 816] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 817] Action: [Move to LEFT ARM]\\n\",\n \"[Step 817] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 818] Action: [Move to LEFT ARM]\\n\",\n \"[Step 818] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 819] Action: [Move to LEFT ARM]\\n\",\n \"[Step 819] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 820] Action: [Move to LEFT ARM]\\n\",\n \"[Step 820] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 821] Action: [Move to LEFT ARM]\\n\",\n \"[Step 821] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 822] Action: [Move to LEFT ARM]\\n\",\n \"[Step 822] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 823] Action: [Move to LEFT ARM]\\n\",\n \"[Step 823] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 824] Action: [Move to LEFT ARM]\\n\",\n \"[Step 824] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 825] Action: [Move to LEFT ARM]\\n\",\n \"[Step 825] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 826] Action: [Move to LEFT ARM]\\n\",\n \"[Step 826] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 827] Action: [Move to LEFT ARM]\\n\",\n \"[Step 827] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 828] Action: [Move to LEFT ARM]\\n\",\n \"[Step 828] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 829] Action: [Move to LEFT ARM]\\n\",\n \"[Step 829] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 830] Action: [Move to LEFT ARM]\\n\",\n \"[Step 830] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 831] Action: [Move to LEFT ARM]\\n\",\n \"[Step 831] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 832] Action: [Move to LEFT ARM]\\n\",\n \"[Step 832] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 833] Action: [Move to LEFT ARM]\\n\",\n \"[Step 833] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 834] Action: [Move to LEFT ARM]\\n\",\n \"[Step 834] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 835] Action: [Move to LEFT ARM]\\n\",\n \"[Step 835] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 836] Action: [Move to LEFT ARM]\\n\",\n \"[Step 836] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 837] Action: [Move to LEFT ARM]\\n\",\n \"[Step 837] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 838] Action: [Move to LEFT ARM]\\n\",\n \"[Step 838] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 839] Action: [Move to LEFT ARM]\\n\",\n \"[Step 839] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 840] Action: [Move to LEFT ARM]\\n\",\n \"[Step 840] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 841] Action: [Move to LEFT ARM]\\n\",\n \"[Step 841] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 842] Action: [Move to LEFT ARM]\\n\",\n \"[Step 842] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 843] Action: [Move to LEFT ARM]\\n\",\n \"[Step 843] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 844] Action: [Move to LEFT ARM]\\n\",\n \"[Step 844] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 845] Action: [Move to LEFT ARM]\\n\",\n \"[Step 845] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 846] Action: [Move to LEFT ARM]\\n\",\n \"[Step 846] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 847] Action: [Move to LEFT ARM]\\n\",\n \"[Step 847] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 848] Action: [Move to LEFT ARM]\\n\",\n \"[Step 848] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 849] Action: [Move to LEFT ARM]\\n\",\n \"[Step 849] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 850] Action: [Move to LEFT ARM]\\n\",\n \"[Step 850] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 851] Action: [Move to LEFT ARM]\\n\",\n \"[Step 851] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 852] Action: [Move to LEFT ARM]\\n\",\n \"[Step 852] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 853] Action: [Move to LEFT ARM]\\n\",\n \"[Step 853] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 854] Action: [Move to LEFT ARM]\\n\",\n \"[Step 854] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 855] Action: [Move to LEFT ARM]\\n\",\n \"[Step 855] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 856] Action: [Move to LEFT ARM]\\n\",\n \"[Step 856] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 857] Action: [Move to LEFT ARM]\\n\",\n \"[Step 857] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 858] Action: [Move to LEFT ARM]\\n\",\n \"[Step 858] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 859] Action: [Move to LEFT ARM]\\n\",\n \"[Step 859] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 860] Action: [Move to LEFT ARM]\\n\",\n \"[Step 860] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 861] Action: [Move to LEFT ARM]\\n\",\n \"[Step 861] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 862] Action: [Move to LEFT ARM]\\n\",\n \"[Step 862] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 863] Action: [Move to LEFT ARM]\\n\",\n \"[Step 863] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 864] Action: [Move to LEFT ARM]\\n\",\n \"[Step 864] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 865] Action: [Move to LEFT ARM]\\n\",\n \"[Step 865] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 866] Action: [Move to LEFT ARM]\\n\",\n \"[Step 866] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 867] Action: [Move to LEFT ARM]\\n\",\n \"[Step 867] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 868] Action: [Move to LEFT ARM]\\n\",\n \"[Step 868] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 869] Action: [Move to LEFT ARM]\\n\",\n \"[Step 869] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 870] Action: [Move to LEFT ARM]\\n\",\n \"[Step 870] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 871] Action: [Move to LEFT ARM]\\n\",\n \"[Step 871] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 872] Action: [Move to LEFT ARM]\\n\",\n \"[Step 872] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 873] Action: [Move to LEFT ARM]\\n\",\n \"[Step 873] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 874] Action: [Move to LEFT ARM]\\n\",\n \"[Step 874] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 875] Action: [Move to LEFT ARM]\\n\",\n \"[Step 875] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 876] Action: [Move to LEFT ARM]\\n\",\n \"[Step 876] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 877] Action: [Move to LEFT ARM]\\n\",\n \"[Step 877] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 878] Action: [Move to LEFT ARM]\\n\",\n \"[Step 878] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 879] Action: [Move to LEFT ARM]\\n\",\n \"[Step 879] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 880] Action: [Move to LEFT ARM]\\n\",\n \"[Step 880] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 881] Action: [Move to LEFT ARM]\\n\",\n \"[Step 881] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 882] Action: [Move to LEFT ARM]\\n\",\n \"[Step 882] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 883] Action: [Move to LEFT ARM]\\n\",\n \"[Step 883] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 884] Action: [Move to LEFT ARM]\\n\",\n \"[Step 884] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 885] Action: [Move to LEFT ARM]\\n\",\n \"[Step 885] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 886] Action: [Move to LEFT ARM]\\n\",\n \"[Step 886] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 887] Action: [Move to LEFT ARM]\\n\",\n \"[Step 887] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 888] Action: [Move to LEFT ARM]\\n\",\n \"[Step 888] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 889] Action: [Move to LEFT ARM]\\n\",\n \"[Step 889] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 890] Action: [Move to LEFT ARM]\\n\",\n \"[Step 890] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 891] Action: [Move to LEFT ARM]\\n\",\n \"[Step 891] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 892] Action: [Move to LEFT ARM]\\n\",\n \"[Step 892] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 893] Action: [Move to LEFT ARM]\\n\",\n \"[Step 893] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 894] Action: [Move to LEFT ARM]\\n\",\n \"[Step 894] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 895] Action: [Move to LEFT ARM]\\n\",\n \"[Step 895] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 896] Action: [Move to LEFT ARM]\\n\",\n \"[Step 896] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 897] Action: [Move to LEFT ARM]\\n\",\n \"[Step 897] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 898] Action: [Move to LEFT ARM]\\n\",\n \"[Step 898] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 899] Action: [Move to LEFT ARM]\\n\",\n \"[Step 899] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 900] Action: [Move to LEFT ARM]\\n\",\n \"[Step 900] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 901] Action: [Move to LEFT ARM]\\n\",\n \"[Step 901] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 902] Action: [Move to LEFT ARM]\\n\",\n \"[Step 902] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 903] Action: [Move to LEFT ARM]\\n\",\n \"[Step 903] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 904] Action: [Move to LEFT ARM]\\n\",\n \"[Step 904] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 905] Action: [Move to LEFT ARM]\\n\",\n \"[Step 905] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 906] Action: [Move to LEFT ARM]\\n\",\n \"[Step 906] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 907] Action: [Move to LEFT ARM]\\n\",\n \"[Step 907] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 908] Action: [Move to LEFT ARM]\\n\",\n \"[Step 908] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 909] Action: [Move to LEFT ARM]\\n\",\n \"[Step 909] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 910] Action: [Move to LEFT ARM]\\n\",\n \"[Step 910] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 911] Action: [Move to LEFT ARM]\\n\",\n \"[Step 911] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 912] Action: [Move to LEFT ARM]\\n\",\n \"[Step 912] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 913] Action: [Move to LEFT ARM]\\n\",\n \"[Step 913] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 914] Action: [Move to LEFT ARM]\\n\",\n \"[Step 914] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 915] Action: [Move to LEFT ARM]\\n\",\n \"[Step 915] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 916] Action: [Move to LEFT ARM]\\n\",\n \"[Step 916] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 917] Action: [Move to LEFT ARM]\\n\",\n \"[Step 917] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 918] Action: [Move to LEFT ARM]\\n\",\n \"[Step 918] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 919] Action: [Move to LEFT ARM]\\n\",\n \"[Step 919] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 920] Action: [Move to LEFT ARM]\\n\",\n \"[Step 920] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 921] Action: [Move to LEFT ARM]\\n\",\n \"[Step 921] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 922] Action: [Move to LEFT ARM]\\n\",\n \"[Step 922] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 923] Action: [Move to LEFT ARM]\\n\",\n \"[Step 923] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 924] Action: [Move to LEFT ARM]\\n\",\n \"[Step 924] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 925] Action: [Move to LEFT ARM]\\n\",\n \"[Step 925] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 926] Action: [Move to LEFT ARM]\\n\",\n \"[Step 926] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 927] Action: [Move to LEFT ARM]\\n\",\n \"[Step 927] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 928] Action: [Move to LEFT ARM]\\n\",\n \"[Step 928] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 929] Action: [Move to LEFT ARM]\\n\",\n \"[Step 929] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 930] Action: [Move to LEFT ARM]\\n\",\n \"[Step 930] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 931] Action: [Move to LEFT ARM]\\n\",\n \"[Step 931] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 932] Action: [Move to LEFT ARM]\\n\",\n \"[Step 932] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 933] Action: [Move to LEFT ARM]\\n\",\n \"[Step 933] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 934] Action: [Move to LEFT ARM]\\n\",\n \"[Step 934] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 935] Action: [Move to LEFT ARM]\\n\",\n \"[Step 935] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 936] Action: [Move to LEFT ARM]\\n\",\n \"[Step 936] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 937] Action: [Move to LEFT ARM]\\n\",\n \"[Step 937] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 938] Action: [Move to LEFT ARM]\\n\",\n \"[Step 938] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 939] Action: [Move to LEFT ARM]\\n\",\n \"[Step 939] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 940] Action: [Move to LEFT ARM]\\n\",\n \"[Step 940] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 941] Action: [Move to LEFT ARM]\\n\",\n \"[Step 941] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 942] Action: [Move to LEFT ARM]\\n\",\n \"[Step 942] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 943] Action: [Move to LEFT ARM]\\n\",\n \"[Step 943] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 944] Action: [Move to LEFT ARM]\\n\",\n \"[Step 944] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 945] Action: [Move to LEFT ARM]\\n\",\n \"[Step 945] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 946] Action: [Move to LEFT ARM]\\n\",\n \"[Step 946] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 947] Action: [Move to LEFT ARM]\\n\",\n \"[Step 947] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 948] Action: [Move to LEFT ARM]\\n\",\n \"[Step 948] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 949] Action: [Move to LEFT ARM]\\n\",\n \"[Step 949] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 950] Action: [Move to LEFT ARM]\\n\",\n \"[Step 950] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 951] Action: [Move to LEFT ARM]\\n\",\n \"[Step 951] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 952] Action: [Move to LEFT ARM]\\n\",\n \"[Step 952] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 953] Action: [Move to LEFT ARM]\\n\",\n \"[Step 953] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 954] Action: [Move to LEFT ARM]\\n\",\n \"[Step 954] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 955] Action: [Move to LEFT ARM]\\n\",\n \"[Step 955] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 956] Action: [Move to LEFT ARM]\\n\",\n \"[Step 956] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 957] Action: [Move to LEFT ARM]\\n\",\n \"[Step 957] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 958] Action: [Move to LEFT ARM]\\n\",\n \"[Step 958] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 959] Action: [Move to LEFT ARM]\\n\",\n \"[Step 959] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 960] Action: [Move to LEFT ARM]\\n\",\n \"[Step 960] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 961] Action: [Move to LEFT ARM]\\n\",\n \"[Step 961] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 962] Action: [Move to LEFT ARM]\\n\",\n \"[Step 962] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 963] Action: [Move to LEFT ARM]\\n\",\n \"[Step 963] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 964] Action: [Move to LEFT ARM]\\n\",\n \"[Step 964] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 965] Action: [Move to LEFT ARM]\\n\",\n \"[Step 965] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 966] Action: [Move to LEFT ARM]\\n\",\n \"[Step 966] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 967] Action: [Move to LEFT ARM]\\n\",\n \"[Step 967] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 968] Action: [Move to LEFT ARM]\\n\",\n \"[Step 968] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 969] Action: [Move to LEFT ARM]\\n\",\n \"[Step 969] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 970] Action: [Move to LEFT ARM]\\n\",\n \"[Step 970] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 971] Action: [Move to LEFT ARM]\\n\",\n \"[Step 971] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 972] Action: [Move to LEFT ARM]\\n\",\n \"[Step 972] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 973] Action: [Move to LEFT ARM]\\n\",\n \"[Step 973] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 974] Action: [Move to LEFT ARM]\\n\",\n \"[Step 974] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 975] Action: [Move to LEFT ARM]\\n\",\n \"[Step 975] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 976] Action: [Move to LEFT ARM]\\n\",\n \"[Step 976] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 977] Action: [Move to LEFT ARM]\\n\",\n \"[Step 977] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 978] Action: [Move to LEFT ARM]\\n\",\n \"[Step 978] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 979] Action: [Move to LEFT ARM]\\n\",\n \"[Step 979] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 980] Action: [Move to LEFT ARM]\\n\",\n \"[Step 980] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 981] Action: [Move to LEFT ARM]\\n\",\n \"[Step 981] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 982] Action: [Move to LEFT ARM]\\n\",\n \"[Step 982] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 983] Action: [Move to LEFT ARM]\\n\",\n \"[Step 983] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 984] Action: [Move to LEFT ARM]\\n\",\n \"[Step 984] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 985] Action: [Move to LEFT ARM]\\n\",\n \"[Step 985] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 986] Action: [Move to LEFT ARM]\\n\",\n \"[Step 986] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 987] Action: [Move to LEFT ARM]\\n\",\n \"[Step 987] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 988] Action: [Move to LEFT ARM]\\n\",\n \"[Step 988] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 989] Action: [Move to LEFT ARM]\\n\",\n \"[Step 989] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 990] Action: [Move to LEFT ARM]\\n\",\n \"[Step 990] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 991] Action: [Move to LEFT ARM]\\n\",\n \"[Step 991] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 992] Action: [Move to LEFT ARM]\\n\",\n \"[Step 992] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 993] Action: [Move to LEFT ARM]\\n\",\n \"[Step 993] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 994] Action: [Move to LEFT ARM]\\n\",\n \"[Step 994] Observation: [LEFT ARM, Loss!, Null]\\n\",\n \"[Step 995] Action: [Move to LEFT ARM]\\n\",\n \"[Step 995] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 996] Action: [Move to LEFT ARM]\\n\",\n \"[Step 996] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 997] Action: [Move to LEFT ARM]\\n\",\n \"[Step 997] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 998] Action: [Move to LEFT ARM]\\n\",\n \"[Step 998] Observation: [LEFT ARM, Reward!, Null]\\n\",\n \"[Step 999] Action: [Move to LEFT ARM]\\n\",\n \"[Step 999] Observation: [LEFT ARM, Loss!, Null]\\n\"\n ]\n }\n ],\n \"source\": [\n \"T = 1000 # number of timesteps\\n\",\n \"\\n\",\n \"obs = env.reset() # reset the environment and get an initial observation\\n\",\n \"\\n\",\n \"# these are useful for displaying read-outs during the loop over time\\n\",\n \"reward_conditions = [\\\"Right Arm Better\\\", \\\"Left arm Better\\\"]\\n\",\n \"location_observations = ['CENTER','RIGHT ARM','LEFT ARM','CUE LOCATION']\\n\",\n \"reward_observations = ['No reward','Reward!','Loss!']\\n\",\n \"cue_observations = ['Null','Cue Right','Cue Left']\\n\",\n \"msg = \\\"\\\"\\\" === Starting experiment === \\\\n Reward condition: {}, Observation: [{}, {}, {}]\\\"\\\"\\\"\\n\",\n \"print(msg.format(reward_conditions[env.reward_condition], location_observations[obs[0]], reward_observations[obs[1]], cue_observations[obs[2]]))\\n\",\n \"\\n\",\n \"pA_history = []\\n\",\n \"\\n\",\n \"all_actions = np.zeros((T, 2))\\n\",\n \"for t in range(T):\\n\",\n \" \\n\",\n \" qx = agent.infer_states(obs)\\n\",\n \"\\n\",\n \" q_pi, efe = agent.infer_policies()\\n\",\n \"\\n\",\n \" action = agent.sample_action()\\n\",\n \"\\n\",\n \" pA_t = agent.update_A(obs)\\n\",\n \" pA_history.append(pA_t)\\n\",\n \" \\n\",\n \" msg = \\\"\\\"\\\"[Step {}] Action: [Move to {}]\\\"\\\"\\\"\\n\",\n \" print(msg.format(t, location_observations[int(action[0])]))\\n\",\n \"\\n\",\n \" obs = env.step(action)\\n\",\n \"\\n\",\n \" all_actions[t,:] = action\\n\",\n \"\\n\",\n \" msg = \\\"\\\"\\\"[Step {}] Observation: [{}, {}, {}]\\\"\\\"\\\"\\n\",\n \" print(msg.format(t, location_observations[int(obs[0])], reward_observations[int(obs[1])], cue_observations[int(obs[2])]))\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"metadata\": {\n \"scrolled\": true\n },\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n 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\",\n 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\",\n 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(agent.A[1][1:,:,0],'Final beliefs about reward contingencies under the condition that the reward condition is RIGHT ARM BETTER')\\n\",\n \"plot_likelihood(A_gp[1][1:,:,0],'True reward contingencies under the condition that the reward condition is RIGHT ARM BETTER')\\n\",\n \"\\n\",\n \"plot_likelihood(agent.A[1][1:,:,1],'Final beliefs about reward contingencies under the condition that the reward condition is LEFT ARM BETTER')\\n\",\n \"plot_likelihood(A_gp[1][1:,:,1],'True reward contingencies under the condition that the reward condition is LEFT ARM BETTER')\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n },\n {\n \"data\": {\n \"image/png\": 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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {\n \"needs_background\": \"light\"\n },\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plot_likelihood(agent.A[2][1:,:,1],'Final beliefs about cue mapping')\\n\",\n \"plot_likelihood(A_gp[2][1:,:,1],'True contingencies underlying the cue mapping')\"\n ]\n }\n ],\n \"metadata\": {\n \"kernelspec\": {\n \"display_name\": \"Python 3.8.8 ('base')\",\n \"language\": \"python\",\n \"name\": \"python3\"\n },\n \"language_info\": {\n \"codemirror_mode\": {\n \"name\": \"ipython\",\n \"version\": 3\n },\n \"file_extension\": \".py\",\n \"mimetype\": \"text/x-python\",\n \"name\": \"python\",\n \"nbconvert_exporter\": \"python\",\n \"pygments_lexer\": \"ipython3\",\n \"version\": \"3.8.8\"\n },\n \"vscode\": {\n \"interpreter\": {\n \"hash\": \"70b7ceca5df5387258d861d4588082cea9500e731be001548c95afd8cd8c3af8\"\n }\n }\n },\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "examples/model_fitting/fitting_with_pybefit.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"id\": \"0\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"The autoreload extension is already loaded. To reload it, use:\\n\",\n \" %reload_ext autoreload\\n\"\n ]\n }\n ],\n \"source\": [\n \"%load_ext autoreload\\n\",\n \"%autoreload 2\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"id\": \"1\",\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"from jax import numpy as jnp, random as jr\\n\",\n \"from jax import tree_util as jtu\\n\",\n \"from jax import vmap, nn, lax\\n\",\n \"\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import numpy as np\\n\",\n \"\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"from pymdp.envs import TMaze\\n\",\n \"\\n\",\n \"from pybefit.inference import (\\n\",\n \" run_nuts,\\n\",\n \" run_svi,\\n\",\n \" default_dict_nuts,\\n\",\n \" default_dict_numpyro_svi,\\n\",\n \")\\n\",\n \"\\n\",\n \"from pybefit.inference import NumpyroModel, NumpyroGuide\\n\",\n \"from pybefit.inference import Normal, NormalPosterior\\n\",\n \"from pybefit.inference.numpyro.likelihoods import pymdp_likelihood as likelihood\\n\",\n \"from numpyro.infer import Predictive\\n\",\n \"\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"2\",\n \"metadata\": {},\n \"source\": [\n \"## Fitting the parameters of active inference agents performing in the `T-Maze` environment\\n\",\n \"\\n\",\n \"We set up a TMaze instance with a fully reliable cue-to-reward mapping, so the cue unambiguously reveals the rewarding arm. We also set the rewarded-arm outcome mapping to be probabilistic at 80%. This means that in the rewarded arm, reward is observed with probability 0.8 and punishment with probability 0.2, while these probabilities are inverted in the punished arm (`dependent_outcomes=True`).\\n\",\n \"\\n\",\n \"We also parameterize 10 different agent-environment pairs (`batch_size=10`), 100 experimental blocks (episodes) per agent, and 5 timesteps per block.\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"3\",\n \"metadata\": {},\n \"source\": [\n \"
\\n\",\n \"Explanatory note on batch_size, subject, block, timestep, and trial terminology\\n\",\n \"\\n\",\n \"Experimental data collected from individual participants or subjects in psychological and psychiatric studies often follows a multi-level temporal structure. Typically, each subject participates in a task independently from other participants, and each subject performs multiple episodes or blocks sequentially (for example, 20 blocks of 100 trials per block).\\n\",\n \"\\n\",\n \"Depending on the experimental design, blocks may be independent or may include between-block correlations (for example, regular changes in initial task state across blocks). Within each block, individual \\\"trials\\\" or \\\"timesteps\\\" occur sequentially. There can also be within-block, between-trial correlation structure, and this is an assumption we make in `pymdp`: a single active inference process unfolds across these timesteps.\\n\",\n \"\\n\",\n \"Because the word \\\"trial\\\" often refers to events that have their own internal temporal structure, this notebook uses `timesteps` to reduce ambiguity. This aligns with reinforcement learning and active inference workflows, where these are naturally treated as timesteps and blocks are naturally treated as episodes.\\n\",\n \"\\n\",\n \"
\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"id\": \"4\",\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"seed_key = jr.PRNGKey(101)\\n\",\n \"\\n\",\n \"# setting the parameters for the environment\\n\",\n \"num_blocks = 100 # number of blocks (number of multi-timestep episodes that are run sequentially, per agent)\\n\",\n \"num_timesteps = 5 # number of timesteps (or \\\"trials\\\") per block\\n\",\n \"\\n\",\n \"reward_condition = None # 0 is reward in left arm, 1 is reward in right arm, None is random allocation\\n\",\n \"reward_probability = 0.8 # 80% chance of reward in the correct arm\\n\",\n \"punishment_probability = 0.0 # only used when dependent_outcomes=False\\n\",\n \"cue_validity = 1.0 # 100% valid cues\\n\",\n \"dependent_outcomes = True # if True, reward and punishment probabilities are coupled across arms via reward_probability. If False, punishment occurs with the fixed punishment_probability.\\n\",\n \"\\n\",\n \"# initialising the environment. see tmaze.py in pymdp/envs for the implementation details.\\n\",\n \"task = TMaze( \\n\",\n \" reward_probability=reward_probability, \\n\",\n \" punishment_probability=punishment_probability, \\n\",\n \" cue_validity=cue_validity, \\n\",\n \" reward_condition=reward_condition,\\n\",\n \" dependent_outcomes=dependent_outcomes\\n\",\n \")\\n\",\n \"\\n\",\n \"batch_size = 10 # batch_size, which in this case corresponds to the number of agents to fit in parallel\\n\",\n \"key, _key = jr.split(seed_key)\\n\",\n \"init_obs, init_states = vmap(task.reset)(jr.split(_key, batch_size))\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"id\": \"5\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_95807/2592818604.py:42: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" return Agent(\\n\"\n ]\n }\n ],\n \"source\": [\n \"# Constrained recoverable setup: infer only reward-probability beliefs.\\n\",\n \"# Keep preference strength (lambda) and initial reward-state prior fixed.\\n\",\n \"num_params = 1\\n\",\n \"num_agents = batch_size\\n\",\n \"prior = Normal(num_params, num_agents, backend=\\\"numpyro\\\")\\n\",\n \"\\n\",\n \"\\n\",\n \"def transform(z):\\n\",\n \" na, _ = z.shape\\n\",\n \"\\n\",\n \" reward_prob = 0.5 + 0.5 * nn.sigmoid(z[..., 0]) # constrain reward probability to be between 0.5 and 1\\n\",\n \" lam = jnp.full((na,), 1.2)\\n\",\n \"\\n\",\n \" A = lax.stop_gradient(task.A)\\n\",\n \" A = jtu.tree_map(lambda x: jnp.broadcast_to(x, (na,) + x.shape), A)\\n\",\n \" B = lax.stop_gradient(task.B)\\n\",\n \" B = jtu.tree_map(lambda x: jnp.broadcast_to(x, (na,) + x.shape), B)\\n\",\n \"\\n\",\n \" one_minus = 1.0 - reward_prob\\n\",\n \"\\n\",\n \" reward_left = jnp.stack([reward_prob, one_minus], -1)\\n\",\n \" punish_left = jnp.stack([one_minus, reward_prob], -1)\\n\",\n \" reward_right = jnp.stack([one_minus, reward_prob], -1)\\n\",\n \" punish_right = jnp.stack([reward_prob, one_minus], -1)\\n\",\n \" zeros = jnp.zeros_like(reward_left)\\n\",\n \"\\n\",\n \" side = jnp.broadcast_to(jnp.array([[1., 1.], [0., 0.], [0., 0.]]), (na, 3, 2))\\n\",\n \" left_col = jnp.stack([zeros, reward_left, punish_left], axis=-2)\\n\",\n \" right_col = jnp.stack([zeros, reward_right, punish_right], axis=-2)\\n\",\n \" A[1] = jnp.stack([side, left_col, right_col, side, side], axis=-2)\\n\",\n \"\\n\",\n \" C = [\\n\",\n \" jnp.zeros((na, A[0].shape[1])),\\n\",\n \" jnp.expand_dims(lam, -1) * jnp.array([0., 1., -1.]),\\n\",\n \" jnp.zeros((na, A[2].shape[1])),\\n\",\n \" ]\\n\",\n \" D = [\\n\",\n \" jnp.zeros((na, B[0].shape[1])).at[:, 0].set(1.0),\\n\",\n \" jnp.full((na, 2), 0.5),\\n\",\n \" ]\\n\",\n \"\\n\",\n \" return Agent(\\n\",\n \" A,\\n\",\n \" B,\\n\",\n \" C=C,\\n\",\n \" D=D,\\n\",\n \" policy_len=2,\\n\",\n \" A_dependencies=task.A_dependencies,\\n\",\n \" B_dependencies=task.B_dependencies,\\n\",\n \" batch_size=na,\\n\",\n \" action_selection=\\\"stochastic\\\",\\n\",\n \" )\\n\",\n \"\\n\",\n \"\\n\",\n \"key, _key = jr.split(seed_key)\\n\",\n \"# Use a broad, deterministic latent grid so recoverability is visible across agents.\\n\",\n \"z = jnp.linspace(-2.5, 2.5, num_agents).reshape(num_agents, num_params)\\n\",\n \"\\n\",\n \"agents = transform(z)\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"6\",\n \"metadata\": {},\n \"source\": [\n \"### Sample from the TMaze environment and visualize the results from one block, showing the expected behavior (visit the cue, then choose an arm)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"id\": \"7\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_95807/2592818604.py:42: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" return Agent(\\n\"\n ]\n }\n ],\n \"source\": [\n \"opts_task = {\\n\",\n \" \\\"task\\\": task,\\n\",\n \" \\\"num_blocks\\\": num_blocks,\\n\",\n \" \\\"num_trials\\\": num_timesteps,\\n\",\n \" \\\"num_agents\\\": num_agents,\\n\",\n \"}\\n\",\n \"opts_model = {\\\"prior\\\": {}, \\\"transform\\\": {}, \\\"likelihood\\\": opts_task}\\n\",\n \"\\n\",\n \"model = NumpyroModel(prior, transform, likelihood, opts=opts_model)\\n\",\n \"\\n\",\n \"pred = Predictive(model, num_samples=1)\\n\",\n \"key, _key = jr.split(key)\\n\",\n \"samples = pred(_key)\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 4,\n \"id\": \"8\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"frames = []\\n\",\n \"for t in range(num_timesteps): # iterate over timesteps\\n\",\n \" # get observations for this timestep\\n\",\n \" observations_t = [\\n\",\n \" samples[\\\"outcomes\\\"][0][0,0,:, t], # subset by predictive sample (first leading dimension) and block (second leading dimension)\\n\",\n \" samples[\\\"outcomes\\\"][1][0,0,:, t], \\n\",\n \" samples[\\\"outcomes\\\"][2][0,0,:, t] \\n\",\n \" ]\\n\",\n \" observations_t = jtu.tree_map(lambda x: jnp.expand_dims(x, -1), observations_t) # add lagging dimension as is done before returning in task.step()\\n\",\n \" \\n\",\n \" frame = task.render(mode=\\\"rgb_array\\\", observations=observations_t).astype(jnp.uint8) # render the environment using the observations for this timestep\\n\",\n \" plt.close() # close the figure to prevent memory leak\\n\",\n \" frames.append(frame)\\n\",\n \"\\n\",\n \"frames = jnp.array(frames, dtype=jnp.uint8)\\n\",\n \"\\n\",\n \"## Make a panel of subplots showing the frames at different timesteps of the video sequence (don't assume mediapy dependency)\\n\",\n \"fig, axes = plt.subplots(1, num_timesteps, figsize=(15, 5))\\n\",\n \"for i in range(num_timesteps):\\n\",\n \" axes[i].imshow(frames[i])\\n\",\n \" axes[i].axis('off')\\n\",\n \" axes[i].set_title(f'Timestep {i+1}')\\n\",\n \"plt.show()\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"9\",\n \"metadata\": {},\n \"source\": [\n \"### Inference Method 1: HMC with NUTS\\n\",\n \"\\n\",\n \"Use the No U-Turn Sampler (NUTS) for Hamiltonian Monte Carlo sampling-based inference to sample from the parameter posterior. `pybefit` provides useful wrappers for setting up an NUTS-HMC run.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 5,\n \"id\": \"10\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"{'seed': 0, 'num_samples': 100, 'num_warmup': 400, 'sampler_kwargs': {'kernel': {}, 'mcmc': {'progress_bar': True}}}\\n\"\n ]\n },\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_95807/2592818604.py:42: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" return Agent(\\n\",\n \"sample: 100%|██████████| 500/500 [05:56<00:00, 1.40it/s, 7 steps of size 7.24e-01. acc. prob=0.82] \\n\"\n ]\n }\n ],\n \"source\": [\n \"# perform inference on parameters using no-u-turn sampler (NUTS)\\n\",\n \"# opts_sampling dictionary can be used to specify various parameters\\n\",\n \"# either for the NUTS kernel or MCMC sampler\\n\",\n \"measurements = {\\n\",\n \" \\\"outcomes\\\": [outcomes[0] for outcomes in samples[\\\"outcomes\\\"]],\\n\",\n \" \\\"multiactions\\\": samples[\\\"multiactions\\\"][0],\\n\",\n \"}\\n\",\n \"\\n\",\n \"opts_sampling = default_dict_nuts\\n\",\n \"opts_sampling[\\\"num_warmup\\\"] = 400\\n\",\n \"opts_sampling[\\\"num_samples\\\"] = 100\\n\",\n \"opts_sampling[\\\"sampler_kwargs\\\"] = {\\\"kernel\\\": {}, \\\"mcmc\\\": {\\\"progress_bar\\\": True}}\\n\",\n \"print(opts_sampling)\\n\",\n \"\\n\",\n \"mcmc_samples, mcmc = run_nuts(model, measurements, opts=opts_sampling)\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"11\",\n \"metadata\": {},\n \"source\": [\n \"### Plot each ground truth parameter alongside their posterior means (mean taken over parallel HMC samples/chains)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 6,\n \"id\": \"12\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 6,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plt.figure(figsize=(16, 5))\\n\",\n \"ground_truth_z = samples['z'][0]\\n\",\n \"for i in range(num_params):\\n\",\n \" plt.scatter(ground_truth_z[:, i], mcmc_samples[\\\"z\\\"].mean(0)[:, i], label=i)\\n\",\n \"\\n\",\n \"plt.plot((ground_truth_z.min(), ground_truth_z.max()), (ground_truth_z.min(), ground_truth_z.max()), \\\"k--\\\")\\n\",\n \"plt.ylabel(\\\"posterior mean (MCMC)\\\")\\n\",\n \"plt.xlabel(\\\"true value\\\")\\n\",\n \"plt.legend(title=\\\"parameter id\\\")\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"13\",\n \"metadata\": {},\n \"source\": [\n \"### Transform the latent parameter corresponding to the reward probability into probability space and investigate overlap between ground-truth and inferred parameter\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 7,\n \"id\": \"14\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"reward-probability Pearson r: 0.906\\n\",\n \"reward-probability bimodality score: 0.100\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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2ENBsxX+74dJn0n7Da/tRt3Z+WvvjiC/tH/fvvv8uoUaOsv2Pr1q0t4PXnn39akE5/AGjfBqUBLv3BoSXFSgN0GlTUHxBeuk8DZSoqKkrq1asnM2bMsMDnAw88YAHPFStWXHEde/bskVtuuUW6du1qQVANesYPgl7J4MGD5dZbb7XU77vuuktuv/122bhxY4Jz9Fr9+/e3/RoQ1UDiW2+9Jf/5z39k7dq1tk8ne23dujXB5z311FPyxBNP2PffuHFjW58GYZUGOTXAOWnSJNmwYYMMGTJEnnvuOfnuu+8SXEMni+nX1b8zDdZqSbcGLFPC+/c4d+5cK/3Wa11//fUWmP3qq6+c8/TOkgZi77333hR9HQAAAAAAUpMGIEePHm3DbDSucNttt8nixYud4w8++KBMnTrV3nPre91evXrZefAjHlzi5MmTms5of17s3Llzng0bNtifKTHr7/2eMs9M95S+6FHm/x96PC20aNHCU6dOnQT7Xn75Zc8NN9yQYN+ePXvse9+8ebNt161b1/Pmm2/axzfddJPn1Vdf9QQFBXkiIyM9e/futXO3bNly2a/buXNnzxNPPHHFdTz77LOeatWqJdj3zDPP2LWPHz9+2Wvr8YceeijBvoYNG3r69u1rH+/cudPOGTlyZIJzihUrZt9HfA0aNPA8/PDDCT7v9ddfd47HxMR4SpQo4RkxYsRl19OvXz/Prbfe6mz36tXLkz9/fs+ZM2ecfR9//LEnd+7cntjYWOfvo3///s7x0qVLe955550E3+OUKVMSrOuvv/5K8HV1TVWrVnW2f/jhB/sap0+fTnSd1/ocBgAAAADgavbv32/vqxs1auQJCAiw97PeR4UKFTw//vijx59diI3zLNl2xPPjX3vtT932p/jaxehBmY60jHvYtA32r/Fiuk/bu+rxdtWKSpbA1G/2qtmN8WnW4YIFC6y8+2Lbt2+3kmstjdbsP80kXLRokQwfPtyyBPVOx7Fjx6RYsWJSsWLF/35/sbHWN0KP79u3z0qZz58/b+XeV1qHZhg2bNgwwT7NWEyKi8/T7Yunb9evX9/5+NSpU7J//35p2rRpgnN029uAN7FrayNevU787MwPP/xQxowZY2no586ds+/34uE1tWrVSvD96zVPnz5tWaOp1TdDp4W/8MILsmzZMmnUqJGlwmsWbK5cuVLl+gAAAAAAXI1WGmoVZmhoqG1rXCB+dWR4eLj1k7zpppukatWqfj3kRitoNf4TcTLK2RcWGixDu1aTDtXDxB8RoExHK3YeS/DkSyxIqcf1vMblC6T61784YKWBMi1bHjFixCXnhoX99x+Elm9rEE6Dd9rrsEqVKrZPg5bHjx+3AKbXm2++aeXTI0eOtP6T+vW0F2L8nouJrSOtpcXXmzBhgjz55JNWKq5Bx5CQEPv+ly9fLumtcOHC9v9x7Nix1qdy1qxZCcrwAQAAAABIC9rqTVub6eRtLdHWGRH63tSbnHTnnXda+zhtq6YJTvhvcLLv16suSV47cDLK9n/co65fBikJUKajQ5FRqXretapbt641pi1TpoxlCCbG24fynXfecYKRGqB8/fXXLUCpmZVe2lNS74Z4h+bo3ZMtW7ZItWrVrrgOvXOiP8ji02zApNDzevbsmWBbe2pejg6q0R+Kutb4wVXd1rs5F19bezwqbd67cuVKG/DjPV8H6Dz88MMJsk4vpoFdza7URr/ea2rGasmSJSW5vE2BvUOL4tO+nTqgSPtili9f/pIMUQAAAAAAUoPGAnT2hA501VkWZ86ccY5p5aV2K9PsSH3ofARknMrajIwhOemocEhwqp53rfr162dl2hrY+uOPPyzANmfOHOndu7cTBMuXL5/UrFnTfqh4h+Fo0G7VqlUWfIwf5NNS719++UWWLFlipdDa5FaH7lyNTrbWATU6lGbz5s3y7bffWplyUuiQGs3w1LUMHTrUBsl4g4iXo19Hs0Z1urd+PU0517JwHaQTn5ZwT5kyxaZ569+V/hD2Dp7R71UHC+nfl35tHdajf4cX0+xRnfatg3R0UrmuUdcXGBiYokxJDXR6hxmdPHnSOaaDfjT4+sorr9j/PwAAAAAA0kKrVq1sIK4mPGlwsnjx4vae+eeff7b3vv5cup2albX+hgBlOgovm996Clzun6ru1+N6XnrwZhJqMPKGG26wsmwtyc6bN2+CAJoGIfUcb4Ayf/78lhVZtGhRqVy5snOe9kHUrEwNlum5elx7S1xNqVKl7Aeb3n3Rno062Vt7WSaFTsTWcmsNon755Zc2KftqGZuPPfaYDBw40LI/9XvWgJ9mcHp7aXpplqg+dE3ac1PP8U4R0+CrTh7v3r279c/USWPxsym92rRpY9fVoK6eq2ntL774oqSEZrm+99578sknn9j/O81W9dL/X9qLUv8/xc8oBQAAAAAguTQLUhN59P2rVg9qZaCXTuLW99IaA9DEHZ2x8MEHH0i7du2cyj9kjsrajCRAJ+W4vYiMRgepaFNXzVDTrLSL+yvs3LnTev0FBwenuNeAiv8X7w1a+muvgZTQuzKa4ZiUIKg/0EzNw4cPX1Iuf7FrfQ4DAAAAAHxPTEyMlWhrP0l97Nq1yzmm7zN19oG3Bdrl2sThypZuPyp3fHr1lnbj+zRKk9kkGSm+djGeUelMg48ahLx4WlNRP5/WhJTTf+h///23lcZfLTgJAAAAAMDFpk+fbtV42trMS1uMaYWkVu/Fn3NAcPLaK2t1IE5i2YIB/x8fSq/K2oyEZ5ULNAipDU+1p4Cm7WrPSX3y+VsDVKQO/WWhvTe1l6em1AMAAAAAcDkHDhyQadOmSYUKFayfpNLWZBqc1LZm2ppM32e2bdtWcubM6fZyfYrGfTQ5TStrAy5TWTu0azW/jA8RoHSJPtl8IV3XTXQn+K+FCxe6vQQAAAAAQAamA2K1bFtnPyxbtszeT996661OgFLnS+j++vXrS5YsWdxerk+jsjZxBCgBAAAAAAB8jAYhn3/+eZvdsGnTpgTHNBAZv2xb6QBYpA8qay9FgBIAAAAAACCT04GoOnm7UaNGzmDZ+fPnW3AyW7Zsli2ppdtawl2iRAm3l+v3qKxNiABlClFejMyK5y4AAAAA+AbtGzljxgwr3541a5acP39eDh8+LHnz5rXjzz33nJw9e1Y6duxo05SBjIoAZTLpXQel/8B1ohWQ2URHR9uf9BUBAAAAgMxn3759MnnyZOsn+euvv0psbKxzrFixYrJ161Zp0KCBbWu2JJAZEKBMJg3q6J2IQ4cO2bZOtNK0aSAziIuLs7tp+rzNmpV//gAAAACQGargLly44CRMTZ06VR577DHn+HXXXSc33XSTlW/Xq1dPAgMDXVwtkDJEKFKgaNGi9qc3SAlkJvrLqlSpUgTWAQAAACCD0oDkokWLnMnbzzzzjPTt29fJihw/frwFJPVRoUIFt5cLXLMADw3pLnHq1CnrzXDy5EnJkyfPZc/TNOqYmJh0XRtwrYKCgrijBgAAAAAZzJkzZ2TOnDkWkNS+kseOHXOOde7cWaZPn+7q+oC0iq8pMiivsdybPn4AAAAAAOBaJ3CHhYVJZGSks69AgQLStWtXy5Js166dq+sD0hoBSgAAAAAAgHSiQ2w0S3L79u0yatQo2xccHCwNGzaUHTt2OP0kmzRpwuwA+A1KvK8xBRUAAAAAAOBKw0r/+OMPC0pqT8mNGzcmmMitk7eVNwbBvAD4Ckq8AQAAAAAAXPbpp5/K0KFDJSIiwtmnWZGtWrWyTMmcOXM6+zWQA/grApQAAAAAAADX6MSJEzJz5kxp2rSplC5d2ind1uBkSEiIdOrUyUq3O3bsKHnz5nV7uUCGQoASAAAAAAAgBfbs2WNl2/pYuHChXLhwQUaMGCFPP/20HdchN7Nnz5aWLVtK9uzZ3V4ukGERoAQAAAAAAEgi7af33nvvWU/JVatWJTh23XXXSf78+Z1tzZRs3769C6sEMhcClAAAAAAAAJehWZE6zMZbth0UFCSvv/66nD171gbaaEm3d/J2hQoV3F4ukCkRoAQAAAAAAIjnzJkz8vPPP1uW5PTp06Vo0aKyfv16O5YjRw4ZMmSIFCpUSLp06SKFCxd2e7lApkeAEgAAAAAA+L1Dhw7JtGnTrJ/kL7/8IlFRUc4xzZQ8fPiwBSXVM8884+JKAd9DgBIAAAAAAPg9DTqOGzfO2S5XrpyVbWv5dpMmTSRrVkIoQFoJFJd9+OGHUqZMGQkODpaGDRvKihUrrnj+yJEjpXLlypZSXbJkSRkwYECCuxovvvii3dmI/6hSpUo6fCcAAAAAACAji4uLs7jDc889ZwNt/vzzT+eYBiLr1asnL7/8sqxdu1a2bdsmb7/9tlx//fUEJ4E05uq/sIkTJ8rAgQNl1KhRFpzU4KNOt9q8eXOiPRy+/fZbGTRokIwZM8buXmzZskXuueceC0LqDw0v/SEzd+5cZ5sfJAAAAAAA+Kfz58/LggULrJ/k1KlTJSIiwjmm5dz169e3jzVbUh8A0p+rkTsNKvbp00d69+5t2xqonDFjhgUgNRB5sSVLlth0rDvvvNO2NfPyjjvukOXLlyc4TwOS2sAWAAAAAAD4rw0bNkijRo0kMjLS2Zc7d27p1KmTZUx27NjR1fUBcLnEOzo6WlauXClt27Z19gUGBtr20qVLE/0czZrUz/GWge/YsUNmzpxpP1ji27p1qxQrVsz6Rdx1112ye/fuq95NOXXqVIIHAAAAAADIPPbs2WNt5DT5yatSpUqSLVs2CQsLkwcffFBmzZolR44csYpOTXjKmzevq2sG4HIGpf5AiI2NlSJFiiTYr9ubNm1K9HM0c1I/r1mzZuLxeOTChQvy0EMPWe8ILy0V16a22qdS07aHDRsmzZs3l3Xr1klISEii1x0+fLidBwAAAAAAMgeNC+h7fS3d1seqVatsf6lSpSwYqe3gtMLyjz/+sApMTYoCkDFlquaMCxculNdee00++ugjC0Rqw9r+/ftbA9vBgwfbOfHTs2vWrGnnlS5dWr777ju57777Er3us88+a70wvTSDUgfwAAAAAACAjOf111+X0aNHy86dO519GpBs3LixlW7HxMRIUFCQ7dfqSgAZm2sByoIFC0qWLFnk4MGDCfbr9uX6R2oQ8u6775b777/ftmvUqCFnzpyRBx54QJ5//vlE74ZouramdGsw83KyZ89uDwAAAAAAkLHo+/5ffvlFunTp4gzB3b9/vwUn9b18u3btLCipxy+u0gSQObiW36x3MurVqyfz5s1z9sXFxdm23vFIzNmzZy8JQmqQ05vanZjTp0/L9u3brd8EAAAAAADI+A4fPmwDdHWqtiY43XzzzbJ48WLnuCYq/fDDD9YGbtq0aVYxSXASyLxcLfHWsupevXpJ/fr1JTw8XEaOHGl3RrxTvXv27CnFixe3HpGqa9euNvm7Tp06Tom3ZlXqfm+g8sknn7RtLevWOypDhw61Y9r8FgAAAAAAZExaUfn111/LTz/9JL///rslMXlpD8njx48729WrV7cHAN/gaoCye/fudldkyJAhcuDAAaldu7bMnj3bueuh07fjZ0y+8MIL1lNC/9y3b58UKlTIgpGvvvqqc87evXstGHn06FE7rgN1li1bZh8DAAAAAICMQQOQWvWYJ08eZwq3Jh151a1b1zIotXxbW7xpPACAbwrwXK422o/pkJzQ0FA5efKk84MSAAAAAABcm+joaFmwYIFlSU6dOtX6R44dO9aOaXhCE4400ahbt242jRuAf8TXMtUUbwAAAAAAkLlocGLWrFny448/2p8atPBauHChBSY1O1IfEyZMcHWtANxBgBIAAAAAAKSZli1byurVq53tokWLWoaklm63atWK0m0ABCgBAAAAAMC10SzI9evXW+m2zpb4+eefJUeOHHasU6dOEhUVZQFJ7SmpQ3Ljz5sAAHpQJoIelAAAAAAAXFlsbKxN29agpD62b9/uHNP+kjrUVsXExEi2bNlcXCkAN9CDEgAAAAAApJmZM2dKr1695MiRI86+7Nmz29AbzZJs3Lixs5/gJICrIUAJAAAAAAAu6/DhwzJ9+nQpV66ctGjRwvaVL1/egpP58uWTLl26WPn2DTfcILlz53Z7uQAyIQKUAAAAAAAgAS3X1rJtnbytZdxxcXFy2223OQHKypUry+LFi6Vhw4aSNSuhBQDXhp8iAAAAAADABt0MHTpUpkyZIuvWrUtwrE6dOhaMjK9p06bpvEIAvooAJQAAAAAAfig6OlrWrFkjDRo0sO2AgACbvq3BySxZskjLli2tn2S3bt2kdOnSbi8XgA8jQAkAAAAAgJ/QabqzZs2y8m0ddHP27FnrMZk3b147PmjQIDlz5ox06tTJ+ksCQHogQAkAAAAAgA+LiIiwXpL6WLBggcTExDjHihQpIlu2bJHw8HDb1mE3AJDeCFACAAAAAOBjvSRjY2Od4TXaU7Jfv37OcR1wo4FIfWhgMjAw0MXVAgABSgAAAAAAMj0NSC5ZssSZvP3EE09I37597Zj2kPz666+tn6Q+qlSp4vZyASCBAI/eWkECp06dktDQUOvNkSdPHreXAwAAAADAJbR/5Ny5cy0gOW3aNDly5IhzTHtIzpgxw9X1AfBvp5IRXyODEgAAAACATCYqKkqKFStmb/y9dNBNly5dLEuyffv2rq4PqSc2ziMrdh6TQ5FRUjgkWMLL5pcsgQFuLwtIVQQoAQAAAADIwHbs2GGl21u3bpWPPvrI9gUHB0uDBg1swI0GJLWfZPPmzSVbtmxuLxepaPa6CBk2bYNEnIxy9oWFBsvQrtWkQ/UwV9cGpCZKvBNBiTcAAAAAwC36Nn3VqlVWuq2Byb///ts5tm/fPsucVMePH7esyYAAsul8NTjZ9+tVcnHQxvt/++MedQlSIkOjxBsAAAAAgExozJgxMnToUNm7d6+zL0uWLHL99ddbpmSOHDmc/fny5XNplUiPsm7NnEwso8zz/0FKPd6uWlHKveETCFACAAAAAOBSdtHs2bOlUaNGUqpUKdunJdoanMyVK5d06NDBgpKdO3eW/Pnzu71cpCPtORm/rDuxIKUe1/Maly+QrmsD0gIBSgAAAAAA0klERIRMnTrVyrfnz58v0dHRMmLECHn66afteNeuXWX69OnSpk0b6zMJ/6QDcVLzPMCnApQbN26UCRMmyKJFi2TXrl1y9uxZKVSokNSpU8cmhN16662SPXv2tFstAAAAAACZMFPyww8/tH6Sy5cvT3CsUqVK1qPNS3tKasYk/JtO607N8wCfGJKjzXn1bs7ixYuladOmEh4ebk15tffFsWPHZN26dRa01B+6et7jjz+eqQOVDMkBAAAAAKRUbGysZUqWKFHCts+dOycFCxa0JB+lJd3eydtVqlRxebXIqD0om42YLwdORiXah1K7ThYNDZbFz7SmByX8Z0iOZkY+9dRT8v3339vdnMtZunSpvPvuu/LWW2/Jc889l/yVAwAAAACQCWkQcu7cuZYlqSXcWm24fv16O6bJPc8//7wFKbWEOyyMycu4Mg06Du1azaZ4a/gxfpDSG47U4wQn4VcZlDExMdaoN6mSe35GQwYlAAAAAOBqjh49KjNmzLB+knPmzHEyJJUm92zZssUClUBKzV4XYdO64w/MCQsNtuBkh+oEuuE78bUkBSj9DQFKAAAAAMDV9O7dW8aNG+dslyxZ0sq2tXz7+uuvz9SJO8hY5d46rVsH4mjPyfCy+cmchM/F1wKTelGdLlatWjW7+MX0C1133XXWhxIAAAAAAF+hOT06l2HIkCFSq1Yt+fPPP51jGojUfXpMz9Fhsu+9955N4CY4idSiwcjG5QvIjbWL258EJ+HXU7xHjhwpffr0STTiqdHQBx98UN5++21p3rx5aq8RAAAAAIB0o23Lfv31V+snqY89e/Y4x3S7fv369rF30A0AIJ0ClGvWrJERI0Zc9vgNN9wg//nPf65xOQAAAAAAuGfjxo3SpEkTOXHihLMvZ86c0qFDBwtIdu7c2dkfEEAmGwCka4Dy4MGDV0xRz5o1qxw+fDhVFgUAAAAAQFqLiIiwidtKqwJVxYoVLfBYuHBh6datmwUltWRbJ3EDAFwOUBYvXlzWrVsnFSpUSPT42rVrJSyMCVIAAAAAgIzbT3LTpk02dVtLtZcvX+4Mt3nggQcsMKnJNytWrJCyZctKlixZ3F4yAPiFJAcoO3XqJIMHD7a09uDg4ATHzp07J0OHDpUuXbqkxRoBAAAAALgm2pJs9OjRsnXr1gT7GzZsaH0ko6OjJXv27Lbvcok5AACXA5QvvPCCTJ48WSpVqiSPPPKIVK5c2fbr3acPP/xQYmNj5fnnn0+jZQIAAAAAkDSaRDN//nxp3769ZUSq3bt3W3AyKChIWrdubUHJrl27SrFixdxeLgD4vQCP5rgn0a5du6Rv374yZ84cS423CwQE2A99DVJqCrwvOHXqlE0mP3nyZKJTywEAAAAAGcvRo0dlxowZVro9e/ZsOXv2rCxYsEBatmzptCXTBButCuR9HgBkrPhakjMoVenSpWXmzJly/Phx2bZtmwUptYFwvnz5rnXNAAAAAAAky6FDh2T8+PHWU3LRokVW2edVokQJC1p61axZ0x4AgIwnWQFKLw1INmjQIPVXAwAAAADAZWiSzJkzZyR37txO2fbjjz/uHK9Ro4aVbuvk7bp161rFHwDAhwKU9957b5LOGzNmzLWsBwAAAAAAR0xMjPz222/O5O02bdrI2LFj7Vi9evXktttukyZNmlhQsly5cm4vFwCQlgHKcePGWYl3nTp1nP6TAAAAAACktsjISJt9oEFJ7St54sQJ55gOv9H3pJodqY9Jkya5ulYAQDoGKHU4jvb22Llzp/Tu3Vt69Ogh+fPnT4UlAAAAAADwPy1atJC//vrL2S5YsKB069bNsiTbtm1L6TYA+JjApJ6oU7ojIiLk6aeflmnTpknJkiXl3//+d4KJ3gAAAAAAJJVO1R4xYoS0atVKzp075+zXSdsVKlSQJ5980obfHDhwQD7//HMLUubMmdPVNQMAUl+AJ4XRxV27dlnZ95dffikXLlyQ9evXO42K/WkMOgAAAAAgaeLi4mT58uVOP8nNmzc7x6ZOnSpdu3a1j6OjoyVbtmxkSgKAn8TXUjTFWwUGBtovC41vxsbGpvQyAAAAAAA/MHv2bLnnnnvk4MGDzj4NQrZu3dombzds2NDZHxQU5NIqAQBuSFaA8vz58zJ58mSb1L148WLp0qWLfPDBB5Z+rwFLAAAAAACOHz9uw21KlSol119/ve0rW7asBSc1m6ZTp04WlNT3klStAQCSHKB8+OGHZcKECdZ78t5777WBOdqoGAAAAAAAbQOmZdv6+PXXX63S7rbbbnMClJUrV7b9jRo1IkMSAJCyAOWoUaPs7le5cuXsl4o+EqMZlgAAAAAA36ctv15++WWZMmWKrF69OsGxGjVqSL169RLs8wYrAQBIUYCyZ8+eNCgGAAAAAD8WExMj69atkzp16ti2vkecOXOmBSe17VezZs2sdPvGG2+05BYAANJ0ircvY4o3AAAAAPzX6dOnZc6cOTZ5W/tKRkZGyuHDhyVv3rxOFZ2+h9IZBbQBAwCk6xRvAAAAAIBvOnTokNNPcu7cuTYw1UuDkJs2bbJekuqWW25xcaUAAF+Q5ABlUn/p0IMSAAAAADKfuLg4K9NW33//vfTr1885Vr58ead0u0mTJpIlSxYXVwoA8DX//e2TBJqSGf+hqf36y+vi/cn14YcfSpkyZSQ4OFgaNmwoK1asuOL5I0eOtOlvOXLksIniAwYMkKioqGu6JgAAAAD4Y0By6dKlMmjQIKlSpYp88sknzrFu3bpJgwYN5NVXX7Wek1u3bpX//Oc/0rx5c4KTAICM04MyJCRE1qxZc02NjydOnGjDd3RCuAYSNfg4adIk2bx5sxQuXPiS87/99lu59957ZcyYMXbXbsuWLXLPPffI7bffLm+//XaKrpkYelACAAAA8EWa3DF//nzrJzlt2jQ5cOCAc6xjx4428AYAgNSQnPiaqwFKDSDqXbkPPvjAuYOnWZGPPvqo3cW72COPPCIbN26UefPmOfueeOIJWb58uSxevDhF10wMAUoAAAAAvhicLFasmBw/ftzZp+93OnXqZOXbHTp0SFFVHAAA1xpfS3KJd2qLjo6WlStXStu2bf+3mMBA29Yyg8Ro1qR+jrdke8eOHXaHT3+hpvSaShs+619a/AcAAAAAZFa7d++W999/3xI1vLQFVr169SxI2bdvX5vMrdO4x48fL927dyc4CQBwjWtTvI8cOSKxsbFSpEiRBPt1WyfCJebOO++0z2vWrJlo4ueFCxfkoYcekueeey7F11TDhw+XYcOGpcr3BQAAAADpTd8frV271kq3dfL2X3/95RzT90thYWH28YQJEyRfvnzOMBwAADJVgHLq1KkJtrV0WkuttWFyfNpMOa0sXLhQXnvtNfnoo4+slHvbtm3Sv39/efnll2Xw4MEpvu6zzz4rAwcOdLY1g1LLwgEAAAAgoxs3bpy8+OKLsmvXLmefBiCbNm1qU7ezZ8/u7C9QoIBLqwQAIBUClNqT5GIPPvhggu2AgADLYEyKggUL2vS3gwcPJtiv20WLFk30czQIeffdd8v9999v2zVq1JAzZ87IAw88IM8//3yKrqn0F3b8X9oAAAAAkBGdPn1afv75Z6lfv76UKlXK9ul7IA1Oagn3DTfcYO/dunTpIoUKFXJ7uQAAJEmS8/o1Y/Jqj6QGJ1VQUJD1P4k/8Mabldm4ceNEP+fs2bOXlCLoL2NvSUNKrgkAAAAAGZkmXHz22WfStWtXS8q49dZbrVTbS4ORU6ZMsZZXWt7du3dvgpMAgEzFtR6USsuqe/XqZXf/wsPDZeTIkZYRqb9QVc+ePaV48eLWI1LpL+S3335b6tSp45R4a1al7vcGKq92TQAAAADI6CIjI2XUqFEWcFyyZIklZHiVK1dOcuXK5WxrT8nEKt4AAPCLAKWOCF+9erX9gkwJnRSnU+OGDBkiBw4ckNq1a8vs2bOdITc6eS5+xuQLL7xgZeT65759++yuoAYnX3311SRfEwAAAAAyGq380vcvOmFbZc2a1fpKahWZ0gQM7SepgcjrrrvO3hcBAOArAjzxb8UlU0hIiKxZsybFAcqMSofkhIaGysmTJy0ICwAAAACp7fz587JgwQKbvK1DSTUTcv369c5xHQaqQ210EGmJEiVcXSsAAGkZX3O1xBsAAAAA/MmJEydk5syZFpTUSi8t5Y4/AOfQoUNSuHBh29Z2VgAA+INrClD26NGDDEMAAAAASCLtmT927FhnW0u6NUNSS7dbtmwp2bNnd3V9AABkugDlxx9/nHorAQAAAAAfoF20/v77bxtwo5mSo0ePlnr16tkxDUauWLHC6Sep++P33QcAwB8lOUC5dOlSOXr0qHTp0sXZ9+WXX8rQoUNtSrb+cn3//fe54wcAAADA71y4cEF+//13C0hqYHLnzp3OMd32Bii9gUkAAJCCAOVLL71kJQfeAKXeEbzvvvvknnvukapVq8qbb75p5Qk6aQ4AAAAA/MXmzZulSZMmcuzYMWdfcHCw3HDDDRaQjJ/kwfRtAMj8YuM8smLnMTkUGSWFQ4IlvGx+yRLIz/d0CVCuXr3apsh5TZgwQRo2bCiffvqpbZcsWdKyKQlQAgAAAPBVOsRm+vTpEhcXJ/fff7/tK1++vP2pE7c1GKkZku3atZNcuXK5vFoAQGqbvS5Chk3bIBEno5x9YaHBMrRrNelQPczVtflFgPL48eNSpEgRZ/vXX3+Vjh07OtsNGjSQPXv2pP4KAQAAAMBFW7dudfpJLlmyxHpMaoKGVpRpRmTWrFltvwYq9WMAgO8GJ/t+vUo8F+0/cDLK9n/coy5ByhRKcjdmDU56+6hER0fLqlWrpFGjRs7xyMhIyZYtW0rXAQAAAAAZysiRI+W6666TSpUqyVNPPWU9JjU4qf0k+/TpY++LvCpXrkxwEgB8vKxbMycvDk4q7z49ruch+ZL8G7RTp04yaNAgGTFihN05zJkzpzRv3tw5vnbtWqe0AQAAAAAyk/Pnz8vChQulTZs2TqBxx44dsmHDBttu1aqV9ZPUKdyaPQkA8C/aczJ+WffFNCypx/W8xuULpOva/CpAqf0nb7nlFmnRooXkzp1bvvjiCwkKCnKOjxkzxppAAwAAAEBmcOLECZk5c6aVb8+aNcuqwhYsWGDDQZX2mGzcuLG1tsqbN6/bywUAuEgH4qTmeUhhgLJgwYLy22+/ycmTJy1AmSVLlgTHJ02aZPsBAAAAIKM6cuSITJw40arCNGPywoULzrGwsDA5fPiws12zZk17AACg07pT8zykMECpAcmIiAgpXLhwosfz58+f1EsBAAAAQLrQnpHnzp2zFlXqn3/+kUceecQ5XrVqVZu6rY/69etLYGCS2/QDAPxIeNn8Nq1bB+Ik1mUyQESKhgbbeUjDAKX+YgcAAACAjE6zInWgjXfytpZsa0sqpQNuNBjZpEkT6ympA3AAALiaLIEBMrRrNZvWrcHI+FEy3VZ6XM9D8jFmDgAAAECmd+bMGfn5558tKDl9+nQ5evSocywmJsYSLgICAuwxZcoUV9cKAMicOlQPk4971LVp3fEH5mjmpAYn9TjSIUD52WefXbXP5GOPPZbCpQAAAABAyugwz5UrVzrb+fLlk65du1qWpA7z1MAkAADXSoOQ7aoVtWndOhBHe05qWTeZk+kYoBw1atQlw3Hi01/6BCgBAAAApJVt27Y5U7enTZsmOXLksP0ahNSsSQ1Iagl3s2bNJGtWCsYAAKlPg5GNyxdwexk+JcCTxOaS2iz6wIEDlx2S40tOnToloaGhNrE8T548bi8HAAAA8FtxcXGWGam9JDUwuX79eufY1KlTLUtSRUVFSfbs2cmUBAAgE8bXknxLkV/0AAAAANKT9pS89957Zd++fc4+zYrUcm7NlGzQoIGzPzg42KVVAgCAa8UUbwAAAACu0+wKLdsuUaKElWer0qVLW3BS++B37NjRgpKdOnWy/pIAAMAPA5RDhw696oAcAAAAAEiqvXv3Wpm2lm4vWLDApm3fdtttToCycuXKMm/ePGnatKmVbwMAAD8PUNapU0fmzp17yX6tJa9UqZKEhTFKHQAAAMDVK7OGDx8uU6ZMkT///DPBsSpVqkjNmjUT7GvdunU6rxAAAGTYAKVOwrtSf8rbb79dPv30U8mZM2dqrQ0AAABAJhcbGysbNmyQGjVqOO8dNGtSg5P6cePGja10Wx+aMQkAAPxP1uRMz7tcrxidqtevXz955ZVX5LXXXkvN9QEAAADIZM6ePSu//PKLlW5PmzZNTpw4IYcPH5a8efPa8SeffNL26QTuIkWKuL1cAADgsgBPKk2/mT17tjz++OOyadMm8acx6AAAAABEjhw5ItOnT5cff/zRpm+fO3fOOaZDbfRYkyZNXF0jAADImPG1JGdQXo32i9Em1wAAAAD8g1ZZBQYG2sffffedVVV56QRubROlpdvNmzeXrFlT7a0HAADwMan2KmHHjh1SrFix1LocAAAAgAxGi6+0vZNmSWr59sMPPyx9+/a1Y926dZPPPvvMApIamNRhN9pjEgAAIF0ClKtXr7Y+Mp07d06NywEAAADIIKKjo2XhwoUWkNTHvn37nGM67MYboCxRooSsWrXKxZUCAACfD1Bq35jE7oCeOXNGLly4IO3atZNhw4al9voAAAAAuOT8+fMWeNT+kl65c+eWDh06WJZkp06dXF0fAADwswDlyJEjE92vTS4rV64s1apVS811AQAAAEhHmhmpGZFbtmyRd955x/Zlz55dateuLX///beVbuujdevWEhwc7PZyAQCAD0m1Kd6+hCneAAAA8HX6NmDDhg1OP8k//vjDObZ//34JCwuzjw8fPiwFChRwhuEAAABk2CneAAAAADKHr776ytozbd++3dmn7ZwaNWpkpdtBQUHO/kKFCrm0SgAA4C+SHKDUO6ZXm8Knx7UfJQAAAICM4ezZszJ37lypU6eOlCxZ0tmvwUkt4W7Tpo0FJbt27SpFixZ1da0AAMA/JTlAOWXKlMseW7p0qbz33nsSFxeXWusCAAAAkEI61Gb69OlWuj1nzhw5d+6cvPHGG/LUU0/Z8S5dusikSZOkffv2EhIS4vZyAQCAn0tygFIbYl9s8+bNMmjQIJk2bZrcdddd8tJLL6X2+gAA8DmxcR5ZsfOYHIqMksIhwRJeNr9kCbxylQIAXM3p06fl008/tZ6SixcvTpA8UKpUKcuW9MqXL5/cdtttLq0UAAAgFXpQatPsoUOHyhdffGF3XVevXi3Vq1dPyaUAAPArs9dFyLBpGyTiZJSzLyw0WIZ2rSYdqv93IAUAJHXIzcGDB52y7CxZssgLL7xgJd2qVq1aVrqtiQY6iftq7ZoAAAAyRYBSp+689tpr8v7779uLnHnz5knz5s3TbnUAAPhYcLLv16vEc9H+AyejbP/HPeoSpARwRdHR0fLrr79a6bY+dCLm+vXr7ViOHDmshFuzIzUoWaZMGbeXCwAAkLoBSu1ZM2LECLtDO378+ERLvgEAwOXLujVz8uLgpNJ9mtekx9tVK0q5N4AETp06JbNnz7bS7ZkzZ1rSgFeuXLksi7JIkSK2/eKLL7q4UgAAgJQJ8GhtSBKneOtd2bZt21r5yOVMnjxZfOFFYGhoqL3407vSAABcq6Xbj8odny676nnj+zSSxuULpMuaAGQO9957r4wdO9bZLly4sHTr1s3Kt3UCd3BwsKvrAwAAuNb4WpIzKHv27EnfGgAAUkgH4qTmeQB8i+YMbNq0ybIktXT7o48+krp169oxDUb+/vvvTj/Jhg0bXjFhAAAAILNJcoBy3LhxabsSAAB8mE7rTs3zAGR+sbGxsmzZMicouXXrVueY7vMGKDUoqcFJAAAAX5WiKd4AACB5wsvmt2ndOhAnsd4qWqNQNDTYzgPg+7Zs2WLDJg8dOuTsCwoKspJtDUZq1qQXVUwAAMDXBSblpIceekj27t2bpAtOnDhRvvnmm2tdFwAAPkUH3wztWs0+vjjU4N3W4wzIAXzP0aNH5csvv5QxY8Y4+8qVKycXLlywvkx33XWXfPfdd3LkyBEbgvPAAw/YYEoAAAB/kaQMykKFCsl1110nTZs2la5du0r9+vWlWLFi1pD7+PHjsmHDBlm8eLFMmDDB9o8ePTrtVw4AQCbToXqYfNyjrk3rjjj5v16TmjmpwUk9DsA37Ny508q29bFo0SIr5y5ZsqT07t3bMiKzZs1q+ytWrCjZsmVze7kAAACZY4r3wYMH5bPPPrMgpAYk4wsJCbHp3vfff7906NBBMjumeAMA0lJsnEdW7DxmA3G056SWdZM5CfiG999/314zr127NsH+WrVqWS/JZ599lqnbAADAL5xKRnwtyQHK+DRrcvfu3XLu3DkpWLCglC9f3qd64xCgBAAAwNXExMTIb7/9Ji1atLCMSPXoo4/KBx98YFO2tcekt59k2bJl3V4uAABAho2vpWhITr58+ewBAAAA+JPIyEiZPXu2TdnWfpEnTpyQBQsWSMuWLe34fffdJw0aNJDOnTtLgQIF3F4uAABApsAUbwAAAOAKjh07JpMmTbJ+kvPmzZPo6GjnWOHCheXAgQPOdu3ate0BAACApCNACQAAAMSjHZCioqIkR44ctr1jxw556KGHnOM62EZLt/XRsGFDK+cGAABAygVKBvDhhx9KmTJlrGG4vshbsWLFZc/V8hntd3nxQ8tovO65555LjvvC8B4AAACkDZ2yvWTJEnn66aelSpUq8vDDDzvH6tWrJ127dpXhw4fbsMjNmzfLG2+8IU2aNCE4CQAA4AsZlBMnTpSBAwfKqFGjLDg5cuRIad++vb3w05KZi02ePDlBWc3Ro0dtKuK//vWvBOdpQHLs2LHOdvbs2dP4OwEAAEBmogMftWRb+0lOmzZNDh065Bw7ffq0ZVJ6b3ZPnTrV1bUCAAD4MtcDlG+//bb06dNHevfubdsaqJwxY4aMGTNGBg0adMn5+fPnT7A9YcIEyZkz5yUBSg1IFi1aNI1XDwAAgMzq+uuvlz///NPZ1imTWpWjpdt6s1sDkwAAAMiAJd4HDx6Uu+++W4oVKyZZs2a1spb4j+TQTMiVK1dK27Zt/7egwEDbXrp0aZKu8fnnn8vtt98uuXLlSrB/4cKFloFZuXJl6du3r2VaXs758+dt9Hn8BwAAAHzDP//8I++++64FHTVr0qtdu3ZSokQJ6devn/zyyy+WQfnNN9/Yje+QkBBX1wwAAOBPkp1Bqf0dd+/eLYMHD5awsLBrurN85MgR6/dTpEiRBPt1e9OmTVf9fO1VuW7dOgtSxqcvPm+55RYpW7asbN++XZ577jnp2LGjBT0TC6JqP6Fhw4al+PsAAABAxqGl2atXr7bSbZ28vWbNGufY3LlzrZ+k0tezr776KpmSAAAAmS1AuXjxYlm0aJHUrl1b3KaByRo1akh4eHiC/ZpR6aXHa9asKeXLl7esyjZt2lxynWeffdb6YHppBmXJkiXTePUAAABIbRqAvO++++yGevwKnebNm8uNN95oA2+8vFO6AQAAkMkClBq407vSqaFgwYKW0ahl4/Hp9tX6R545c8b6T7700ktX/TrlypWzr7Vt27ZEA5Tar5IhOgAAAJlLZGSkzJ4921oPNW3a1HmtqsFJDT7q4EXtJ6l9JfW1IAAAAHykB6VO2dbhNdrL51oFBQXZXWydnugVFxdn240bN77i506aNMl6R/bo0eOqX2fv3r3Wg1JL0gEAAJB5HThwQEaPHu0EHf/973/b61Mv7T8+Z84cayU0ZcoU6dWrF8FJAAAAX8ug7N69u5w9e9ZKpnV6drZs2RIcP3bsWLKup6XV+sKxfv36VqqtLzA1O9I71btnz55SvHhx6xN5cXm33hEvUKBAgv2nT5+2fpK33nqrZWFqD8qnn35aKlSoYHfRAQAAkLlo9c5//vMfCzguW7YsQTWPviatVq1agvNvuOEGF1YJAACAdAtQxr9DnRo04Hn48GEZMmSI3RHX3pZaquMdnKMlOto3KL7NmzdbL8yff/75kutpyfjatWvliy++kBMnTljJj75IffnllynjBgAAyAS0okYHJnoDjzrE5ocffpDly5fbtt7U1n6S+tBzGHIDAACQuQV4UquhpA/RITmhoaFy8uRJyZMnj9vLAQAA8HlRUVHW5kenbk+dOtXa8+hN7Lx58zrtfXSfTuDW6hoAAAD4Tnwt2RmUF7+QjI6OTrCPgB4AAACS4vjx4zJjxgz58ccfrYJG2/zEf025fv16Z/jNv/71LxdXCgAAgLSU7AClvnB85pln5LvvvrO72BeLjY1NrbUBAADAx2jxjrcke/z48dKvXz/nmGZGao9xLd1u0aKFDVQEAACA70v2FG8dODN//nz5+OOPrafjZ599ZkNptNfjl19+mTarBAAAQKYNSK5evdpeL9apU0c++eQT51i3bt2kRo0a8sILL8iff/4pe/bskQ8++EDatWtHcBIAAMCPJLsHZalSpSwQ2bJlSyu9WbVqlU3I/uqrr+wu+MyZMyWzowclAABAyl24cEEWLVpkpdvaU3LXrl3OsQ4dOsisWbNcXR8AAAAyeQ/KY8eOSbly5exjvbhuq2bNmknfvn1TumYAAAD4gPPnz9sN7UOHDjn7cuTIIe3bt7fS7S5duri6PgAAAGQ8yQ5QanBy586d9sKzSpUq1osyPDxcpk2b5kxZBAAAgO87cOCAvQbcvHmz/Oc//7F92gKoZs2aVtatE7e1p2Tbtm0lZ86cbi8XAAAAvlLi/c4770iWLFnksccek7lz59oLT71ETEyMvP3229K/f3/J7CjxBgAASJwGI7VsW8u3ly1bZq8D1f79+yUsLMw+PnjwoBQsWNBeMwIAAMA/nUrLEu8BAwY4H+vd8E2bNsnKlSutD6XeLQcAAIDv+fbbb+Xll1+2137xNWjQwEq3s2b938vKIkWKuLBCAAAAZFbJDlDGFxUVJaVLl7YHAAAAfIO+xps/f77dfC5RooTti42NteBktmzZpHXr1haU1CncxYsXd3u5AAAAyOQCk/sJ+uJU757ri9HcuXPLjh07bP/gwYPl888/T4s1AgAAII0dP35cvv76a/nXv/4lhQoVks6dO8v48eOd4zrcZsKECXL48GGZPXu2DUckOAkAAABXApSvvvqqjBs3Tt544w0JCgpy9levXl0+++yzVFkUAAAA0t6ZM2fk/ffflzZt2lhQ8u6775bvv/9eTp8+bcFHzZb0ypcvn3Tv3t36CAEAAACuDsnRXpOffPKJvZANCQmRNWvW2GRvLflp3Lix3X3P7BiSAwAAfJG+7Dty5IgFI9W5c+dsmM3Zs2dt+7rrrrOp2/qoV6+eBAQEuLxiAAAAZFZpOiRn3759FqS8WFxcnE3yBgAAQMZx4cIFWbRokTN5O1euXLJ+/Xo7liNHDhk4cKDkzZvXekom9hoPAAAASGvJDlBWq1bNXuRePBhHy4Hq1KmTmmsDAABACmiJ9s8//2wByenTpyeocAkODpYDBw5I0aJFbVt7iwMAAACZKkA5ZMgQ6dWrl2VSatbk5MmTZfPmzfLll1/aC2AAAAC467HHHpOxY8c62wUKFJCuXbtalmS7du0sixIAAADItENy9IXttGnTZO7cufbiVgOWGzdutH36ghcAAADpY8uWLfLmm29K06ZNZdWqVc7+bt26WY/wAQMGyK+//moZkxqw1N6SBCcBAACQ6Yfk+AOG5AAAgIxIq1f++OMPp5+k3iT2Gjx4sLz00kvOeTrghiE3AAAA8MkhORf3N9IXwPER0AMAAEh9W7dulRYtWkhERISzL2vWrNKqVSurcNGHV2BgsotkAAAAANckO0C5c+dOeeSRR2ThwoUSFRXl7NdETL1LHxsbm9prBAAA8CsnTpyQmTNnSkxMjPX+VmXLlrXXXiEhIdKpUycLSHbs2NEmcANui43zyIqdx+RQZJQUDgmW8LL5JUsgGbwAACCNApQ9evSwYOSYMWOkSJEilA4BAACkgj179ljptj70RvCFCxekVKlS0rNnT3u9pdmS2k+yUqVKkj17dreXCzhmr4uQYdM2SMTJ/yUvhIUGy9Cu1aRD9TBX1wYAAHw0QLlmzRpZuXKlVK5cOW1WBAAA4Ec+/vhj+eyzzxIMuVHVqlWzoTbnz5+X4OBg21ejRg2XVglcPjjZ9+tVcnFT+wMno2z/xz3qEqQEAABXlewGRQ0aNLA7/AAAAEgezYrULEj902vDhg0WnNQsyWbNmtlUbp3OvX79enn11Ved4CSQEcu6NXMysYmb3n16XM8DAABI1QxKvcP/0EMPyb59+6R69eqSLVu2BMdr1qyZ3EsCAAD4rDNnzsjPP/9spdvTpk2TY8eOyYIFC6Rly5Z2/N5775U6depIly5dpHDhwm4vF0gy7TkZv6z7YhqW1ON6XuPyBdJ1bQAAwMcDlIcPH5bt27dL7969nX16x58hOQAAAP91/PhxmTJlivz444/yyy+/JBgsWKBAAdm/f7+zrcFJfQCZjQ7ESc3zAACA/0p2gNJ7l3/8+PEMyQEAAPh/2ivSO7xGb+bed999zjGdwK39JHXydtOmTW3gDZDZ6bTu1DwPAAD4r2S/Ot61a5dMnTpVKlSokDYrAgAAyATi4uLkzz//tCxJLd8ODw+XsWPH2rF69epJp06dpFGjRhaY1LY43NSFrwkvm9+mdetAnMS6TOozvmhosJ0HAACQqgHK1q1b2yRvApQAAMAfsyS1f6QGJPURERGRoKzb2/JGHzNmzHB1rUBayxIYIEO7VrNp3RqMjB+k9Ibj9bieBwAAkKoByq5du8qAAQPk77//lho1alwyJKdbt27JvSQAAECm0KJFC1m+fLmzHRISIh07drQsSf2TLEn4mw7Vw+TjHnVtWnf8gTmaOanBST0OAABwNQEevdWfDIGBgZe/mI8MyTl16pSEhobKyZMnJU+ePG4vBwAApLM9e/ZYS5tZs2bJpEmTJEeOHLb/ueeek3HjxlkvSX20atXK6TsJ+LPYOI9N69aBONpzUsu6yZwEAMC/nUpGfC3ZAUp/QIASAAD/oi+H1q1b5/STXLlypXNMA5VaQaLOnj0rwcHBV7xhCwAAAECSFV9jhCQAAPBr8+fPl/vvv1927tyZoCqkSZMmVrpdp04dZ3/OnDldWiUAAADguwhQAoAfoPQO+K8zZ87IL7/8IoULF7YApCpevLgFJ7VUu127dhaU7NKlixQpUsTt5QIAAAB+gQAlAPi42esiLhleEMbwAviRw4cPy7Rp06x8W4OTUVFRcttttzkBysqVK9vE7euvv15y587t9nIBAAAAv0OAEgB8PDjZ9+tVcnGz4QMno2y/Tl4lSAlf7Sn5zjvvyJQpU2TJkiUSFxfnHCtdurRUqlQpwfmdOnVyYZUAAAAAVLI6vF+4cEG+/PJLOXjwIH97AJAJyro1czKxSWjefXpczwMyOw1Abtq0KUEPyYkTJ8rixYvtmPaRHDZsmKxevdrKuV999VVX1wsAAAAghRmUWbNmlYceekg2btyYnE8DALhAe07GL+u+mIYl9bie17h8gXRdG5AaoqOjZcGCBVa6rZO2Dx06ZOXcefPmteMDBw60fd26dbOsSQAAAAA+UuIdHh5u2Qe80AeAjE0H4qTmeUBGcPLkSZk5c6b89NNP9mdkZKRzTPtH/v3339K8eXPb7t69u4srBQAAAJBmAcqHH37YMhL27Nkj9erVk1y5ciU4XrNmzeReEgCQBnRad2qeB7jZT1JLttU333wj/fr1c44VLVrUMiR18narVq0kOJjnMwAAAJDZBHj0VX8yBAZe2rZS3zR43zzExsZKZnfq1CkJDQ21LI08efK4vRwASBHtLdlsxHwbiJPYD3oN9xQNDZbFz7SWLIH/Df4AGYG+pli/fr1lSWr59v333y8PPvigHdu7d6/ccMMNcuONN9pDKzsSe20CAAAAIPPE15KdQamN5QEAGZ8GHYd2rWbTujX8GD9I6Q1H6nGCk8gI9AanTtvWgKQGJrdv3+4cK1CggBOgLFGihGzYsMHFlQIAAABIbckOUNJ7EgAyjw7Vw+TjHnVtWnf8gTmaOanBST0OZIRhN2XKlJGIiAhnX/bs2aVt27ZWut21a1dX1wcAAAAggwUolWY1jBw50pnmXa1aNenfv7+UL18+tdcHALhGGoRsV62oTevWgTjaczK8bH4yJ+GKI0eOyPTp0+01xIgRI2xfUFCQvZaIioqSLl26WOl2+/btbegNAAAAAN+X7B6Uc+bMsWb0tWvXlqZNm9q+33//XdasWSPTpk2Tdu3aSWZHD0oAAFKP3tjUsm19LF68WOLi4mz//v37JSzsv1m8mj1ZsGBByZYtm8urBQAAAJDhe1AOGjRIBgwYIK+//vol+5955hmfCFACAIBrN2HCBHn11Vdl3bp1CfbXqVPHsiSzZMni7PMGKgEAAAD4n2QHKLUk67vvvrtk/7333mtl3wAAwD/7SC5cuFCuu+46KV68uO2LiYmx4KQGIlu0aGH9JLUKg37WAAAAAOILlGQqVKiQrF69+pL9uq9w4cLJvRwAAMjEJRsTJ06UO+64w14faN/Ib7/91jmu/SS/+uorOXTokMybN08effRRgpMAAAAArj2Dsk+fPvLAAw/Ijh07pEmTJk4PSm10P3DgwOReDgAAZCJnzpyRL7/80vpJzp8/37IkvYoUKSIBAf8bvpQvXz7p0aOHSysFAAAA4LNDcvR0LeV+6623rLm9KlasmDz11FPy2GOPJXhjklkxJAcAgP/93j927JgUKFDAts+dO2fDbM6ePWvbVapUsX6SWr4dHh4ugYHJLs4AAAAA4IOSE19L9rsIDUDqkJy9e/faF9CHfty/f/8UByc//PBDKVOmjAQHB0vDhg1lxYoVlz23ZcuW9nUufnTu3DnBm6khQ4ZYw/0cOXJI27ZtZevWrSlaGwAA/iY2NlYWLVokTz75pFSsWNH6R3rp71V9HaCVE5s2bbLe1Do4r1GjRgQnAQAAAKRPiXd8ISEhcq20d5WWho8aNcqCk5qdqT2sNm/enGhPy8mTJ1sjfq+jR49KrVq15F//+pez74033pD33ntPvvjiCylbtqwMHjzYrrlhwwYLggIAgIQ0I3Lu3Lny448/yvTp0+Xw4cPOsezZs8uBAwekaNGitv3KK6+4uFIAAAAAflniXbduXWtur72k6tSpc8VMyVWrViVrARqUbNCggXzwwQe2HRcXJyVLlrRG+oMGDbrq52tAU7MlIyIiJFeuXJY9qSXnTzzxhGV+KM3y1L5Y48aNk9tvv/2q16TEGwDgb+677z4ZM2aMs62/87U6QUu39SZf7ty5XV0fAAAAgMwlOfG1JGVQam8pzZ5Q+kYltWgm5MqVK+XZZ5919ml5mJZkL126NEnX+Pzzzy3oqMFJtXPnTsvy0Gt46V+GBkL1mkkJUAIA4Kt0yJ0OuNFMyXfeecduQqquXbvazUj9na+P5s2bS7Zs2dxeLgAAAAA/kKQA5dChQ52eVK1atZKaNWtK3rx5r/mLHzlyxK6p2Y3x6bb2tboa7VW5bt06C1J6aXDSe42Lr+k9drHz58/bI36EFwAAX6CVBVrdoAFJDUz+/fffzjHdFz9AqYFJXxh2BwAAAMCHe1BmyZJFbrjhBmuInxoBymulgckaNWrY1NBrMXz4cBk2bFiqrQsAgIxg27ZtdmNRh9nF/11+/fXXWzDy5ptvTrAfAAAAANyQ7HGb1atXt/Kw1FCwYEF7Q3Tw4MEE+3Xb24j/cs6cOSMTJkywnlnxeT8vOdfUEnPvRHJ97NmzJ4XfEQAA7tDsfx089+WXXzr7ypQpY78vtQ3KLbfcYscOHTok8+fPl/79+0upUqVcXTMAAAAApGiKt07u1OEzL7/8stSrV8/p/eiVnKEyQUFBdg3teeXtbalDcnT7kUceueLnTpo0ycqye/TokWC/Tu3WQKReo3bt2s6btuXLl0vfvn0TvZb21/T22AQAILPYv3+/TJ061Uq1NegYExNjQce7777bSrWzZs1q+ytXriw5cuRwe7kAAAAAkDoByk6dOtmf3bp1S9CnSntc6bb2lEyOgQMHSq9evaR+/fpWqq1TuTXbo3fv3na8Z8+eUrx4cSvDvri8W4OaBQoUSLBf1/D4449bILVixYoWsBw8eLBN9k7NAT8AALhl9OjR9ntQezHHV6lSJSvdjoqKcgKS3pt1AAAAAOAzAcoFCxak6gK6d+8uhw8fliFDhtgQG30jNXv2bGfIze7du22yd3ybN2+WxYsXy88//5zoNZ9++mkLcj7wwANy4sQJadasmV0zODg4VdcOAEBa0xt/y5Ytk4YNG1pGpNJBN97gZKNGjSwoqTfhqlSp4vJqAQAAACD5Ajya+ogEtCQ8NDTU+lEmp2QdAIDUcO7cOZk7d65N3dYSbr2Rt3DhQmnRooUd16ncf/75p03eDgsLc3u5AAAAAHBN8bVkZ1CqRYsWySeffGLDcrQXpJZgf/XVV1ZOrdmKAAAgefSXtgYk9aFZ/2fPnnWO6S91rSjwqlu3rj0AAAAAwC+neP/www/Svn17622lGRw6qMb7xuq1115LizUCAOCTdKiN19atW60n8+TJky04WbJkSRsYp5mUmkGpg28AAAAAwBclu8S7Tp06MmDAABteExISImvWrJFy5crJX3/9JR07drQ+kpkdJd4AgLSgv3L196VmSerkbc2CHDt2rHOsQ4cO1lNS+0lqT+b4w+gAAAAAIDNJ0xJvHVBz/fXXX7Jfv6AOpAEAAAmzJH/77TcLSGpgcs+ePc6xgwcPSlxcnA2D02DknDlzXF0rAAAAALgh2QHKokWLyrZt26RMmTIJ9utUbc2kBAAA/6M39XQKt1fOnDktU1Inb3fu3NmCkwAAAADgz5IdoOzTp4/0799fxowZY9ke+/fvl6VLl8qTTz4pgwcPTptVAgCQwUVERNjE7VmzZsn48eOtV7Nq1aqVDZXTidtaut2mTRvnGAAAAAAgBT0o9XQdhjN8+HBnwmj27NktQPnyyy+LL6AHJQAgKb8PN23a5PSTXL58uXNs2rRp0qVLF/v49OnTFpDMkiWLi6sFAAAAgIwbX0t2gNIrOjraSr31jVe1atUkd+7c4isIUAIArmThwoXy4IMPypYtWxLsb9iwoZVu33XXXVKqVCnX1gcAAAAAPj0k595775V3333XJnhrYNLrzJkz8uijj1rpNwAAvuLcuXMyb948KVCggDRu3Nj2hYWFWXAyKCjISrY1KKkl3MWKFXN7uQAAAACQ6SQ7g1JL1LTPVuHChRPsP3LkiA3QuXDhgmR2ZFACgH87evSozJgxw8q3dbK23oS79dZb5fvvv09Qxt2iRQt+TwAAAABAemVQ6kU1lqmPyMhICQ4Odo7FxsbKzJkzLwlaAgCQWejvt/fff1+mTJkiixYtst9tXiVKlJAKFSokOF8zJgEAAAAA1y7JAcq8efPa1G59VKpU6ZLjun/YsGGpsCQAANInILl9+3Yn8Ki/x7755htZsWKFbdesWdOmbmv5dp06dew4AAAAAMDFAOWCBQvszVzr1q3lhx9+kPz58zvHtAdX6dKl6b0FAMjQYmJi5LfffrPSbX3s379fDh8+bDfh1OOPPy4HDx60oGTZsmXdXi4AAAAA+IVk96DctWuXTSb15UwSelACgO/QtiSzZ8+2gKT2lTxx4oRzLEeOHHbs+uuvd3WNAAAAAODP8bXA5F5848aN8vvvvzvbH374odSuXVvuvPNOOX78eMpWDABAKop/7+2rr76Sf//731a+rcHJggULyr333msBSx3wRnASAAAAANyV7ADlU089ZRFQ9ffff8vAgQOlU6dOsnPnTvsYAAA3bNq0SV5//XVp3LixjB492tnfrVs3qVixojzxxBM2/ObAgQPy+eef2/6cOXO6umYAAAAAQDJ6UHppILJatWr2sfai1Cmmr732mqxatcoClcjYYuM8smLnMTkUGSWFQ4IlvGx+yRLou+X6AHxXXFycLFu2zDIhf/zxR9myZYtzTMsHHnzwQWcCd/xjAAAAAIBMHqDUgThnz561j+fOnSs9e/a0j3VojjezEhnT7HURMmzaBok4GeXsCwsNlqFdq0mH6mGurg0AkiM6OlrKly8ve/fudfZly5bNBrnpgBvNjgQAAAAA+GiAslmzZlbK3bRpU1mxYoVMnDjR9mt2imapIOMGJ/t+vUounoh04GSU7f+4R12ClAAypGPHjtlwmw0bNsjw4cOdm2WVK1e2G2OdO3e2oGSHDh2sATMAAAAAwMeneO/evVsefvhh2bNnjzz22GNy33332f4BAwZIbGysvPfee5LZ+doUby3rbjZifoLMyfi0wLtoaLAsfqY15d4AMoRdu3Y5pdu//fab/X5R+/fvl7Cw/95M0ezJwoULW7ASAAAAAJB542vJzqAsVaqUTJ8+/ZL977zzTnIvhXSiPScvF5xUGqHW43pe4/IF0nVtABDfpEmTrK/x6tWrE+yvXr263HTTTRIY+L/ZbmTtAwAAAIBvSHaAUmkmi2a1bNy40bavu+466/eVJUuW1F4fUoEOxEnN8wAgNVy4cMGmaleqVEmKFy9u+86dO2fBSQ1EaksRDUpq+Xa5cuXcXi4AAAAAIKMEKLdt22bTuvft22f9v5T2BCtZsqT1CNOhBchYdFp3ap4HACl1+vRpmTNnjpVvazb+8ePH5Y033pCnnnrKjnfp0kXGjh1rfxYsWNDt5QIAAAAAMmKAUvtOahBy2bJlNrlbHT16VHr06GHHNEiJjCW8bH6b1q0DcTxX6EGp5wFAajt79qx8++23lnk/d+5cOX/+vHNMg5BxcXHOtv5eueeee1xaKQAAAAAgUwzJyZUrlwUna9SokWD/mjVrbLK3Zsdkdr42JCf+FG8V/3+4dyQOU7wBpKYTJ05I3rx5nbJtDURqoFLpTS5v6XaTJk1oDwIAAAAAPihNh+Rkz55dIiMjL9mvgUkmqWZcGnzUIOSwaRsSDMzRzMmhXasRnARwTTQLcsWKFZYlqeXbGnRct26dHcuRI4dl2OfOndsCk9WqVZOAAO/tEQAAAACAv0t2BmXPnj1l1apV8vnnn0t4eLjtW758ufTp00fq1asn48aNk8zOFzMovWLjPDatWwfiaM9JLevOEkigAEDyRUVFyfz58y0gOXXqVDlw4IBzLFu2bLJr1y4JC+PmBwAAAAD4o1PJiK8lO0CpZXu9evWSadOm2RtQ7yRWneKtwUn9wpmdLwcoASC16I2pzz77zNnWn5c6RE2zJDt06OATvw8AAAAAABmwxFt7imm2zNatW2Xjxo1Wple1alWpUKFCCpcLAMjIdu/ebT/39fHmm29KnTp1bL8GI2fNmmW9JPXRsmVLWn0AAAAAAJIt2QFKr4oVKzpBSXqJAYDv0MT6tWvXOv0k//rrL+fYlClTnAClZs5rtiS/AwAAAAAA6R6g1P6T77zzjmVReoOVjz/+uNx///3XtBgAgLu2b98ubdu2lX/++cfZFxgYKM2aNbMsyZtvvtnZz/RtAAAAAIArAcohQ4bI22+/LY8++qg0btzY9i1dulQGDBhgZYAvvfRSqiwMAJC2Tp8+LT///LOcPXtWevToYftKly5t/UF08vYNN9xgGZKdO3eWQoUKub1cAAAAAICPSvaQHH2T+t5778kdd9yRYP/48eMtaHnkyBHJ7BiSA8BXHTx40Iacafn23Llz5fz581KqVCnLmPSWaq9atUqqVKkiOXPmdHu5AAAAAIBMKk2H5MTExEj9+vUv2V+vXj2b5g0AyHi0NceYMWMs4z3+faly5cpZlmRUVJRlTaq6deu6uFIAAAAAgL8JTO4n3H333fLxxx9fsn/06NFy1113pda6AAApFBcXJ8uWLUtw02j16tWyZMkSC07qTaaXX35Z/v77b9m2bZu89dZbTnASAAAAAIBMMyRH+5Y1atTItpcvX279J3v27CkDBw50ztNelQCAtKel2vPnz7fS7alTp8qBAwdk4cKF0qJFCzt+zz33SNWqVW3ydokSJdxeLgAAAAAAKQ9Qrlu3zin/02mvqmDBgvbQY17eXmYAgLTr56H9JH/66SeZNWuWDb3xCgkJsb6S3gCltuHQBwAAAAAAmT5AuWDBgrRZCQDgqrRsO2vW//7o3rJlizN9WxUrVswyJLWnZMuWLSV79uwurhQAAAAAgDQs8QYApA/tGam9IrV0WzMla9WqZcNulGZEtmnTRho2bCg33nij9ZYMDEx2a2EAAAAAAFxFgBLXLDbOIyt2HpNDkVFSOCRYwsvmlyyBlPgD15Il+fvvvztByZ07dzrH9u7da0NwNBCprTTmzp3r6loBAAAAALhWBChxTWavi5Bh0zZIxMkoZ19YaLAM7VpNOlQPc3VtQGal5dkaoPQKDg6Wdu3aWel2ly5dyJIEAAAAAPgUApS4puBk369Xieei/QdORtn+j3vUJUgJXMGhQ4dk+vTpMnPmTPnqq68kR44ctv/666+XTZs2WTBSg5IanMyVK5fbywUAAAAAIE0EeLTBGS6ZjBsaGionT56UPHnyuL2cDFvW3WzE/ASZk/FpgXfR0GBZ/Exryr2BeLZu3Wpl2/rQLEnvj2Cdxq0BSRUZGWnBSu8wHAAAAAAAfDm+xrtfpIj2nLxccFJpyEWP63mNyxdI17UBGdFvv/0mffv2lQ0bNiTYr4NudMBN9erVnX0hISEurBAAAAAAAHcQoESK6ECc1DwP8CXnz5+XBQsWSL58+WzCtipSpIgFJzUrUntMaul2t27dpGTJkm4vFwAAAAAAVxGgRIrotO7UPA/I7E6cOCGzZs2yydv6p5Zp33bbbTJp0iQ7XrlyZZk8ebK0atVK8ubN6/ZyAQAAAADIMAhQIkXCy+a3ad06EMdzhR6Ueh7gq7R/5KhRo2TKlCmWMXnhwgXnWFhYmJQuXTrB+TfffLMLqwQAAAAAIGMjQIkU0cE3Q7tWs2ndGoyMH6T0jsTR42k1IEeH9Gh/Sy0h1yxNDYQyjAfpEZD8559/pGzZsrYdEBAg48aNkxUrVth2tWrVrJ+klm/Xr19fAgMDXV4xAAAAAAAZHwFKpFiH6mHycY+6MmzahgQDczRzUoOTejwtzF4XccnXDEvjrwn/pVmROm1bp25r+faePXvk8OHDTpn2Y489JhERERaYrFixotvLBQAAAAAg0wnwaEqQiz788EN588035cCBA1KrVi15//33JTw8/Ip93p5//nnr5Xbs2DEroRw5cqR06tTJjr/44osybNiwBJ+jvd82bdqUJmPQkb7ZjBqc1KzNi5+03q+mAVOClLhWZ8+elZ9//tkCktOnT5ejR486x4KDg63HpA66AQAAAAAA1x5fczWDcuLEiTJw4EDr4aaTbjXQ2L59e9m8ebMULlz4kvOjo6OlXbt2duz777+X4sWLy65duy4ZOHHdddfJ3LlznW2dmou0o8HIxuULpEsgVDMnE4uoe/4/SKnH21UrSrk3romWbffr18/Zzp8/v3Tp0sVKt2+44QbJlSuXq+sDAAAAAMCXuBq5e/vtt6VPnz7Su3dv29ZA5YwZM2TMmDEyaNCgS87X/Zo1uWTJEsmWLZvtK1OmzCXnaUCyaNGi6fAdID1plmb8su7EgpR6XM9Lj4ApMr9t27ZZlqSWb999993ywAMP2P5u3brJW2+9ZX9qULJp06bc6AAAAAAAII249o5bsyFXrlwpzz77rLNPB0q0bdtWli5dmujnTJ06VRo3bmyZTRpQKFSokNx5553yzDPPSJYsWZzztm7dKsWKFbNSTD1/+PDhUqpUqcuu5fz58/aIn4KKjEdLyFPzPPifuLg4+fPPP51+khs2bHCO5cyZ0wlQlihRwoKXOgQHAAAAAAD4aIDyyJEjEhsbK0WKFEmwX7cv1y9yx44dMn/+fLnrrrtk5syZFkB4+OGHJSYmRoYOHWrnaKm4lmdq30kdXKH9KJs3by7r1q2TkJCQRK+rAcyL+1Yi49H+lql5HvyL3hSpVKmStYXw0qzIFi1aWJakZkvGR3ASAAAAAID0kTWzZT9p/8nRo0dbxmS9evVk3759NmTHG6Ds2LGjc37NmjUtYKmDdL777ju57777Er2uZnFqL8z4GZQlS5ZMh+8IyaHDd3Ra94GTUYn2oQz4/wnieh78mzbg1ZsY69evl1deecX2BQUFSYUKFWzgjf6c0KnbOlwrX758bi8XAAAAAAC/5lqAsmDBghZkPHjwYIL9un25/pFhYWHWezJ+OXfVqlVtArhmR2kA4mI6QEezpjTb8nKyZ89uD2RsOvhmaNdqNsVbg5Hxg5TeXDc9zoAc/7R3715rA6Gl2wsXLrTMaqUtIfRnh7ePrd7k0PYPAAAAAAAgYwh06wtrMFEzIOfNm5cgQ1K3tW9kYnRQhQYa9TyvLVu2WPAhseCkOn36tGzfvt0JUCBz61A9TD7uUdcyJePTbd2vx+FfJk+eLA0aNLCsZw1G/vLLLxacrFKlivWnjU970RKcBAAAAAAgY3G1xFvLqnv16iX169eX8PBwGTlypJw5c8aZ6t2zZ08pXry49YhUffv2lQ8++ED69+8vjz76qA3Dee211+Sxxx5zrvnkk09K165drax7//79VvqtGZd33HGHa98nUpcGIdtVK2rTunUgjvac1LJuMid9n/at/f33361UWwdheW9C6OAb7RmpNze0dFsf2ocWAAAAAABkfK4GKLt37y6HDx+WIUOGWJl27dq1Zfbs2c7gnN27d9tkby/NkJozZ44MGDDA+ktq8FKDlfGzpLTMU4OR2mdOp3w3a9ZMli1bZh/Dd2gwsnH5Am4vA+ng7NmzlhWppdvTp0+3AVtvvPGGPPXUU3a8S5cu8umnn9qNiYuHbgEAAAAAgI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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"inferred_reward_probabilities = 0.5 + 0.5 * nn.sigmoid(mcmc_samples[\\\"z\\\"].mean(0)[:, 0])\\n\",\n \"ground_truth_reward_probabilities = 0.5 + 0.5 * nn.sigmoid(ground_truth_z[:, 0])\\n\",\n \"\\n\",\n \"plt.figure(figsize=(16, 5))\\n\",\n \"plt.scatter(ground_truth_reward_probabilities, inferred_reward_probabilities, label=\\\"reward probability\\\")\\n\",\n \"\\n\",\n \"plt.plot((ground_truth_reward_probabilities.min(), ground_truth_reward_probabilities.max()), (ground_truth_reward_probabilities.min(), ground_truth_reward_probabilities.max()), \\\"k--\\\")\\n\",\n \"plt.ylabel(\\\"posterior mean (NUTS-HMC)\\\")\\n\",\n \"plt.xlabel(\\\"true value\\\")\\n\",\n \"plt.legend(title=\\\"parameter id\\\")\\n\",\n \"\\n\",\n \"corr = np.corrcoef(\\n\",\n \" np.array(ground_truth_reward_probabilities),\\n\",\n \" np.array(inferred_reward_probabilities),\\n\",\n \")[0, 1]\\n\",\n \"\\n\",\n \"bimodality_score = np.clip(\\n\",\n \" np.mean((np.array(inferred_reward_probabilities) < 0.2) | (np.array(inferred_reward_probabilities) > 0.8))\\n\",\n \" - np.mean((np.array(inferred_reward_probabilities) >= 0.35) & (np.array(inferred_reward_probabilities) <= 0.65)),\\n\",\n \" 0.0,\\n\",\n \" 1.0,\\n\",\n \")\\n\",\n \"\\n\",\n \"print(f\\\"reward-probability Pearson r: {corr:.3f}\\\")\\n\",\n \"print(f\\\"reward-probability bimodality score: {bimodality_score:.3f}\\\")\\n\",\n \"\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 8,\n \"id\": \"15\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# Inspect full NUTS posterior shape per subject (not just posterior means)\\n\",\n \"z_samples = np.array(mcmc_samples[\\\"z\\\"])\\n\",\n \"\\n\",\n \"# Handle optional chain dimension: [chains, draws, agents, params] -> [draws_total, agents, params]\\n\",\n \"if z_samples.ndim == 4:\\n\",\n \" z_samples = z_samples.reshape(-1, z_samples.shape[-2], z_samples.shape[-1])\\n\",\n \"elif z_samples.ndim != 3:\\n\",\n \" raise ValueError(f\\\"Unexpected mcmc_samples['z'] shape: {z_samples.shape}\\\")\\n\",\n \"\\n\",\n \"reward_prob_samples = 0.5 + 0.5 / (1.0 + np.exp(-z_samples[..., 0])) # [draws, agents]\\n\",\n \"true_reward_prob = np.array(0.5 + 0.5 * nn.sigmoid(ground_truth_z[:, 0]))\\n\",\n \"posterior_mean = reward_prob_samples.mean(axis=0)\\n\",\n \"\\n\",\n \"subject_ids = np.arange(num_agents)\\n\",\n \"sort_idx = np.argsort(true_reward_prob)\\n\",\n \"subject_ids_sorted = subject_ids[sort_idx]\\n\",\n \"true_reward_prob_sorted = true_reward_prob[sort_idx]\\n\",\n \"posterior_mean_sorted = posterior_mean[sort_idx]\\n\",\n \"reward_prob_samples_sorted = reward_prob_samples[:, sort_idx]\\n\",\n \"\\n\",\n \"plot_positions = np.arange(num_agents)\\n\",\n \"\\n\",\n \"fig, axes = plt.subplots(2, 1, figsize=(16, 10), constrained_layout=True)\\n\",\n \"\\n\",\n \"# 1) Violin plot: per-subject posterior distributions + true values (sorted by true reward prob)\\n\",\n \"parts = axes[0].violinplot(\\n\",\n \" [reward_prob_samples_sorted[:, i] for i in range(num_agents)],\\n\",\n \" positions=plot_positions,\\n\",\n \" showmeans=False,\\n\",\n \" showmedians=True,\\n\",\n \" showextrema=False,\\n\",\n \")\\n\",\n \"for pc in parts['bodies']:\\n\",\n \" pc.set_alpha(0.35)\\n\",\n \"\\n\",\n \"axes[0].scatter(plot_positions, true_reward_prob_sorted, color='crimson', marker='x', s=80, label='true reward prob')\\n\",\n \"axes[0].scatter(plot_positions, posterior_mean_sorted, color='black', s=20, label='posterior mean')\\n\",\n \"axes[0].set_ylabel('reward probability')\\n\",\n \"axes[0].set_xlabel('subject id (sorted by true reward probability)')\\n\",\n \"axes[0].set_ylim(0.5, 1.0)\\n\",\n \"axes[0].set_xticks(plot_positions)\\n\",\n \"axes[0].set_xticklabels(subject_ids_sorted)\\n\",\n \"axes[0].set_title('NUTS posterior distribution per subject (violin, sorted)')\\n\",\n \"axes[0].legend(loc='upper left')\\n\",\n \"\\n\",\n \"# 2) Density heatmap: posterior mass over probability bins by subject (same sorted order)\\n\",\n \"bins = np.linspace(0.0, 1.0, 60)\\n\",\n \"density = np.stack([\\n\",\n \" np.histogram(reward_prob_samples_sorted[:, i], bins=bins, density=True)[0]\\n\",\n \" for i in range(num_agents)\\n\",\n \"], axis=1) # [num_bins-1, num_agents]\\n\",\n \"\\n\",\n \"im = axes[1].imshow(\\n\",\n \" density,\\n\",\n \" aspect='auto',\\n\",\n \" origin='lower',\\n\",\n \" extent=[-0.5, num_agents - 0.5, bins[0], bins[-1]],\\n\",\n \" cmap='viridis',\\n\",\n \")\\n\",\n \"axes[1].plot(plot_positions, true_reward_prob_sorted, color='crimson', linestyle='--', marker='x', label='true reward prob')\\n\",\n \"axes[1].set_ylabel('reward probability')\\n\",\n \"axes[1].set_xlabel('subject id (sorted by true reward probability)')\\n\",\n \"axes[1].set_ylim(0.5, 1.0)\\n\",\n \"axes[1].set_xticks(plot_positions)\\n\",\n \"axes[1].set_xticklabels(subject_ids_sorted)\\n\",\n \"axes[1].set_title('NUTS posterior density by subject (sorted)')\\n\",\n \"axes[1].legend(loc='upper left')\\n\",\n \"fig.colorbar(im, ax=axes[1], label='density')\\n\",\n \"\\n\",\n \"plt.show()\\n\",\n \"\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"16\",\n \"metadata\": {},\n \"source\": [\n \"### Inference Method 2: Black-Box Stochastic Variational Inference\\n\",\n \"\\n\",\n \"Use NumPyro's `SVI` functionality to run variational inference with a `MultivariateNormal` variational posterior (that is, a Normal guide). SVI runs a black-box variational inference procedure where ELBO gradients are estimated using samples from the guide. This allows less constrained likelihood modeling than traditional mean-field variational Bayesian treatments, where likelihoods are often limited to conjugate-exponential forms.\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 9,\n \"id\": \"17\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"{'seed': 0, 'enumerate': False, 'iter_steps': 1000, 'optim': None, 'optim_kwargs': {'learning_rate': 0.001}, 'elbo_kwargs': {'num_particles': 10, 'max_plate_nesting': 1}, 'svi_kwargs': {'progress_bar': True, 'stable_update': True}, 'sample_kwargs': {'num_samples': 100}}\\n\"\n ]\n },\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_95807/2592818604.py:42: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" return Agent(\\n\",\n \" 76%|███████▌ | 757/1000 [09:16<02:59, 1.35it/s, init loss: 7789.5132, avg. loss [701-750]: 7768.9961]\"\n ]\n }\n ],\n \"source\": [\n \"# perform inference on parameters using black-box stochastic variational inference (SVI in numpyro)\\n\",\n \"# opts_svi dictionary can be used to specify various parameters\\n\",\n \"# for the SVI optimization algorithm\\n\",\n \"measurements = {\\n\",\n \" \\\"outcomes\\\": [outcomes[0] for outcomes in samples[\\\"outcomes\\\"]],\\n\",\n \" \\\"multiactions\\\": samples[\\\"multiactions\\\"][0],\\n\",\n \"}\\n\",\n \"\\n\",\n \"posterior = NumpyroGuide(NormalPosterior(num_params, num_agents, backend=\\\"numpyro\\\"))\\n\",\n \"\\n\",\n \"# perform inference using stochastic variational inference\\n\",\n \"opts_svi = default_dict_numpyro_svi | {\\\"iter_steps\\\": 1_000}\\n\",\n \"print(opts_svi)\\n\",\n \"\\n\",\n \"svi_samples, svi, results = run_svi(model, posterior, measurements, opts=opts_svi)\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"18\",\n \"metadata\": {},\n \"source\": [\n \"### Plot the variational free energy over time (negative ELBO)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 10,\n \"id\": \"19\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"[]\"\n ]\n },\n \"execution_count\": 10,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plt.plot(results.losses)\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"20\",\n \"metadata\": {},\n \"source\": [\n \"### Plot each ground truth parameter alongside their posterior means (mean taken over posterior samples from the guide)\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 11,\n \"id\": \"21\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"text/plain\": [\n \"\"\n ]\n },\n \"execution_count\": 11,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"plt.figure(figsize=(16, 5))\\n\",\n \"ground_truth_z = samples['z'][0]\\n\",\n \"for i in range(num_params):\\n\",\n \" plt.scatter(ground_truth_z[:, i], svi_samples[\\\"z\\\"].mean(0)[:, i], label=i)\\n\",\n \"\\n\",\n \"plt.plot((ground_truth_z.min(), ground_truth_z.max()), (ground_truth_z.min(), ground_truth_z.max()), \\\"k--\\\")\\n\",\n \"plt.ylabel(\\\"posterior mean (SVI)\\\")\\n\",\n \"plt.xlabel(\\\"true value\\\")\\n\",\n \"plt.legend(title=\\\"parameter id\\\")\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"id\": \"22\",\n \"metadata\": {},\n \"source\": [\n \"### Transform the latent parameter corresponding to the reward probability into probability space and investigate overlap between ground-truth and inferred parameter\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 12,\n \"id\": \"23\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"reward-probability Pearson r: 0.905\\n\",\n \"reward-probability bimodality score: 0.300\\n\"\n ]\n },\n {\n \"data\": {\n \"image/png\": 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SA8sSJExIbGyuFCxdOsF+3t27dmuh9NHNS79e0aVPxeDxy+fJl+6WjvSO8tFRcm9pqn0pN2x4+fLg0a9ZMNm7cKLly5Ur0uhrA1PMAAAAAAEDmoHEBfa2vpdt6W7dune3XBKWHHnrI2sFpheWvv/5qFZiaFJWZaHCy/5frxHPF/iMR0bZ/bM/aBCnhMzLVv84lS5bIyJEj5YMPPrBfPD/++KOVhGsDWy9Nz/7HP/4h1atXt36WmmF55swZ+e677655Xc3ijIiIcG76rgsAAAAAAMiYRo8eLeXKlbPX/kOGDLEYgQYktfLy0UcflZiYmATTuDNbcFLLujVz8srgpPLu0+N6HuALXMugLFCggKVdHz16NMF+3b5W/8jBgwdbOfcDDzxg2zfffLOcP39eHnzwQfn3v/+d6C+cPHnyWEq3Tt+6Fk3tzizp3QAAAAAA+BN93T9//nzp0qWLMwT30KFDsmfPHnst365dOyvd1uNXVmlmVtpzMn5Z95U0LKnH9bxG5fKn69qAtODaWwjBwcFSp04dWbhwobMvLi7OtrVvZGKioqKuCkJqkNOb2p2Yc+fOya5du6zfBAAAAAAAyPiOHz9uA3R1qrYmON1+++2yYsUK57gmKv3www/WBm769Oly//33+0xwUulAnNQ8D8joXJ3iPXDgQOnTp4/UrVvXht6MGTPG3hnxTvXu3bu3FCtWzHpEqq5du9rk71q1almvSc2K1KxK3e8NVD7zzDO2XapUKXtHZejQoXZMp30DAAAAAICMSSsqdTDuTz/9JD///LMlMXlpD8nTp08729WqVbObr9Jp3al5HpDRuRqg7NGjh70rov0ijhw5IjVr1pQ5c+Y473rs27cvQcbkSy+9ZD0l9OPBgwelYMGCFox89dVXnXMOHDhgwciTJ0/acR2os2rVKvscAAAAAABkDBqA1KrH3Llz27bOg9CkI6/atWtbBqWWb2uLN40H+Iv6ZfLZtG4diJNYvaj+JIqEhdh5gC8I8FyrNtqPnT17VsLCwmxgjvcXJQAAAAAAuDGXLl2SxYsXW5bktGnTrH/khAkT7JiGJzThSBONunXrZtO4/Zl3ireKH7jxhmmZ4g1fiq8RoEwEAUoAAAAAAFKHvraePXu2TJ061T7qa+74pdu7d+/2q+zI5AYpdVp3/IE5mlk5tGtVgpPwqfiaqyXeAAAAAADAt7Vs2VLWr1/vbBcpUsQyJLV0u1WrVgQnr0ODkO2qFrFp3ToQR3tOall3UCA/M/gWApQAAAAAAOCGaHHmpk2brHRbZ0vMmzdPQkND7VinTp0kOjraApLaU1KH5MafN4Hr02Bko3L53V4GkKYo8U4EJd4AAAAAAFxfbGysTdvWoKTedu3a5RzT/pI61FbFxMRI1qxZXVwpADdQ4g0AAAAAANLMrFmzpE+fPnLixAlnX7Zs2WzojWZJNmrUyNlPcBLA3yFACQAAAAAArun48eMyY8YMKVu2rLRo0cL2lStXzoKTefPmlS5dulj59i233CI5c+Z0e7kAMiEClAAAAAAAIAEt19aybZ28rWXccXFx0r17dydAWalSJVmxYoU0aNBAsmQhtADgxvBbBAAAAAAA2KCboUOHypQpU2Tjxo0JjtWqVcuCkfE1adIknVcIwFcRoAQAAAAAwA9dunRJ/vjjD6lXr55tBwQE2PRtDU4GBQVJy5YtrZ9kt27dpFSpUm4vF4API0AJAAAAAICf0Gm6s2fPtvJtHXQTFRVlPSbz5MljxwcNGiTnz5+XTp06WX9JAEgPBCgBAAAAAPBhhw8ftl6Selu8eLHExMQ4xwoXLizbt2+X+vXr27YOuwGA9EaAEgAAAAAAH+slGRsb6wyv0Z6SAwYMcI7rgBsNROpNA5OBgYEurhbIfGLjPLJmzyk5FhkthXKFSP0y+SQoMMDtZWVqBCgBAAAAAMjkNCD5yy+/OJO3n376aenfv78d0x6SX375pfWT1FvlypXdXi6Qac3ZeFiGT98shyOinX3hYSEytGtV6VAt3NW1ZWYBHn1rBQmcPXtWwsLCrDdH7ty53V4OAAAAAABX0f6RCxYssIDk9OnT5cSJE84x7SE5c+ZMV9cH+GJwsv+X6+TKQJo3d3Jsz9oEKVMYXyODEgAAAACATCY6OlqKFi1qL/y9dNBNly5dLEuyffv2rq4P8MWybs2cTCzLz/N/QUo93q5qEcq9U4AAJQAAAAAAGdju3butdHvHjh3ywQcf2L6QkBCpV6+eDbjRgKT2k2zWrJlkzZrV7eUCPkl7TsYv604sSKnH9bxG5fKn69p8AQFKAAAAAAAyEO3Etm7dOivd1sDkn3/+6Rx76aWXLHNSfffdd5Y1GRBAthaQ1nQgTmqeh4QIUAIAAAAAkEGMHz9ehg4dKgcOHHD2BQUFSfPmzS1TMjQ01NmfN29el1YJ+B+d1p2a5yEhApQAAAAAALg0QGLOnDnSsGFDKVmypO3TEm0NTubIkUM6dOhgQcnOnTtLvnz53F4u4Nfql8ln07qPREQn2odS85iLhIXYeUi+wBTcBwAAAAAApMDhw4flww8/lI4dO0rBggWlR48e8u233zrHu3btKjNmzLCJ3N9//7306tWL4CSQAejgm6Fdq9rnVzZV8G7rcQbkpAwZlAAAAAAApHGm5Pvvv2/9JFevXp3gWMWKFSUsLMzZ1p6SmjEJIOPpUC1cxvasbdO64w/M0cxJDU7qcaRMgEe77+KqPx76ByIiIkJy587t9nIAAAAAAJlIbGysZUoWL17cti9cuCAFChSQqKgo29aSbu/k7cqVK7u8WgDJFRvnsWndOhBHe05qWTeZkzcWXyODEgAAAACAG6RByAULFliW5LRp06x8e9OmTXZMB9v8+9//tiCllnCHh5NlBWRmGoxsVC6/28vwKQQoAQAAAABIgZMnT8rMmTNl6tSpMnfuXCdDUsXExMjx48ctUKlefPFFF1cKABkbAUoAAAAAAFLgmWeekYkTJzrbJUqUsLJtLd9u3ry5TeQGAPw9ApQAAAAAAFyDjm34/fffLUtSy7c//fRTqVu3rh3TQKQe8/aTrFmzpgQE0IcOAJKLACUAAAAAAPFoefbSpUstIKm3/fv3O8d0O36AUgOTAIAbQ4ASAAAAAID/s2XLFmncuLGcOXPG2Zc9e3bp0KGDBSQ7d+7s7CdbEgBSBwFKAAAAAIBfOnz4sE3cVg899JB9rFChggUeCxUqJN26dbOgZJs2bWwSNwAgbRCgBAAAAAD4TT/JrVu3Ov0kV69e7Qy3efDBBy0wmSVLFlmzZo2UKVNGgoKC3F4yAPgFApQAAAAAAJ/3n//8Rz766CPZsWNHgv0NGjSwPpKXLl2SbNmy2b7y5cu7tEoA8E8EKAEAAAAAPuXChQuyaNEiad++vWVEqn379llwMjg4WFq3bm1Bya5du0rRokXdXi4A+D0ClAAAAACATO/kyZMyc+ZMK92eM2eOREVFyeLFi6Vly5Z2/IEHHpCmTZvasJvcuXO7vVwAQDwEKAEAAAAAmdKxY8fkm2++sZ6Sy5cvl9jYWOdY8eLFLWjpVb16dbsBADIeApQAAAAAgEwz5Ob8+fOSM2dOp2z7ySefdI7ffPPNVrqtk7dr165tQ28AABkfAUoAAAAAQIYVExMjy5YtcyZvt2nTRiZMmGDH6tSpI927d5fGjRtbULJs2bJuLxcAkAIEKAEAAAAAGUpkZKTMnTvXgpLaV/LMmTPOMR1+o5mUmh2pt8mTJ7u6VgDAjSNACQAAAADIUFq0aCG///67s12gQAHp1q2bZUm2bduW0m0A8DEEKAEAAAAArti6daszdXvWrFkSGhpq+3XStmZRevtJNmrUSIKCgtxeLgAgjQR4NDceCZw9e1bCwsIkIiJCcufO7fZyAAAAAMAnxMXFyerVq51+ktu2bXOOTZs2Tbp27WqfX7p0SbJmzUqmJAD4SXyNDEoAAAAAQJrTLMm+ffvK0aNHnX0ahGzdurVlSjZo0MDZHxwc7NIqAQBuIEAJAAAAAEhVp0+ftuE2JUuWlObNm9u+MmXKWHBSs2k6depkQUkt5aZqDQBAgBIAAAAAcMP27t1rZdt6W7p0qcTGxkr37t2dAGWlSpVsf8OGDcmQBAAkQIASAAAAAJAiOtJgxIgRMmXKFFm/fn2CYzfffLPUqVMnwT5vsBIAgPgIUAIAAAAAkiQmJkY2btwotWrVsm0dYqPTtzU4GRgYKE2bNnUmb5ctW9bt5QIAfDVAefHiRZu6pun7UVFRUrBgQfvjpP1EAAAAAAC+5dy5czJ37lybvK19JSMjI+X48eOSJ08eO/7cc8/ZpNYuXbpIgQIF3F4uAMCXA5Q///yzvPPOOzJ9+nR710wbG4eGhsqpU6csaKnvjj344IPy8MMPS65cudJ21QAAAACANHPs2DGnn+SCBQvsNZ+XBiG3bt1qvSTVHXfc4eJKAQC+IDApJ3Xr1k169OghpUuXlnnz5tk7ZidPnpQDBw5YFuWOHTvkpZdekoULF0rFihVl/vz5ab9yAAAAAECqiYuLcz7//vvvLQFFMyY1OFmuXDl5+umnZdmyZXLkyBEnOAkAQLoFKDt37ix79uyR119/XZo1a2aZk/Fp9mSfPn1kzpw5FqTU3iNJ9f7771vgMyQkRBo0aCBr1qy57vljxoyx6W+6hhIlSshTTz0l0dHRN3RNAAAAAPDHgOTKlStl0KBBUrlyZfnwww8TJKnUq1dPXn31Ves5qUkp//nPf+z1YFBQkKvrBgD4ngCPjl1zyaRJk6R3794ybtw4CyRq8HHy5Mmybds2KVSo0FXnf/3113LffffJ+PHjpXHjxrJ9+3bp27ev/Otf/5K33norRddMjPZP0RL2iIgIyZ07d6p/3wAAAADgBk3uWLRokfWT1PZdmg3p1bFjRxt4AwBAakhOfM3VAKUGEPVduffee895B0+zIh977DF7F+9Kjz76qGzZssWyNL20zECH9qxYsSJF10wMAUoAAAAAvhicLFq0qJw+fdrZp693OnXqZJO3O3ToYK+DAABIDcmJryV5SE7evHklICDgb8/ToTlJcenSJVm7dq288MILzj4tDW/btq2VGSRGsya//PJLK9muX7++7N69297h69WrV4qvqbSnSvymz/oDBAAAAIDMat++fTbgRqvO3n33XdunLbDq1KkjmzdvlltvvdWCki1btpTg4GC3lwsA8HNJDlC+/fbbSQpQJtWJEyckNjZWChcunGC/butEuMTcfffddr+mTZuKJn5evnzZpoa/+OKLKb6mGjVqlAwfPjxVvi8AAAAASG/6+mjDhg1Wuq2Byd9//905pq+XwsPD7fNvv/3Wkk+SMzcAAIAME6DULEW3myEvWbJERo4cKR988IGVcu/cuVOeeOIJGTFihAwePDjF19WMy4EDBybIoNSycAAAAADI6CZOnCjDhg2TvXv3Ovs0ANmkSRPLlMyWLZuzP3/+/C6tEgCAVAhQFi9e3CZ133///VKhQgW5UQUKFLCA59GjRxPs1+0iRYokeh8NQmqg9IEHHrDtm2++Wc6fPy8PPvig/Pvf/07RNZX+wY7/RxsAAAAAMqJz587JvHnzpG7dulKyZEnbp6+BNDipJdy33HKLlW536dJFChYs6PZyAQBIkiTn9T/yyCPy/fffS+XKlaVZs2b2Ll1UVJSklPY50f4n8Qfe6EAb3W7UqFGi99Gvd2UpgjerU0saUnJNAAAAAMjINOHik08+ka5du1pSxp133mml2l4ajJwyZYq1vNLy7nvvvZfgJADANwOUmr2oJdUa7CtbtqxN1NY+Jv369bMp2imhZdUff/yxfPbZZzadu3///pYRqX9QVe/evRMMvNE/yGPHjrU/xnv27JH58+fbunS/N1D5d9cEAAAAgIwuMjJS3njjDeu/733dNWPGDBvuqa/HcuTI4ZyrPSU1azL+PgAAfLLE20unvOnt/ffft0ChZlJqdmKVKlWs/Dt+L8e/06NHDzl+/LgMGTJEjhw5IjVr1pQ5c+Y4Q2508lz8jMmXXnrJBvXox4MHD9q7ghqcfPXVV5N8TQAAAADIaLTyS1+/FC1a1LazZMlifSW9VWta0u2dvH3TTTel6gBTAADcFuDR2ugbNHPmTMt2PHPmjE3Rzux0SE5YWJhERERI7ty53V4OAAAAAB+k2ZCLFy+2ydvTpk2zTMhNmzY5x3UYqA616datm80EAADAV+Nryc6g9NJ38r777juZMGGCrFixQsqVKyfPPvtsSi8HAAAAAD5PkzpmzZplQUmt9NJS7vgDcI4dOyaFChWybW1nBQCAP0h2gPKXX36R8ePHy+TJk+Xy5cvSvXt3e2evefPmabNCAAAAAPAR2hJLkzy8tKRbMyS1dFtbaWXLls3V9QEAkKEDlK+//rr9Id2+fbv1P9GGzXfddZfkypUrbVcIAAAAAJmIdtH6888/baK2Zkp+9NFHUqdOHTumwcg1a9Y4/SR1f/y++wAA+KMk96DUgTQ9e/a0QTjVqlUTX0YPSgAAAADJodVlP//8swUkNTC5Z88e55iWar/88sv2ub78YsANAMAfnE2LHpSHDh2SrFmzpsb6AAAAAMBnbNu2TRo3biynTp1y9oWEhMgtt9ximZJdunRx9hOcBADgakmuJfjtt99kxowZCfZ9/vnnUqZMGWvi/OCDD9oUOgAAAADwVTrERnvyf/LJJ84+HRiqdOJ2nz59ZMqUKXLixAnLpLzvvvucoTcAAOAGMyiHDx8urVq1ct79054qWu7dt29fqVKlivWk1AbPw4YNS+olAQAAACDD27Fjh9NPUoeGapl2iRIl7PWQZkRmyZLF9mugUj8HAADJk+S/nn/88Ye88sorzva3334rDRo0kI8//ti29Q/00KFDCVACAAAA8Aljxoyx1zubN29OsF8H22jp9qVLl5yp25UqVXJplQAA+FGA8vTp01K4cGFne+nSpdKxY0dnu169erJ///7UXyEAAAAApDFtV7VkyRJp06aNkwW5e/duC07qtlaTaVBSp3BrcgYAAHAhQKnBSZ1Ep3+M9Z3CdevWWdm3V2RkJEN0AAAAAGQaZ86ckVmzZln59uzZs+01zeLFi6Vly5Z2/IEHHpBGjRpZYkaePHncXi4AAD4ryQHKTp06yaBBg+S1116z3ivZs2eXZs2aOcc3bNjgNIcGAAAAgIxIh9dMmjTJXtNoxuTly5edY+Hh4XL8+HFnu3r16nYDAAAZJEA5YsQIueOOO6RFixaSM2dO+eyzzyQ4ONg5rpPsbrnllrRaJwAAAAAkmw60uXDhgiVYqL/++kseffRR57gO/LztttvsVrduXQkMDHRxtQAA+KcAj/7FToaIiAgLUAYFBSXYf+rUKdsfP2iZWZ09e1bCwsLse82dO7fbywEAAACQDJoV+fPPPzuTt7VkWxMqlL780cSLxo0bW0/JihUrur1cAAB8UnLia0nOoPTSCycmX758yb0UAAAAAKSK8+fPy7x58ywoOWPGDDl58qRzLCYmxgKTAQEBdpsyZYqrawUAACkIUD788MPy0ksvSfHixf/2XO3nou9Y3nPPPUm5NAAAAADcMG1FtXbtWmc7b9680rVrV8uS1FZUGpgEAACZOEBZsGBBuemmm6RJkyb2R157sxQtWlRCQkLk9OnTsnnzZlmxYoV8++23tv+jjz5K+5UDAAAA8Ds7d+50pm5Pnz5dQkNDbb8GITVrUgOS2k+yadOmkiVLsgvGAABARu5BefToUfnkk08sCKkByfhy5colbdu2lQceeEA6dOggmR09KAEAAICMIS4uzjIjtZekBiY3bdrkHJs2bZolUKjo6GjJli0bmZIAAGTC+Fqyh+QozZrct2+fTcMrUKCAlCtXzqeeCBCgBAAAANynPSXvu+8+OXjwoLNPsyK1nFszJf/xj39IkSJFXF0jAABwYUiOt5+L3gAAAAAgNeiLFy3b1r73Wp6tSpUqZcHJnDlzSseOHS0o2alTJ16LAADgY2jKAgAAAMAVBw4csDJtLd1evHixTdvu3r27E6CsVKmSLFy40Hrha/k2AADwTQQoAQAAAKQb7TA1atQomTJlivz2228JjlWuXFmqV6+eYF/r1q3TeYUAACC9EaAEACCdxcZ5ZM2eU3IsMloK5QqR+mXySVCg7/RyBoD4YmNjbcjmzTffbNvau16zJjU4qZ83atTISrf1phmTAADA/xCgBAAgHc3ZeFiGT98shyOinX3hYSEytGtV6VAt3NW1AUBqiYqKkvnz51vp9vTp0+XMmTNy/PhxyZMnjx1/5plnbJ9O4C5cuLDbywUAAC5L0RRvX8cUbwBAWgUn+3+5Tq78w+vNnRzbszZBSgCZ1okTJ2TGjBkydepUm7594cIF55gOtdFjjRs3dnWNAAAgY8bXApN78aNHj0qvXr2kaNGikiVLFgkKCkpwAwAAiZd1a+ZkYu8KevfpcT0PADKLuLg45/PvvvtO7r33Xsua1OCkTuB+4oknZNGiRXLs2DGCkwAAIPVKvPv27Sv79u2TwYMHS3h4uPWNAQAA16c9J+OXdV9Jw5J6XM9rVC5/uq4NAJJKi6/Wrl1rWZIaiHzkkUekf//+dqxbt27yySefWC/J2267zYbd8FoBAACkSYByxYoVsnz5cqlZs2Zy7woAgN/SgTipeR4ApJdLly7JkiVLLCCpt4MHDzrHdNiNN0BZvHhxWbdunYsrBQAAfhOgLFGihL1zCgAAkk6ndafmeQCQHi5evGiBR+0v6ZUzZ07p0KGDZUl26tTJ1fUBAAA/DVCOGTNGBg0aJB9++KGULl06bVYFAICPqV8mn03rPhIRnWgfSi2CLBIWYucBgBs0M1IzIrdv3y5vv/227cuWLZtVTv35559Wuq231q1bS0gIb6YAAAAXp3jrBL6oqCi5fPmyZM+eXbJmzZrg+KlTpySzY4o3ACAtp3ir+H98meINwA36MmDz5s1OP8lff/3VOXbo0CHrN6+OHz8u+fPnl8DAZM/XBAAAfuxsMuJrKcqgBAAAyafBRw1C6rTu+ANzNHNyaNeqBCcBpJsvvvhChg8fLrt27XL26UCbhg0bWul2cHCws79gwYIurRIAAPiLZAco+/TpkzYrAQDAD2gQsl3VIjatWwfiaM9JLesOCmTSLYC0odVPCxYskFq1alk/eS8NTmoJd5s2bSwo2bVrVylSpIirawUAAP4p2QHK+KKjo22qX3yURAMAcH0ajGxULr/bywDgw3SozYwZM6x0e+7cuXLhwgV5/fXX5dlnn7XjXbp0kcmTJ0v79u0lV65cbi8XAAD4uWQHKM+fPy/PP/+8fPfdd3Ly5MmrjsfGxqbW2gAAAAAk0blz5+Tjjz+2npIrVqyQuLg451jJkiUtWzJ+X/nu3bu7tFIAAIAbDFA+99xzsnjxYhk7dqz06tVL3n//fZv4p1O9R48endzLAQAAAEjhkJujR486ZdlBQUHy0ksvWUm3qlGjhpVu6+RtncStPSYBAAB8IkA5ffp0+fzzz6Vly5Zy7733SrNmzaR8+fJSqlQp+eqrr+See+5Jm5UCAAAAfk7bKy1dutRKt/Wm7ZU2bdpkx0JDQ62EW7MjNShZunRpt5cLAACQNgHKU6dOSdmyZe1zfUKk26pp06bSv3//5F4OAAAAwHWcPXtW5syZY6Xbs2bNkoiICOdYjhw5LIuycOHCtj1s2DAXVwoAAJAygcm9gwYn9+zZY59XrlzZelF6Myvz5MmTwmUAAAAASMyTTz4pPXr0kG+++caCk4UKFZIHHnjAhuDoMBxvcBIAAMBvMii1rPuPP/6QFi1ayKBBg6Rr167y3nvvSUxMjLz11ltps0oAAADAx/tJbt261bIktXT7gw8+kNq1a9uxbt26yc8//+z0k2zQoIH1mwQAAPAVAR59NnQD9u7dK2vXrrU+lNWrVxdfKaMJCwuzd6i1jB0AAABIbbGxsbJq1SonKLljxw7n2ODBg+Xll1+2z/XpOgNuAACAL8fXkp1BGV90dLQNx9EbAAAAgKTZvn27DZs8duyYsy84OFjatGljmZKaNelFcBIAAPi6LCl5p3fkyJEybtw4a8itT660L6W+y6uTAu+///60WSkAAACQCZ08eVJmzpwply9flvvuu8/26fNn3dasgi5duljpdocOHSRXrlxuLxcAACDjByhfffVV+eyzz+T111+Xfv36OfurVasmY8aMIUAJAAAAv6dDJbVsW2/Lly+3N/lLlChh/dw1IzJLliy2v0KFCpI1a1a3lwsAAJC5ApSff/65fPTRR1Z+8vDDDzv7a9SoYY29AQAAAH/17rvvyieffCIbNmxIsF+fK2uW5MWLFyUkJMT2Va1a1aVVAgAAZPIA5cGDB20gzpXi4uJskjcAAADgD/S577Jly6RFixaWEam0/ZEGJ3XKtvaY9PaTLFOmjNvLBQAA8J0Apb7Tq+UoVw7G+f7776VWrVqpuTYAAAAgQ4mMjJQ5c+bY5O1Zs2bJmTNnZPHixdKyZUs7ru2O6tWrJ507d5b8+fO7vVwAAADfDFAOGTJE+vTpY5mUmjX5448/yrZt26z0e8aMGWmzSgAAAMAlp06dksmTJ1s/yYULF8qlS5ecY4UKFZIjR4442zVr1rQbAAAAki7A4/F4JJk0g/Lll1+WP/74Q86dOye1a9e2wOUtt9wivuDs2bM2UTEiIkJy587t9nIAAACQjvTpcXR0tISGhtr2b7/9ZlmRXjrYRku39dagQQMr5wYAAEDK42uBkgLaT2f+/Ply7NgxiYqKkhUrVtxQcPL999+X0qVLW8NwfZK3Zs2aa56r5TM6+fDKm5bRePXt2/eq4x06dEjx+gAAAODbdMr2L7/8Is8995xUrlxZHnnkEedYnTp1pGvXrjJq1CjZvHmzVQ+9/vrr0rhxY4KTAAAAbpR4x6fZk1rmHV9yMw4nTZokAwcOlHHjxllwcsyYMdK+fXt74qclM1fSkvL4ZTUnT560qYj/+Mc/EpynAckJEyY429myZUvWugAAAODbLly4YCXb2k9y+vTp9uZ7/Oe5mknpfbN72rRprq4VAADAlyU7QLlnzx559NFHZcmSJVb64uV9AqfvPifHW2+9Jf369ZN7773XtjVQOXPmTBk/frwMGjToqvPz5cuXYPvbb7+V7NmzXxWg1IBkkSJFkvndAQAAwF80b97cyre9tARJq3K0dFvf7NbntgAAAMiAAcqePXtaMFIDiIULF76hJ26aCbl27Vp54YUXnH2BgYHStm1bWblyZZKu8emnn8q//vUvyZEjR4L9GkDVDMy8efNK69at5ZVXXrnmJMWLFy/aLX6NPAAAAHzDX3/9ZQNuZs+eLVOmTHF6S7Zr184G3Nx6660WlNSAZXBwsNvLBQAA8DvJDlDqYBwNKlaqVOmGv/iJEycs41IDnfHp9tatW//2/tqrcuPGjRakjE/f8b7jjjukTJkysmvXLnnxxRelY8eOFvRMrE+Q9hMaPnz4DX8/AAAAcJ++mb5+/Xor3dbApD5/9VqwYIH1k1SDBw+WV199lUxJAACAzBag1AmG+/fvT5UA5Y3SwOTNN98s9evXT7BfMyq99Hj16tWlXLlyllXZpk2bq66jGZzaBzN+BmWJEiXSePUAAABIbRqAvP/++2Xfvn0JKnR0yKNmSurAGy9vJiUAAAAyWYDyk08+kYcfflgOHjwo1apVk6xZsyY4rsHApCpQoIBlNB49ejTBft3+u/6R58+ft/6TL7/88t9+nbJly9rX2rlzZ6IBSu1XyRAdAACAzCUyMlLmzJkjRYsWlSZNmtg+fZNZg5MafNTBi1q6rX0l9bkgAAAAfCRAefz4cSub9g61UVoWk5IhOdrjR9/F1umJ+uRR6VRw3dZBPNczefJk6xupPTH/zoEDB2zad3h4eJLXBgAAgIxHe0bqRG0t3dZsSe1p3r17dydAqVU+c+fOlaZNm9ogRQAAAPhggPK+++6TWrVqyTfffHPDQ3KUllb36dNH6tata6XaY8aMsexIbwC0d+/eUqxYMesTeWV5twY1rxx8c+7cOesneeedd1oWpgZTn3vuOSlfvry9iw4AAIDMRd8I/89//mMDblatWmXbXtrGp2rVqgnOv+WWW1xYJQAAANItQLl3715711oDfqmhR48elpU5ZMgQe0e8Zs2aVqrjHZyjJTraNyi+bdu2yYoVK2TevHlXXU9Lxjds2CCfffaZnDlzxkp+9EnqiBEjKOMGAADIBLSiRgcmegOP+ob4Dz/8IKtXr7ZtfVNb+0nqTc9hyA0AAEDmFuCJ/xZ0EujUw759+1qGoq/SITlhYWESEREhuXPndns5AAAAPi86Otra/Gjptr4Zru159E3sPHnyOO19dJ8+F9XqGgAAAPhOfC3ZGZT6pPCpp56SP//80yZkXzkkp1u3bslfMQAAAPzO6dOnZebMmTJ16lSroNE2P176JHbTpk1Ob8l//OMfLq4UAAAAGSqD8spy6wQXS+aQnIyKDEoAAIC04R2sqD744AMZMGCAc0wzI7XHuJZut2jRwgYqAgAAIHNK0wxK7QkEAAAAJDUg+ccff1jptmZKPvTQQ/Lwww87lTfjxo2zgKQGJmvXrk0/SQAAAD+U7AAlAAAAcD2XL1+W5cuXW0BSA5M6ZNFLt70ByuLFi9twQwAAAPg3ApQAAABINRcvXpSSJUvKsWPHnH2hoaHSvn17y5Ts0qWLq+sDAABAxkOAEgAAACly5MgRmT59umzbtk3+85//2L5s2bJJ9erVZf369TZcUUu327ZtK9mzZ3d7uQAAAPCVITn+gCE5AAAAidNgpLef5KpVq6zHpDp06JCEh4fb50ePHpUCBQpIUFCQy6sFAACAzw3J0X5CX3/9tZXoFC5c+EbXCQAAgExCnwOOGDFCtm7dmmB/vXr1rHQ7S5b//7SS54kAAABIjmQFKPWJpzY137JlS7K+CAAAADKP6OhoWbRokZVq6yAbFRsba8HJrFmzSuvWrS0oqVO4ixUr5vZyAQAAkMkFJvcO9evXt55CAAAA8B2nT5+WL7/8Uv7xj39IwYIFpXPnzvLNN984x3W4zbfffivHjx+XOXPmSP/+/QlOAgAAwJ0hOY888ogMHDhQ9u/fL3Xq1JEcOXIkOK7vtAMAACDjO3/+vIwfP976SS5dutSyJL00+KjZkl558+aVHj16uLRSAAAA+LJkD8kJDLw66TIgIMAapOvH+E9sMyuG5AAAAF+kz9dOnDhhGZLqwoULNswmKirKtm+66Sabuq03fSNan9sBAAAAGWpIjtqzZ0+KFgUAAID0p0MOly9f7kze1uqXTZs22bHQ0FCrjMmTJ4/1lCxfvrzbywUAAIAfSnYGpT8ggxIAAGRm586dk3nz5llAcsaMGdZf0iskJMTecC5SpIirawQAAIBvO5uWGZRq165dMmbMGGead9WqVeWJJ56QcuXKpWzFAAAASDWPP/64TJgwwdnOnz+/dO3a1bIk27Vrd1UPcQAAACBTTfGeO3euBSTXrFljA3H0tnr1autZNH/+/LRZJQAAAK6yfft2eeONN6RJkyaybt06Z3+3bt2kbNmy8tRTT9nwmyNHjljAUntLEpwEAABApi/xrlWrlrRv315Gjx6dYP+gQYOslCj+k+PMihJvAACQEcXFxcmvv/7q9JP0VrOowYMHy8svv+ycpwNuGHIDAACAzBBfS3aAUvsW/fnnn1KhQoWr3sHXbMro6GjJ7AhQAgCAjGbHjh3SokULOXz4sLMvS5Ys0qpVKyvd1lvx4sVdXSMAAACQLj0oCxYsKOvXr78qQKn7ChUqlNzLAQAA4ApnzpyRWbNmSUxMjPTp08f2lSlTxt4IzpUrl3Tq1MkCkh07drQJ3AAAAEBmluwAZb9+/eTBBx+U3bt3S+PGjW3fzz//LK+99poMHDgwLdYIAADg8/bv32+l23pbsmSJXL58WUqWLCm9e/e2Um3NltR+khUrVpRs2bK5vVwAAADAvQCl9jfSd+7ffPNNeeGFF2xf0aJFZdiwYTYxEgAAAEk3duxY+eSTT67q461DCXWozcWLF63Fjrr55ptdWiUAAACQgQKU+g6+ToTUW2RkpO3TgCUAAACuT7MitfJEp25rRqTavHmzBSf1OZbu9/aTvLKdDgAAAOCrkh2gjI/AJAAAwPWdP39e5s2bZ6Xb06dPl1OnTsnixYulZcuWdvy+++6TWrVqSZcuXejnDQAAAL+UpABl7dq1ZeHChZI3b157Aq3v8F/LleVJAAAA/ub06dMyZcoUmTp1qsyfP9+G23jlz59fDh065Gzrcyu9AQAAAP4qSQFKLTPyNmPXXkgAAABISHtFep8v7dq1S+6//37nmE7g1udQ+pwqfnk3AAAAAJEAj8fjSerJsbGx1jepevXqkidPHvFVZ8+elbCwMImIiJDcuXO7vRwAAJABxcXFyW+//WZZklq+Xb9+fZkwYYId06dXWrLdsGFDC0xWq1btuhUoAAAAgD/H15L19n1QUJDccsstsmXLFp8OUAIAAFwrS1L7R2pAUm+HDx9OUNatgUkNROpt5syZrq4VAAAAyCySXV+kGQC7d++2UiUAAAB/0qJFC1m9enWCgYEdO3a0LEn9SJYkAAAAkA4ByldeeUWeeeYZGTFihNSpU0dy5MiR4Dgl0QAAILPbv3+/TJs2TWbPni2TJ0+W0NBQ29+6dWvZt2+f9ZLUW6tWrZy+kwAAAADSoQelCgwM/P93jpcl4C1p0j6VmR09KAEA8C/6PGbjxo1OP8m1a9c6xzRQ2bVrV/s8KipKQkJCEjwfAgAAAJCOPSiV9l0CAADwFYsWLZIHHnhA9uzZ4+zTN10bN25spdu1atVy9mfPnt2lVQIAAAC+K0tKei8BAABkRufPn5f58+dLoUKFLACpihUrZsFJLdVu166dBSV1AnfhwoXdXi4AAADgF5IdoFTLly+XDz/80IblaF8mfWL/xRdf2OCcpk2bpv4qAQAAUuj48eMyffp0K9/W4GR0dLR0797dCVBWqlTJJm43b95ccubM6fZyAQAAAL+T7AZKP/zwg7Rv396axa9bt04uXrxo+7WefOTIkWmxRgAAgGT3lHzrrbekWbNmUqRIEbn//vstSKnByVKlSknFihUTnN+pUyeCkwAAAEBmCVDqFO9x48bJxx9/LFmzZnX2N2nSxAKWAAAA6S0uLk62bt2aoIfkpEmTZMWKFXZM+0gOHz5c1q9fb+Xcr776qqvrBQAAAHADJd7btm2zEqgr6VSeM2fOJPdyAAAAKXLp0iUb3qel2zpp+9ixY1bOnSdPHjs+cOBA29etWzfLmgQAAADgIwFKLZPauXOnlC5dOsF+zVAoW7Zsaq4NAAAgAW0pM2vWLPnpp5/sY2RkpHNMS7T//PNPK+tWPXr0cHGlAAAAANIsQNmvXz954oknZPz48VY+dejQIVm5cqU888wzMnjw4OReDgAA4G/7SepzDvXVV1/JgAEDErxxqhmSOnm7VatWEhIS4uJKAQAAAKRLgHLQoEHWy6lNmzYSFRVl5d7ZsmWzAOVjjz2WokUAAADED0hu2rTJsiS1fPuBBx6Qhx56yI5pMPK9996TW2+91W7169eXwMBkt9QGAAAAkIEEePRVQAr7Pmmp97lz56Rq1ao+Nfny7Nmz1lNTy8hy587t9nIAAPB5sbGx8ssvv1hAUgOTu3btco61b99e5syZ4+r6AAAAAKRdfC3ZGZT33XefvPPOO5IrVy4LTHqdP3/eMii19BsAACA5b3pqb+vDhw87+7Q6o23btla63bVrV1fXBwAAACCDZVAGBQXZC4hChQol2H/ixAnrA3X58mXJ7MigBAAgbejzhRkzZsiWLVvktddec/ZrMHLdunXSpUsXK93WrElfqs4AAAAA/M3ZtMig1ItqLFNvOjEzfhN6LcvSSZpXBi0BAAC0XFvLtvW2YsUK62WtnnzySQkPD7fPv/jiCylQoIBkzZrV5dUCAAAASG9JDlDmyZPHJmjqrWLFilcd1/3Dhw9P7fUBAIBM6ttvv5VXX31VNm7cmGB/rVq1LEtSqzK8vIFKAAAAAP4nyQHKxYsXW/Zk69at5YcffpB8+fI5x4KDg6VUqVJStGjRtFonAADI4H0klyxZIjfddJMUK1bM9sXExFhwUgORLVq0sH6SOoVbnzMAAAAAQIp7UO7du1dKlixpGZO+ih6UAAAk7e/l7NmzbfK2tnrR7ddff12effZZO3769GmZOXOmdOrUKcEbmwAAAAB839m0nOKtTe33798vTZs2te33339fPv74Y5vorZ/nzZs35SsHAAAZ2vnz5+Xzzz+3fpKLFi2yLEmvwoULJ3gDU58T9OzZ06WVAgAAAMgsApN7B82K0Aio+vPPP2XgwIGWGbFnzx77HAAA+A4ttDh58qSzHRgYKM8884zMnTvXgpOVK1eW559/XlauXCmHDh2yYwAAAACQpgFKDURqtqTSXpRdu3aVkSNHWvaklnmlhN63dOnSNhm8QYMGsmbNmmue27JlS2dYT/xb586dE7yYGjJkiDXcDw0NlbZt28qOHTtStDYAAPxNbGysLF++3IKNFSpUsP6RXvp39amnnpLXXntNtm7dapUVo0ePloYNG1rwEgAAAACSK9kl3joQJyoqyj5fsGCB9O7d2z7X3lLezMrkmDRpkmVejhs3zoKTY8aMkfbt28u2bdukUKFCV53/448/WiN+L83qqFGjhvzjH/9w9mn/q//+97/y2WefSZkyZWTw4MF2zc2bN1sQFAAAJKR/2/XvuvaTnDFjhhw/ftw5li1bNjly5IgUKVLEtl955RUXVwoAAABA/H1Ijk7f1ABhkyZNZMSIEZZRqdM6582bJ48++qhs3749WQvQoGS9evXkvffes+24uDgpUaKEPPbYYzJo0KC/vb8GNDVb8vDhw5IjRw7LntRp4k8//bRTZqbNOLUv1sSJE+Vf//rX316TITkAAH9z//33y/jx4xP0j9TqBJ28rW/y5cyZ09X1AQAAAMhckhNfS3YtlgYSs2TJIt9//72MHTvWgpNKy7s7dOiQrGtpoHPt2rVWgu0sKDDQtrWXVVJ8+umnFnTU4KTSgKlmecS/pv4wNBCa1GsCAOCrdu/eLW+//baVba9bt87Zry1bSpUqJY8//rgsXLhQjh49Kl988YXceeedBCcB/K3YOI+s3HVSflp/0D7qNgAAQJqVeJcsWdJKv66kL3aS68SJE9bnSrMb49Nt7Wv1d7RX5caNGy1I6aXBSe81rrym99iVLl68aDevlJSqAwCQEWllgQYitXRbJ2/rgDsv3Ve7dm0nQHnrrbcmmMINAEkxZ+NhGT59sxyOiHb2hYeFyNCuVaVDtXBX1wYAAHw0QKk0qKgvarQxvrrpppus9DsoKEjSkwYmb775Zqlfv/4NXWfUqFEyfPjwVFsXAAAZwc6dO6VVq1Zy4MABZ5/+rW7evLkFI2+//fYE+wEgJcHJ/l+ukyvzJY9ERNv+sT1rE6QEAACpH6DUFzudOnWSgwcPSqVKlZwAn/aNnDlzppQrVy7J1ypQoIC9INIysvh029uI/1rOnz8v3377rbz88ssJ9nvvp9fQKd7xr1mzZs1Er/XCCy/YoJ74GZT6/QAAkFno3y5tt6IVAd4BdqVLl7a/l9oGRftIaj9J7Supg+0A4EZpGbdmTiZWzK37NB9bj7erWkSCAsnOBgAAqdiDUntTaRBy//79VjKmt3379tm0bD2W3IngderUsV5XXjokR7cbNWp03ftOnjzZXoT17NkzwX5dhwYp419TX7StXr36mtfU6aTarDP+DQCAjO7QoUMybtw46wGtb/ppT+bBgwdbWbfSntGLFi2yidw//PCD9OrVi+AkgFSzZs+pBGXdV9LfRHpczwMAAEjVDMqlS5fKqlWrErzAyZ8/v4wePdomeyeXZi726dNH6tata6XaOpVbsz3uvfdeO65ZIDqIR7M0ryzv1kwQ/drxae+sJ598Ul555RWpUKGCBSz1xZpO9tbzAQDI7D766CP7O6i9mOOrWLGilW5HR0dLaGio7btW9QAA3KhjkdGpeh4AAPBfyQ5QarZhZGTkVfvPnTtnGZHJ1aNHD8vsGDJkiA2x0RdSc+bMcYbcaHamTvaOb9u2bbJixQqZN29eotd87rnnLMj54IMPypkzZ6Rp06Z2zZCQkGSvDwAAN2nfZ31jsEGDBpYRqXTQjTc42bBhQwtK6ptwlStXdnm1APxJoVwhqXoeAADwXwEebx1YEmlGo5Z1a+aGdziNlk/369fPyrUnTpwomZ2WhIeFhUlERATl3hm455GWC+k78vqkt36ZfPQ2AuAzLly4IAsWLLCp29OmTbM38pYsWSItWrSw4/p3+LfffrPJ2/H7LQNAej8fa/raIhuIk9gLCn1mViQsRFY835rnaQAA+KGzyYivJTuD8r///a+VZGs/x6xZs9q+y5cv2xTvd955J+WrRqaV3sFCnRapDdfj9zwKDwuRoV2rMiUSQKalf7Q1IKk3zfqPiopyjukfda0o8Kpdu7bdAMBN+nxPn3/ptG595hc/SOl9JqjHCU4CAIBUz6D02rFjh2zZssV6PlapUkXKly8vvoIMyowbLNSvp0+Cr3zQep/2ju1ZmyAlgEwjJibGebNPMyLr1avnHCtRooRTut28eXPnPADIaHjzGAAA3Gh8LcUBSuW9qwYpfQkByowZLPSWEV1rWiRlRAAyOv27+fvvv1uW5NSpUy0LcsKECc4xncatPSU1KKk9mX3t7ysA30X7HQAAkK4l3kr7T7799tuWRal0WrZOzn7ggQdScjlk0ieh+k55YtFt3adPR/V4u6pFUu3JqT7pvVZw0vt19bie16hcwunuAOBmluSyZcssIKmByf379zvHjh49KnFxcTYMToORc+fOdXWtAJBS+nyP518AACClkh2g1Gnbb731ljz22GPWh1KtXLlSnnrqKeuP9fLLL6d4Mcg83AgW6jvyqXke4E/IbHGPlmfrFG6v7NmzW6aklm937tzZgpMAAAAA4M+SHaAcO3asfPzxx3LXXXc5+3RATvXq1S1oSYDSP7gRLNSgSmqeB/gLeoOlj8OHD9vE7dmzZ8s333wjoaGhtr9Vq1aye/dum7itpdtt2rRxjgEAAAAAUhCg1FK1unXrXrW/Tp06Ns0b/sGNYKFmfGlQ5UhEdKKl5d4elHoegOv3itV/R7qfwVIppz0jt27d6vSTXL16tXNs4cKF0qVLF/v8xRdflBEjRkhQUJCLqwUAAACAjCvZdWW9evWyLMorffTRR3LPPfek1rqQwXmDhdcqENX94akcLNRyVM348l7/yq+n9Dhlq0DSesUqPa7nIXmWLFkilStXlqpVq8oLL7zgBCcbNGggI0eOtKoCr5w5cxKcBAAAAIC0GJIzb948mzSq9IWZ9p/s3bu3DBw40DlPe1XCN3mDhZqBpeFATzoFCzXTSzO+rixX1cxJylWBhBgslTouXLhgGZH58+d3ei+Hh4fL9u3bJTg42Eq2tZ+klnAXLVrU7eUCAAAAgO8HKDdu3Ci1a9e2z3ft2mUfCxQoYDc95qXTSOHb3AoW6nV1OjgDP4DrY7BUyp08eVJmzpxp5ds6Wfv8+fNy5513yvfff2/HK1WqZP0mW7RoIblz53Z7uQAAAADgXwHKxYsXp81KkCm5FSzU65PxBVwfg6WS31Py3XfflSlTpsjy5cslNjbWOVa8eHEpX758gvM1YxIAAAAA4FKJNxAfwUIgY2Kw1N8HJLUSwBt41Mz/r776StasWWPb2kdSp25r+XatWrWoDAAAAACANEKAEgB8lFu9YjOymJgYWbZsmZVu6+3QoUNy/PhxyZMnjx1/8skn5ejRoxaULFOmjNvLBQAAAAC/EODRFBIkcPbsWQkLC5OIiAh6iwHI9OZsPHxVr9hwPxosFRkZKXPmzLGApPaVPHPmjHMsNDTUjjVv3tzVNQIAAACAP8fXyKAEAB/nj4Ol9L03b0n2F198IQMGDHCO6VC3bt26WZZk27ZtJXv27C6uFAAAAABABmUiyKAEgMxn69atMnXqVMuU7Nu3rzz00EO2/8CBA9K6dWsLSmpPyUaNGklQUJDbywUAAAAAn3aWDEoAgK+Li4uTVatWWUBSA5Pbt293jukfP2+AUidwxz8GAAAAAMhYCFACADKdS5cuSbly5Sw70itr1qyWKaml25otCQAAAADIHAhQAgAytFOnTtlwm82bN8uoUaNsX3BwsFSqVMlKBjp37mxByQ4dOlj5AAAAAAAgc6EHZSLoQQkA7tq7d69Tur1s2TKJjY21/YcOHZLw8P9NHtfsyUKFClmwEgAAAACQsdCDEgCQKU2ePFlGjhwp69evT7C/WrVqNuAmMDDQ2ae9JQEAAAAAmR8BSj8TG+eRNXtOybHIaCmUK0Tql8knQYEBbi8LgB+6fPmyLF++XCpWrCjFihWzfRcuXLDgpAYimzZtakFJLd8uW7as28sFAAAAAKQRApR+ZM7GwzJ8+mY5HBHt7AsPC5GhXatKh2r/K5kEgLR07tw5mTt3rpVvz5gxQ06fPi2vv/66PPvss3a8S5cuMmHCBPtYoEABt5cLAAAAAEgHBCj9KDjZ/8t1cmXD0SMR0bZ/bM/aBCkBpImoqCj5+uuvrZ/kggUL5OLFi84xDULGxcU52/ny5ZO+ffu6tFIAAAAAgBsIUPpJWbdmTiY2DUn3aYG3Hm9XtQjl3gBSxZkzZyRPnjz2eUBAgDzxxBMWqFTlypVzSrcbN24sQUFBLq8WAAAAAOAmApR+QHtOxi/rTixIqcf1vEbl8qfr2gD4Bs2CXLNmjWVJavm2Bh03btxox0JDQ+Xxxx+XnDlzWmCyatWqFrQEAAAAAEARoPQDOhAnNc8DABUdHS2LFi2ygOS0adPkyJEjzrGsWbPK4cOHJTz8f60jRo0a5eJKAQAAAAAZGQFKP6DTulPzPABQjz32mHzyySfOdu7cuaVTp06WJdmhQwcJCwtzdX0AAAAAgMyBAKUfqF8mn03r1oE4ifWh1ELLImEhdh4AXGnfvn2WJam3N954Q2rVqmX7NRg5e/Zs6yWpt5YtW0pwcLDbywUAAAAAZDIEKP2ADr4Z2rWqTevWYGT8IKW3C5weZ0AOAOXxeGTDhg1OP8nff//dOTZlyhQnQNmtWzfLlqSfJAAAAADgRhCg9BMdqoXL2J61bVp3/IE5mjmpwUk9DgC7du2Stm3byl9//eXsCwwMlKZNm1qW5O233+7sZ/o2AAAAACA1EKD0IxqEbFe1iE3r1oE42nNSy7rJnAT807lz52TevHkSFRUlPXv2tH2lSpWSiIgIm7x9yy23WIZk586dpWDBgm4vFwAAAADgowI8WsuHBM6ePWvDHfRFug59AABfcfToUZk+fbqVby9YsEAuXrwoJUuWtIxJb6n2unXrpHLlypI9e3a3lwsAAAAA8IP4GhmUAOAHPv30Uxk/frysXLnSekx6lS1b1rIko6OjLWtS1a5d28WVAgAAAAD8DQFKAPAxcXFxsmbNGqlbt65kyfK/X/Pr16+XX375xT7X/dpPUgOTN910E0NuAAAAAACuIkAJAD5AS7UXLVpkpdvTpk2TI0eOyJIlS6RFixZ2vG/fvlKlShWbvF28eHG3lwsAAAAAgIMAJQBk4n4e2k/yp59+ktmzZ9vQG69cuXJZX0lvgLJOnTp2AwAAAAAgoyFACQCZyOXLl52y7e3btzvTt1XRokUtQ1JLt1u2bCnZsmVzcaUAAAAAACQNAUoAyMB0oM2ff/5ppduaKVmjRg0bdqM0I7JNmzbSoEED6ympvSUDAwPdXjIAAAAAAMlCgBIAMmCW5M8//+wEJffs2eMcO3DggA3B0UCkDrdZsGCBq2sFAAAAAOBGEaAEgAxGy7M1QOkVEhIi7dq1s9LtLl26kCUJAAAAAPApBCgBwCXHjh2TGTNmyKxZs+SLL76Q0NBQ29+8eXPZunWrBSM1KKnByRw5cri9XAAAAAAA0kSARxuc4arJuGFhYRIRESG5c+d2ezkAfMiOHTusbFtvmiXp/RWs07g1IKkiIyMtWOkdhgMAAAAAgC/H13j1CwDpYNmyZdK/f3/ZvHlzgv066EYH3FSrVs3ZlytXLhdWCAAAAACAOwhQwjWxcR5Zs+eUHIuMlkK5QqR+mXwSFBjg9rKAG3bx4kVZvHix5M2b1yZsq8KFC1twUrMitceklm5369ZNSpQo4fZyAQAAAABwFQFKuGLOxsMyfPpmORwR7ewLDwuRoV2rSodq4a6uDUiJM2fOyOzZs23ytn7UMu3u3bvL5MmT7XilSpXkxx9/lFatWkmePHncXi4AAAAAABkGAUq4Epzs/+U6ubL56ZGIaNs/tmdtgpTIFLR/5Lhx42TKlCmWMXn58mXnWHh4uJQqVSrB+bfffrsLqwQAAAAAIGMjQIl0L+vWzMnEJjPpPi3w1uPtqhah3BsZMiD5119/SZkyZWw7ICBAJk6cKGvWrLHtqlWrWj9JLd+uW7euBAYGurxiAAAAAAAyPgKUSFfaczJ+WXdiQUo9ruc1Kpc/XdcGJEazInXatk7d1vLt/fv3y/Hjx50y7ccff1wOHz5sgckKFSq4vVwAAAAAADId19N73n//fSldurSEhITYMAlvJtL1+rwNGDDAyiezZcsmFStWlFmzZjnHhw0bZllN8W+VK1dOh+8ESaEDcVLzPCAtREVFWTCyb9++UqRIERtq8/bbb8uePXtsyM369eudc++55x555plnCE4CAAAAAJAZMygnTZokAwcOtB5uGpwcM2aMtG/fXrZt2yaFChW66vxLly5Ju3bt7Nj3338vxYoVk7179141cOKmm26SBQsWONsaUEDGoNO6U/M8IC1o2ba+EeKVL18+6dKli5Vu33LLLZIjRw5X1wcAAAAAgC9xNXL31ltvSb9+/eTee++1bQ1Uzpw5U8aPHy+DBg266nzdf+rUKfnll18ka9astk+zL6+kAUnNekLGU79MPpvWrQNxEutDqV0ni4SF2HlAWtu5c6dlSmr5dq9eveTBBx+0/d26dZM333zTPmpQskmTJrzRAQAAAABAGnHtFbdmQ65du1ZeeOEFZ58OlGjbtq2sXLky0ftMmzZNGjVqZJlNGlAoWLCg3H333fL8889LUFCQc96OHTukaNGiVjau548aNUpKlix5zbVcvHjRbl5nz55Nte8TCengm6Fdq9q0bg1Gxg9Sekfi6HEG5CAtxMXFyW+//eb0k9y8ebNzLHv27E6Asnjx4ha81BYRAAAAAADARwOUJ06ckNjYWClcuHCC/bq9devWRO+ze/duWbRokfV8076TGkB45JFHJCYmRoYOHWrnaKm4lmdWqlTJBlcMHz5cmjVrJhs3bpRcuXIlel0NYOp5SB8dqoXL2J61bVp3/IE5mjmpwUk9DqTFmyLas1bbQnhpVmSLFi0sS1KzJeMjOAkAAAAAQPrIktmyn7T/5EcffWQZk3Xq1JGDBw/KG2+84QQoO3bs6JxfvXp1C1iWKlVKvvvuO7n//vsTva5mcWovzPgZlCVKlEiH78h/aRCyXdUiNq1bB+Joz0kt6yZzEqkhIiLC3sTYtGmTvPLKK7YvODhYypcvLydPnrTfEzp1u1OnTpI3b163lwsAAAAAgF9zLUBZoEABCzIePXo0wX7dvlb/SJ3crb0n45dzV6lSRY4cOWLZURqAuJIO0NGsKc22vBadBq43pC8NRjYql9/tZcBHHDhwwNpAaOn2kiVLLLNaaUsI/d3h7WOrb3Jo+wcAAAAAAJAxBLr1hTWYqBmQCxcuTJAhqdvaNzIxOqhCA416ntf27dst+JBYcFKdO3dOdu3a5QQoAPiWH3/8UerVq2dZzxqMnD9/vgUnK1eubP1p49NetAQnAQAAAADIWFwLUCotq/7444/ls88+ky1btkj//v3l/PnzzlTv3r17Jxiio8d1ivcTTzxhgUmd+D1y5EgLSng988wzsnTpUvnrr79s2vftt99uGZd33XWXK98jgNSjfWuXLVsmhw4dSvAmhA6+0Z6RjRs3ltdee8362OrvlNGjR/PmBAAAAAAAGZyrPSh79Oghx48flyFDhliZds2aNWXOnDnO4Jx9+/bZZG8vzZCaO3euPPXUU9ZfslixYhasjJ8lpWWeGozUPnM65btp06ayatUq+xxA5hMVFWVZkVq6PWPGDBuw9frrr8uzzz5rx7t06WJvdHTt2vWqoVsAAAAAACDjC/B4PB63F5HR6JCcsLAwG7SRO3dut5cD+J0LFy7IpEmTLCg5b9482/bSoTZPP/20/Pvf/3Z1jQAAAAAAIHXia5lqijcA3xUZGSm5cuWyz/V9k0ceecQJTJYqVcqmbt92222WFa3DsgAAAAAAgG8gQAnAFRqEXLt2rfz000+WKanbGzdutGPZs2eXRx99VHLkyGGByRo1aliPSQAAAAAA4HsIUAJIN5cuXZIlS5ZYUFJvBw8edI7pMCsdflO0aFHb1j6TAAAAAADA9xGgBJBuNCtSB9p4aYZkx44dLUuyU6dOki9fPlfXBwAAAAAA0h8BSgCpTjMjp02bZlmSo0aNklq1atl+DUbq/m7dulk/ydatW0tISIjbywUAAAAAAC4iQAnghmn/yM2bNzv9JH/99VfnWP369Z0AZdeuXS1bMjAw0MXVAgAAAACAjIQAJYAbsnv3bmnfvr3s3LnT2acDbRo2bGhZknfeeaezP0sWfuUAAAAAAICEiBYASLILFy7I/Pnz5fz583LXXXfZvpIlS8rJkyclW7Zs0rZtW8uQ1EzJIkWKuL1cAAAAAACQCRCgBHBdJ06ckBkzZlj59ty5cy1IqUHJf/3rX5YpqVmRur9KlSqSM2dOt5cLAAAAAAAyGQKUABI1ceJEmTBhgqxYsULi4uKc/Rqc1NJtDVRmz57d9tWrV8/FlQIAAAAAgMyMACUAG3Kzbt06qVGjhtMncu3atbJs2TL7vGbNmla6rYFJPUczJwEAAAAAAFIDAUrAT1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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"inferred_reward_probabilities = 0.5 + 0.5 * nn.sigmoid(svi_samples[\\\"z\\\"].mean(0)[:, 0])\\n\",\n \"ground_truth_reward_probabilities = 0.5 + 0.5 * nn.sigmoid(ground_truth_z[:, 0])\\n\",\n \"\\n\",\n \"plt.figure(figsize=(16, 5))\\n\",\n \"plt.scatter(ground_truth_reward_probabilities, inferred_reward_probabilities, label=\\\"reward probability\\\")\\n\",\n \"\\n\",\n \"plt.plot((ground_truth_reward_probabilities.min(), ground_truth_reward_probabilities.max()), (ground_truth_reward_probabilities.min(), ground_truth_reward_probabilities.max()), \\\"k--\\\")\\n\",\n \"plt.ylabel(\\\"posterior mean (SVI)\\\")\\n\",\n \"plt.xlabel(\\\"true value\\\")\\n\",\n \"plt.legend(title=\\\"parameter id\\\")\\n\",\n \"\\n\",\n \"corr = np.corrcoef(\\n\",\n \" np.array(ground_truth_reward_probabilities),\\n\",\n \" np.array(inferred_reward_probabilities),\\n\",\n \")[0, 1]\\n\",\n \"\\n\",\n \"bimodality_score = np.clip(\\n\",\n \" np.mean((np.array(inferred_reward_probabilities) < 0.2) | (np.array(inferred_reward_probabilities) > 0.8))\\n\",\n \" - np.mean((np.array(inferred_reward_probabilities) >= 0.35) & (np.array(inferred_reward_probabilities) <= 0.65)),\\n\",\n \" 0.0,\\n\",\n \" 1.0,\\n\",\n \")\\n\",\n \"\\n\",\n \"print(f\\\"reward-probability Pearson r: {corr:.3f}\\\")\\n\",\n \"print(f\\\"reward-probability bimodality score: {bimodality_score:.3f}\\\")\\n\",\n \"\\n\",\n \"\\n\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 13,\n \"id\": \"24\",\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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2cqmbVVQRyTAByt3JLp3pqdWHDrV2x+6xatdOMmrgPwxrLN3eqf68J9rYzOgiRxe+5l18fWpXAEbvNUFVlicDOz3Ub23vUI69uieV3D79tZMRVObLDlEq17/wpyles7cKZyhEAAAAAyJXs71rTHExLrKDOB0B+Soopl8go5rqIvS1V1O2TmDuSm87eeGZtjA7NXr36ognbsIWts7eweTcAtiEcAQAAAGCVLZ0p1ZUKZmFAWmul0vG06ACgVKKYZYmMBOFITloDmDcSd/uk5k7aI+XaVitqY7VV6379LpPOqQlTNwPZgcDwKgQAAACAVVZu6QrsvAYGB9Xq5uDOD0BuqBzZJlHCEk22JNRu7wln97wscksrreHk8zAWv4MYKO+TnnS0ocBE82YmmlMTtt70gK6iBVA4nnkBAAAAWLUgtq412FZYqwIMW2CW5s6UemF924Qfr27qiPswvZZMsCyRUVpCUBR3qBB1+6SWrj41ENBQeR/0RVjpOVEwMnQ8MQUkEoykud0AgeBVCAAAAABrSJVHf8ALAm09fWpLR2+g5wkzrG3tVi+ub5/w47m1bezAjVGSaokhZSUlcR+CNcJoRxVH+ySpXpTnIGQnykBgMJFQA6Wlk86bGR6QyOnl56KQ7ud5CwgCr0IAAAAAWEEWsFds7gzlvJeHdL4wf3ivLE7Svz0+ZVSODKGKJr5B5nG2TwpjsLyr5PE6Kump9WrFNy+YMBjJyNxG5PTyc65dF4DLeOYFAAAAYIWN7b2qozecHvNrW3tiGfSKcHX0ZrcjuyOk2QWYXHFxEdUj/0VQlL2WAMORuNsnBR30IDgSdEwWjGTI6aIKRgAEh2deALFr7epTa1u69cfG9p64DwcAABjq1Y0doValLNvM7AmXSB//bCpHRFihG7JTXko7KQlGJChCdvdXGUjtSvukMFqEuaq4iPtIBtcFEIxoGuEBwARkIWJV09ZBqNVlCXX4buVxHxIAADBwM8WmkOeCrNzSpXaeUaNK2cXuhK6+/qzbjhCOxB+O+D53gYAoe80Bt6HKtE8qSqezbp8kwUhQVQKdqbTq6evnNpAFAoFtinmpAgSCuxKA2PUNGyTW1x/cDiAAAOCOVza1h/475HWIBCRwQy6tsmirFa+KJIvClUn2rsY5oyPu9km01spOMkE4klFKOgIEgnsSgNilhwUiw4MSAAAA0dmbVq+1RNN689VNHbodE/yZNyLaqRyJVSXhiKqgasDrAeZbOty7TGEoS3A/EbThA4JDOAIgdqlh4Yi0PuhnQQIAAAzz8sYOPRMkCtLaJNPuE3Zrz6EaRP7uVDDHh2BAqcoyroNspNIDTrZgczHwCQOtx7Yq43oAAkPdJoDYpUdVi8gb05JinuwBAIBS3al+tTrisELCmHlTK9mVablc54hIa60pVcnQjgfjo3KE68D3EKGlu093VEgw8yr0+0lvul/ZXgFTRRs+IDDcmwAYVTmS+ZwdIQAAQLy0oT3rodpB6Uql1ermLjW/oSrS34tg5TpHRMIUwpF4VJWxNMHMkexs7uhVLpLqyOauPjW9pizuQ3H+seLsO/+j4nbNcXsX9PNVVJoBgSGSRqSkXF3ebGY+hs+agJ/kReDoFgZSKg0AACBVI3G1uHppA7NHbH/fMXoDTpBtuBAs2RhV4nmlVhWVI1nZ4mjliNjS6WbwE6SasoQqKvL7sULUlpfGfQiAM9iagEg9vrJ5xE6PNy6YqubUV8R6TIjXWG9a6fcMAADEizFUjWTIRh4JZhZMo3rEh5Zaot3BOQY2qUomnJwlkW2LHdopTU7eJ7Z2u3sb2dyeUmpm3EdhNml3KQFJIY8V3zh2T2U7whEgOIQjiNToQdv9o2ZNwD9jVYlQOQIAADp7t4YTcbf0mju10vsd7T601Mo3UEGw7XJ8DUeqaSuW9bwR6TzgquaulF4z4TlnYvWVpQU9VhQ67yNucvuoKecxAwgKWxMQbzji8AsbZIdwBAAAjOWF9e2xL4J19/WrFVs6Yz0G5CefFlmdqX5aqcUoqh76iaYWVbpxc1anldPJ6cPG/IDsbGp3u+2UVErSWmtyUyr9ng1VX5HUFTQAgkE4gnjDEd58eK93jCBkrK8BAAB/yI7QNc3xVo1kvLyhgzl5FmrvzX1XsYRxHSmqR1yunpCgY8GXLlELv3jxpAGJfF9OJ6cPOyChcsTvYezbtdbChBqq/Q5HfL/8QNAIRxCp0ZUicfWQhjnGqhIhHAEAwG8vrGtXpuhN96tlm6ke8aGtViE/h2DaaoWtKJ1WxX19Krlu44QBSSYYkdPJ6eXnbL/sLrxvdHneiE8BUKFqykutb41VCMIRIFg8AyNSo8vUqRzB2JUj/bEcCwDz+krLRy52nF6lioooMwds1tyZUutau5VJXtnYoRY0VKlkgr1lNpBKH2mJlg/mjsQniuqJvsZpavkVFw4FH/J/+Vy+PlYwkprVuN33w0A4MjlfQoOW7j49eL60hOebiUyvKTOmwjTqeSMNVWVxHwbgFJ6BEWvlCOEIxgpCqBwBIFZu6cx5GPOsunIWGADLPb+uTZlGFqpe3tiuXj+7Lu5DQcgBRz6zShCM8tISvfAX9nvEiQKSOIIRUZX0dxd8tnwJR6S935aOlJpZVx73oRit0dNwZGpVUj9OAggOUTQiNfp1Lm210NM3RuVInjv9ALglnwUqFrUAu21s71GbDF0AW765U/XwGsUKhTwXUDkSr6g2OGQCEglAMgFJxbMvxhKMSCiUoEpgUr6EI75d1nw11pbFVi3+2spl6vGH/6zWrlwW+e+eWUtoBgSNrZWIdAeEfAxH4QjGWmSQyhFpwVbMjgjAW/J8kV840sdOO8Bizxs0a2Q02c3+4vp2tXhufdyHghADDmaOxN9aqy2iuRKjK0h2/PxS/fUogxHBMPbs3jP6tAFmUzvhyGRk5sjUyqTa0hndddXe2qyuOvc09eQjDw59bZ8DDlVnXXa9qq6N5rXBDMIRIHBsT0BkxgpCqBzBeDswaa0F+E16xacHcn8caPPojTPgGpkz0tKV25yhqK1s6lKdVBY4HY7Icw8VQvGpSkYbFEgAsvrLp474mnweVTAiaAc6Od/CgraePh6HshD1higJRp5+9OERX5PPrzxn5GNIWOoqSnm8AEJAOILIjNU7dnQlCfwif/+ecUKQfIdoAnBDvrsDpXIEfmnt6tPtJzIfW2hFYe1rghcMrhoZcZzrzT9O3xXaGsunHeqmibqKQmaMzL38+hFfk8/l61GpLmPeyGR8bDO1pdPszQImmF1fHmkrLakYGegfuU4hn8vXo2ixNbu+IvTfAfiIcASRGatKpJ/iAK9Jdch4ARnhCOC3fEMOWdAiePfLv1Y0qb+9snno4+FXNuvWjLDLmuZuvVPWBjIA1pZj9ZE8BxTaGou5I/GpijAoGD18/dWrLxoxgySqgISd4JPb3OFfULDZs2qZfFQmE2pKZTKS37V+9YoJv79uku8HgXAECAfhCGLFApbfulLjByDdKd6UAj7Ltz2WBPGdEzy2wD1jhek9aW4Dtr0efGmDXdUYMnsE5r6+LLR1L3NH4hNVUDA6GJEZI92v32W7Ie1RBCSEIxPrTvWrLg/fG0Y5S8Nmc6ZEExjMnLtgwu/PmuT7QbTUYj4REA7CEcTaVouNnX6b6EVud4qyIsBnhQxjpbWWP3rTYy+CykIK7KoasW2n/tqWbtUa0dBo5CaImTC23R5dUl5aohLFxZEHI5kZI5kh7VEGJFURz1mxja8hgVRDy+scTGxORNUUc+Yv0sPXi0tGVrfJ5/L12fMXhfr7d5hSGer5Az4jHEFkxspBqBzx20SLV50e7g4CMKwlSgELU/SK90dP39hB+njzrGDm/d3WKgzbql180U44Yr3KEFtrTRSMZEQZkEgYVFJcFMp5u2KLhy21MpqYO5LVfWh6dVkkv+usy65Xi/c7aMTX5HP5eth2iKhCBvARWxQQmbF2dlI54reJWt+w6xfwuyXKWNWG2aJyxB8948yn4jnErqoRWzdESPWIzB6pLS+N+1AQcOWIVDfL8xCL1vGQ1jGFVJBOZDCRUAOlpeMGI6MDEglG5PTyc2GgTc7kmrr8Dkdm1bEoPpm5UyvVpo7wK4yqa+vV0ht+rIevy4wRaaUVdsWImF5TpkMgAOHgmRiRGatIZHDMehL4omuCN6+yUCK7SYuKeFMK+KbQyo+2bjsXWpG78UKQ8UITmEWe51/eaHf1xcsbOtS+86fEfRgIoepDXosSfMWjKsQ2U+mp9WrFNy9QRen0uMHI6IBEghH5uTAwb2Ri6f4BryuCW7rY8JONmXXlOswuZHNVLiQQiSIUyZhLSy0gVLTVQmTGaqFF5YjfJqockRc2vbRFAbwkO7ELXRgb4AnG22HsE30dZlnX2mP9otdrLd2BVCogOEENU+fvGp+qENtqCQk6JgtGMuR0YQUjoirJbvCJtHT3ed2KW8IRny9/tkpLitXsiGaPRE1mMM2qK4/7MACnEY4g3soRnui9JeHHRAPZBf2eAT8V2hZL2jja2qYHubdgy+XrMMsrGzuU7eS17Kub7L8cLr2+DCocDSpkQe4qPRpQXknlyIRaQ2qvZov0wADviT2vrphdX64SJSzdAmHimRixzhwhG/FXNguX8qZ0WkTD1QCYoy2ABSk5jxraoXjbVqubcMx4Wzp6VbMjfeRXNXWpXWbWqLIEO8DjFuQiIguS8clnDkdv2oxQPNfHgWqPgqB82F5dGARe02ZnWnVSB6uTbcC0zbypboY+gEl4JkZkxspBmDnir2x24/GmFPCP7MIOYrfu1uoTN8vrsc14b4ClLaP0KWennbmWbe5ULlUrrNzSpXaeURP3oXgvyFZYnb1mLLb7qLy0WBUXFY25uW48Z9/5H2WCa47bO6fTV4bcQsx2vleOiLbuPjXH0ZZRQZJZpRIkvLC+TbkUFDewWRQIHe8YEZmxXtwOMFLCW9kEH+wUAvyj54UEUFbI44f7BiZpn9PF3BGjK35k3ohLVmzupF2sY+EIm3TiXeQMe+6ICcoSxXpWAsbH7B+uA5+rLOY6dnkAU1E5guiMNXMkjuOAEbJZuORNKeCfIFpq6fNhp6HzJgs/unr7VS1tKIy0Yot7QYIEdevbetSsOnb3xqkzwHlD0qaJCrT4SHucXDY6fOPYPZVtfJqtku99sK+f3ZRBPq65riJZoqbXlKlN7b3KlUoYAOHj2RiRGRjjPXAQu4Nhp7YsBi5LuxTelAJ+KXQY+/A3ktLqpqS4KJDzg3km6yntWs9pV0goIjM6XCSttQhH3NphLa216ip5HRqHqhyDAxtn/vhQHRPGXDHfdLFhMCcSKLgQjjTWlKnyUh4jgCjwSg8xD2QnHPFRLjMFaI0D+CWo+3xQs0tgLqkMmfD7LKoYaWN7r+pxtOWZy5fNFkFXHXcQssbGh+CgKo/B8z6ZqHWmT1L9A3rDD7IjmxSSDmyupGoEiI79jxiweyA7z/FeymWmQDYVJgDcEWQ7LB4//F4EpTWjmVytGsmEsqsdvnymk8XDoMMpdmzHx4fgoIq2WhNKpWmplcF1kT2pGp8zxe4qTgl3ZtaWx30YgDcIRxDp4NTtvkY44qXWHBY/27p5Uwr4QtroBbmgnctjDewzWWUIbbXMI73jN7S5NYh9tDUt3XEfgrc6Q7jP0+s/PpXJaCtHXlu5TD3+8J/V2pXLnL2MtuklEBgxfwX+VF3sMKVSFdMaGIgMWxUQmbEKBZg54qdcAg8WNwF/BL3Tn8oRv2cLyKwA2ckvAy1hhvWtPc63BpHqN5mdVFNeGveheCfoeSNhnSeyU5VM6MfvsNswt7c2q6vOPU09+ciDQ1/b54BD1VmXXa+qa+tD/d0+VMcUIt3v9vNFLtKOP3cGrb4yqWrLS619L2B7uAPYhsoRRGasIIRwxE+5BB5yWmbTAH4IOgyl8sxd8rww2S5xeY3B3BGzrGt1u2rEt8tpGglEgz9PnkfiIrumKyIYRizByNOPPjzia/L5leecGurvTRQXM2x5EqwVTNyFAxPbwdLWWhLq1FWywQKIEuEIYn9xwxO9f1q7U1mfNj0wQEsDwBNBhxnSgoDhyG7q6ctuOGkYbXaQH/l7bWzv8aZCBtELI8iQgdCuVzv5PJRdWmlJxchA/8jXCvK5fD3MFls+DJwvFOHINjwM5deayka2hjqAzajjROwvbvoHB1WxouWFL7pT/Tn3j23pSqlqys4B54XRRk/K6dmZ6Z723uxuKx09adVYE/rhIAubO3q9WWRu7krpYJbHnmiFFYbK+cpOXkRPXv9vau8N7fzXr14x4ffXrV6hZs9fFMrv5r2NX7M6yhI8H0StIlmiplWX6dcfNrE11AFsxjMyItM/znq4vFHmvaM/ZMEgVy1dfWqHKaEcDgCDhNEXWKpRWBx3j4QeWZ2OljjGCHOB09TLO5ee4ZHqCqGtVuZ8CUfiEfZMjplzF0z4/VmTfL8QlUmWYiZTHMDMsLPv/I8ywTXH7V3QzxfT8yXvKgybwhEJcyTUARAtHmIRmfF2C1Iu6xcJOqL4GQB26UqlVd94Kbph1SiwZ7YA4Yg5Nlm0OBEEmxZjXJlD1BVSG0Xa88WnKuQAYc78RXr4enHJyMVI+Vy+HlbViKByZHIlxXSXCDIo8tHMunJVZNF1N7uellpAHHhGRuzhiC8tFrCtRVbOP9Od0m96bXphA8CMEKONcET53lYLZrQ18e2+uLkj99c7yF9Xql+/VrSpIgWTqy4Pf7nirMuu18PXZcZIxuL9DtJfDxMzRyZXWlL4Xt5vHLunckEywb7mfNuZTa8us2Lmmax1zKorj/swAC8RjiAyMltkzK8TjnhD3rQ251EFIrcRaY1TV0lLA8BVYYUj7b1p/RjC7kO3ZBt6yDBlqUgKYoEF+Wvu9CsYyVTDMXckOmFWd1A5Ep/K0hK9YBhW8CWqa+vV0ht+rIevy4wRaaUVZsVIlMGP7coCCARcmfWR5HVM3mbXl1sRjjRUJXnNAMSEZ2REpn9g7HYpacIRb7T1pFV6nNvBZJq6UoQjgMNaQ2qfJwsqsmN9SlUylPNH9NL9Azr0yFZnb1rVV/L3t23emAuaOlO0yIhImNUdEnQhHsXFRaoqWRJJi0QJRKIIRTIL3a4s2psejriC6yJ/M2rLQw9Zg2oBBiAePMIiMn39VI74rrkzVdACAwB3tYTYcifM80b0cl0ka6e1Vux8nR3GzKPohLl4LjOOTF9Uc5mLszmoGskOg6m3qvhvBRXyI9UYUy3YJDOzlnAEiAvhCCKTHiccCWMAL8wk1R9xBCsAzCatZ+QjLCxQuiXXsIOh7PHz9T7o6+WOa+ZIWAYGB1VPH+9X4lLlYjji4GUKQ1WS60lweyncjNoyZbKa8oSTj3WALQhHEJm+8dpqjROawD1NBQwnlX7PYS6eAnB3AdHXlj6uyjUcoXIkXvLcLQPZfeTbEPo4hT0XhJA1PrXl7rXVlYVQZNdWTaom4vTaymXq8Yf/rGfSxKWSRfOCNRpeldFYY/bxAa7jURaR6UuPHY5QOeLP4kihb1zp3Q24KeyWO7I4zlB2d+S6SNnRywJ1nHxeVJbZODIjJ8EgXatnjujz169hzd557CoXW1CxQzx7tRWlOc0ZC0p7a7O66tzT1JOPPDj0tX0OOFSdddn1qrq2PtJjqXXwPhA1uQ5lzo+pmzUaDa9sAVzHK3XEPnMkRTjihS0BtMVi7gjgprArO6RXPO1t3JFr2NHR268GmG8Wm06Pw5HMvAqEvwEnPU6FelD4O8bHxZZCNQ5Ww4SlriKe60qCkacffXjE1+TzK8851ZvrwCUys2V6jZlzR4qLilRDFeEIECfCEURCFiXGe9MyXmgCtxTSUitjc0dvIMcCwL9hzS201nLm9YSEHbmGY2G33MH4fF9U7uC2Z/W8kQweQ+KTTBTrHd+ukIXQKgaNGx0MSCstqRgZ6B/52CKfy9ejbrEl1TMonKkBxJTKJNXtQMwIRxCJiapDUuO024JbNncWHmy09aRpwwY4RlqVRFHi3hxBAINoFpol7MgVc0fis7Udkb+6Pb/8rlQn+V4BFTeX2gpJmzDZxY7sF46jtn71igm/v26S7wc9c6eU1oyBaKg2s3JkapWZxwX4hEdZRKJ3ggDE1L6PCI4EYEEMJZUFMVprAW6JKrSgcsQNHXmGHD7PvYhbHL3ifatq8F0UVR38HePlUhsql4KeKFQkSyIfyj5z7oIJvz9rku8HaQoL54G26EsaGDQRjgDxy/mZ+dBDD1UnnXSS+p//+R9VUcFgZGRnogCkt49KANcFGWhIa60ZteWBnR/MIYuXKzZ3ZnXanWfU6DYLsF9zRIGn3L4kqOV2Y7d8Qw4qR+LT7fmicg+vc52o6pDKZXk/41J7J5vUOBQoVJe5E/REueN/TXN3ZL9vzvxFevi6zBgZ3lqruKRELd7vIDV7/qLIjqWBhfPASMVWfWVSbWzvUSapr+QxAYhbzisE++yzj/riF7+oZs6cqU4++WT1j3/8I5wjg1MmCkB6qBxxXpCzQjYHMLsE5i6Sv7qpI6sPdoG7I4p5I9t+F48ftss35Gjvoa2aidXDPqBC2p25Nr7Pz4mTS+FIbYU7l8XlWRFnXXa9DkKGk8/l61GaVm3mnAxbmRZESFVUecSVUQC2l/Mz89VXX62uuOIKdffdd6vbb79dHXLIIep1r3ud+uQnP6k+9rGPqRkzZuR6lvC8pUL/wCC7eR0XZDjS2t2nd+/Re9U9ubSskF2ilCC7MVy7pTsVaQuvRirPrJZvMMqiZjzk9d1AHjNiXELliHJmHgivPeLjUlstly5LVKbXRB8QVNfWq6U3/FgPX5cZI9JKK8qKEX0MZQndVgzBqTNsuL1UsgCIX16ri4lEQn3wgx9Uv/nNb9SaNWvU8ccfry644AI1d+5cdfTRR6s///nPwR8prNYzSb9p3/tRu74wIoFGUJg74q5ceobT+9sNbT19OiCPCo8d/s4cSQ8MTPpaBMFL9RMMyOsghHv9RnU7i2K2CcYmm+hc2F1dUlykqljszllVWUJVJuOpuJFAZN+D3hZ5MCKoGglerWHhCJVkgBkK2nr96KOPqqVLl6orr7xSNTY2qnPPPVdNmzZNvfe979Wtt4BsFzJ970ftsi2dwVWNZGxqD/48Eb+uHHZ201bLDVGHFc1dKR2wwk4SbkjIkS/mjkSPYGBrMBdlCOybqKpGov5d2F6tAxUXUjUicw+Qu8YYqkfi1ljr32UOm4STElKagkoywNJwZOPGjToM2WOPPdTBBx+sNm3apH7605+qFStWqIsuukjdcsst6o9//KO68cYbwzliWGmy8KOLnVjO2tyeMrpNF2ytHOExwwUSVkRJWvK1s7hlrULDDULV6Ml9DlwPYYryfk3AGi8X5o64cBniMsOztqjFRUVUjoRAwklpV2YKHhMAM+R8T9xhhx3UjjvuqGeMfOITn1DTp0/f7jR77bWXetOb3hTUMcKDRU9a5LgrjCBD2nTJgNOyBGXprpBdtbm0vGF+gBu2dETf5qq5M+XE7lMfFbprm13f0aNyZFs44kJLIBNF2eqK9yvxMm1WQD54/ZG/adVJHRj4MseqoSrJjM0QA4kg234XFNTE1C4OwEg53xPvv/9+XTEykdraWvXAAw/ketZwlCx4TtZOgAULd//2MlMgrEXV2fUVoZw3zF/ckHBMHldMKotG7hWFccybklZe8xuqIv+9iH+HOK81opemnZSW7ud6MG0OUb4hl7y2JeiKhwvBAvMF8pcoKdaVFBvbe5QPZtT5VSkT9QwbE1SWlqhi3ssCRsg5ipYZIy0tLdt9va2tTb3tbW8L6rjgkGxK0Gl14aYw218xd8TfeSMZPG7YrSnillpDv5eh7NYqdNc2w5Sjl6adlNZXwKwcmPVagNce8akuT1g/r8OFgCdOMzyaweFbG7EoVRlSrVFZRtAOWBuOPPjggyqV2n5hoaenRz300ENBHRccks2biM5Uvxpgd6FzwgwwmDvilnwWLZk7YremGFpqZZ6TcmnhBpfaavWrQU/acZiCypGtGMgenqjbbEZZqYKRpFq42uLFxLJEMVVHBZrpSTWFtH0yaS6Ga0ypHKkyJKQBkENbrX//+9/6//Km8rnnnlPr168f+l5/f7+655571Jw5c8I5SlitPYu2SnK76kil2U3jmDDDEVnglLY8FUneZPhaOcLcEbvFVTmSGQQ/q462fLYptPJD+pT39A3wvBEhQoGtaKsVDnkdmI64KofKkXjJe8VsuhKYiPe5hatMJlRtRalqM2BeRJhm1vIaNUyVhrwOrLI47AW8DUf23ntvXcYqH2O1z6qoqFDXXXdd0McHB2T7AlZe5PCi0R06vAh5d7aEL/MaKkP9HTB3sYHKEbtb7cQ5CFFmFhGOuDe/LNuAhXAkOlSObEVIFI723uifRwhH4iUL46+1dCtbjx2Fm1VX7n444kmFTJxVXMVFRXrTTJwqqBwBjJH1vXH58uV6d/+iRYvUo48+qqZPnz70vWQyqRobG1VJCW82sb1sX7y0daeVmhL64SAiUcwE2dTRQzjiiHyCDhYo7NXc1RdreyOpHIFf80aGzkcqzqoDOStkgVBgq37auTnT4oq2WvGyeSOdzcdukpm15erF9e3K5YX7KZXcVsIkG76leiTu95IykB2AZeHI/Pnz9f8HGCiIHBc8U1kO44xzFzEsDUfaWeB0gcwbkrlDuaKtlr3iHore0tWnF22lfznsEFSlGEPZo0U4shXXQzjiWNiSxxCeP+JTW2HvTmubj90k9ZVJPbvF1flxMohdFu8RrorS+MMRKpkBc2T1DH333Xerd73rXaq0tFT/eyLve9/7gjo2OEAWoLLV2s1CtytkR3gUA9N70/06VKujTN1qXX35DUmWxVIWKOy0pTP8x4eJSBm9VI9Mqy6L9TgQQ+VIQOeD7BAKbMX14FYVhyyo8dozvpkTpSXFqi/LzXemkMXuGipHAq0eWbGlU7mIllp+BBPS1kuqhABYFI4cffTRegC7tM6Sf0/0pC/D2XNx/fXXq29+85v6/BcvXqznluy3337jnv7qq69W3/nOd9SqVavUtGnT1LHHHqsuvfRSVV7Ok4jt4UhvekAvdsqLXtj/d4/qTYtUqPAG1W6dBezakR2ctCmwiwRhzZ3xVwo2dxKO2DZ4OQiu7jQ1Vdz9vE1BOBKOtpjCkfYeNubESV73xb3JIldVyRI28wRIAgQXwxFZMJ/Oa9NIxL3mJG29qBACzJFVVCmttCQYyfx7vI9cg5Gf/exnasmSJWrp0qXqiSee0OHIkUceqTZu3Djm6X/yk5+oc845R5/++eefV7feeqs+j6985Ss5/V6Y29dd+tDDfpsiqBqJsn0XwlVISXMhwQriIfOl0ga06NwSc2svxFPxEVTIguwQjmzF1RC8VHpAVxDHoZ25I7GqKbdvIx3D2IMlm1tcDJvkciVKqCaIqq2Wz78fwEixPvJeddVV6uSTT1Ynnnii2n333dWNN96oKisr1W233Tbm6f/+97+rt7zlLer4449XCxYsUO94xzvURz7yET0gHmbOEcg5HGGxyglRBhayc0xua/CzLQaDUe1jym5Peb6Jcyg84qn46M6zjR/yQ8XEVgxkD6d6I77fzWuPONkYNFDlHCwJRlyssKClVnQqy2IOR5g3Ahglq20X1157bdZneMYZZ2R1ulQqpR5//HF17rnnDn2tuLhYHXHEEeqRRx4Z82cOPPBA9aMf/UiHIdJ6a9myZer3v/+9+tjHPjbu7+nt7dUfGW1tbVlfFhSmrWfrwNtcsJPXfun+gUiHLcttTG4302vce4Hsi0IqR9qpHLFOrqF5WFL9A/r2w4KFX+GIVDJIG08Z5orwUTmyFSGRWwFFnMEMJGiwsXLEvmO2YXD5+rYe5ZIZtbyfjbKtVby/n8cEwCRZ3SO/9a1vZXVm0jMv23Bk8+bNug3XjBkzRnxdPn/hhRfG/BmpGJGfO+igg/Suv3Q6rT772c9O2FZL5pFcdNFFWR0TgrW5I/cFMBmuLbMqZNAe7P27R70YIpUqhCP2KmSRgd2b9tmSx3NDWJo6UoQjloTuEmYFGbQQjkTDgA56RqBaKZxNWHHpTPXrwMvFtj42sHGwuY3HbLpGx4IEaRfHgnm0ba1k/TKu5+e4wxkAI2X16Lt8+XJlgr/85S/q61//urrhhhvU/vvvr1555RV15plnqksuuURdcMEFY/6MVKbIXJPhlSNz586N8Kj9tSWPuRPy5CRVB7ITBHaKYwbIxvYetbuqjfz3onDSL1x2ceeLtlp2kXkP0tbIFE1dKbVAVcV9GJhETwGPEWOeXx8r9lGhndRWFI4EL87NEfJ+RV5/1FWy4B2HZKJYL2ya9HpiIhKiyUB2BEuCBAkUXNko1VjD+keUJBipLC1Rnal4bj9VZQRhgEliu0dOmzZNlZSUqA0bNoz4unw+c+bMMX9GAhBpofWpT31Kf77nnnuqzs5O9elPf1qdd955ui3XaGVlZfoD0b9pyLdFliyuE47Ya1NH9OXNUnEki+xlCd542KbQNzQy2LsrlWanlSUkjDAJc678aqkV1vlhfFRMbEVbreC1dffFXrlCOBJvJYYt4YgcqyzEIpxAob2nQ7mgkS4IscwdiSscoXIEMEtWq0lSeSHVGVVVVSOqMMYbsp6NZDKp9t13X3X//fero48+Wn9tYGBAf37aaaeN+TNdXV3bBSASsAjefJmluWtre6x8bMqj4gRmkEXquHbvSKi2w5TKWH434l3caOsmHLGFaWGEzLshWPUwHEnbsaDmAjKBrXifEvxjQpCt9vLdmEMvgnhneGxsV1awcUaKLaSt8qub7A9HiouKVIODA+ZNV12WiKXrhbSQp70rYJasnqmffPJJ1dfXN/Tv8eS6I0KClo9//OPqjW98ox6wfvXVV+tKkBNPPFF//4QTTlBz5szRc0PEUUcdpcOXffbZZ6itllSTyNczIQnMUMiTjCyW0g/cThvb4gu2NhKOWKktgDBNdm/OrKPazAbSNtE0zZ1y++H5xmSFtN4b8/xoqxUZBrJvRUjkVtWIcKWVj61smhfGvJHwNFQlY50bEeTlYIZRPOFIHGipBZgnq3vlAw88MOa/C/XhD39Ybdq0SV144YVq/fr1au+991b33HPP0JD2VatWjagUOf/88/WTn/z/tddeU9OnT9fByNe+9rXAjgnBzYAoNFyZO5WFbtvEWfUjwYy8MKZs3S6y89KE80A0bWVM/Fs1d6UI1zyrHAk6bMH4CAW2GlRcEa4MYzfpGHxmUzgiVS4IR6KkWE2tTKotnXZ3nphGS61YVMdU1RVXKANgfAXdK1evXq3/X8iAc2mhNV4bLRnAPlwikVBLly7VHzCXtCgpdHfwhrYewhHLDAwMxlKWOvx2J+2V6P9sDwmzgtj92drFAoUNJBgxcRe5aa2+EH6YwcyR6Ni+mzcohETBau2Ov2pDHkdoy+jfoqbrQY6NGqrtD0ekcgT+3DdptQeYZ/sJ5pNIp9O6lVVdXZ1asGCB/pB/SzVHpvUW/BZEayVpkSSL7bCH7L7Od86MKRVLiL6lVhCL5TJIL8VOcCseI0zU0t3HAq7hgm6DxeNFNLhfbWNiMGwzE9pqCdmUg3hICyIbdl8nmS0QSThi+215SqXdl8FWct+U+2jUaLUHmCfnR4LTTz9d3XTTTeob3/iGnj8iH/LvW2+9VZ1xxhnhHCWssr6t8AVqWWTfwm5eq0igFTcTjgHZawlwsdzEdk0I7+8dJHm+ae9lgctksjs7SAxkjwZ5wDBcF4GRzVOmPGbz2iNeNiww2nCMtpO2Wja3VZZgpJh5I17dR2m1B5gn53vlT37yE3XHHXeod73rXUNf22uvvXRrrY985CPqO9/5TtDHCMt6ygc1lHt9a4+aTv9Na0grtLhJoCYLnaUx7ABB7loCbIclC+88XphNBp+bqqWzj7YXBgu60kNeq6T7B3SvcoSHPGAbZo4EOwjdlKok5o7Ey4bKEZvaf9lKnsulTZGtYSVVI/GqqyiNtC2bVKpUJnlcAEyT87vCsrIy3UprtIULF6pkkgd238nMifRAMIsYa1u7jXnzg8n7LpvwglRuL3HOPUFumgKsJCh0zhHC3/kv7c9M1dLN7cdkYQxQZyh7+HgNtw1XRXBMeL1p4rH4qMaC4MGGY3TBVItndth87C6IuoqjtoLNWIAT4YgMT7/kkktUb++2BUj599e+9rVxB6vDH+tauwNdcA9yZzncrhox8VgwSSujnrTz8yxgxwJSM881Rj9WhDGvgbkj4SMPgOvPJ/I6RirREA8bKj4JR6Jhc/XFlCrzb8cuq69IRl6pAsA8WT1bf/CDHxzx+Z/+9Ce1ww47qMWLF+vPn376aZVKpdThhx8ezlHCmh7A0gorSK+1dKsp7KYw3oaAWqkFdSyyW9Xm3rM+kDAjyF3Fsgu8ozdtRYsFH7UaHj7IcF95DqPns3nCqvCgcgSwk0mtrOR1TEdPWtVVstgVBxtaVtkQ4LjA1vWCqmRClSVK4j4Mr0mAWVxUFMpGnLHU83wBGCmrVxR1dXUjPj/mmGNGfC7zRoBNHb0q1R/sYsPalm61x5yRtz+YRRYUTWplJe17ZFdhvcU7iHwQRhuspo4U4YihWgza6TsWeUMkA37ZzWWesCo8qBwB7CNhhEmVI5m2jIQj8SgpLtKLy6a27ZQZiOWlLHxHoSpZoq9vqTa1CQvl8ZONUfJ3iKpFs81VToDLslpF+t73vhf+kcB6UuURtO6+fv1ERS9Oc23uDG7OTFDWt/UQjhhuS0cqlNvivIbKwM8X7leOZI6RcMQ8YYUYEqQDsEtXqt+4xU/Twhofd32bGo7QUis60jGgvqJUb9a0CeGIGSSwiCIckWHsVWzkA9yYOQKMpT+ElloZrzUHH7ogOBtazXsRGtZtEcE9XoTxAnSzQRVMGLm4berCxXAscJkprBCDtlrhkzYV2Irrwt3H6bZu85/fXFZjcNsqqpmjZeOgaxuP2UVRhVS2tn8DfJDXM/add96pfv7zn6tVq1bpWSPDPfHEE0EdGywiQ7DD2sklFSl7zKllhoShpErDxDfP3al+VZGklN1EEoyE0ddVKs06e9PsyDGMSf3hbVt0AzNHbMartmG4MmJ7nE40taiidFr1NU6b9LSlGzerwURCpafW53RMzLqLj8nVGSYHNy6ysfqXmTRmiKpLCS21AIcqR6699lp14oknqhkzZqgnn3xS7bfffqqhoUEtW7ZMvetd7wrnKGG8NSFWd8iuUZNmWmBkG5ouQ3eEr2ul4shUYd6feawwc9i5DWwJcXzT20dbLVuxVrwNV0U84YgEIwu+dIla+MWLdfAxEfm+nE5OLz+XLWkt25ni8SQuZocj5h6bi2yrwpB5NMykMUNlMhHJ34JW8YBD4cgNN9ygbrrpJnXdddepZDKpzj77bHXfffepM844Q7W2toZzlDC+ZYpUjoRpNa21jGRi1YgNx+a7je3h/W1s6zXsg7YeMwPU0aT60dSw12epftpq2Up20tNOatvgaEQfjkjFSHFfn0qu2zhhQJIJRuR0cnr5uTCPC8ExuVqYcCRaNWUJqyq4uH2YJezgQs/FYcYM4E44Iq20DjzwQP3viooK1d7erv/9sY99TP30pz8N/ghhvLUt3aG0yBk9QyJt2ABGmF2dsbkjFdogX+Svp68/1EUEqRyR9hYwhy2VI4Le8f5UjvD8EA3Cka24HoJ5/SAfuZBWWsuvuFClZjWOG5AMD0bkdHL6bFpwja6kRjxKS4pVhYG77yUQNfG4XFZcXKQDElvQUsssYbe8qi1P6McrAGbK+d45c+ZM1dTUpP89b9489Y9//EP/e/ny5SxIeSrMllrDS9bXMWTbKDLbweSdcvJ4FHZFE8xreyW7/8MY9o7874c2tauy6Vh90RPiQHZet4YviHUAaYGW78fyZa+qf/z1z2rFslcLOp9CEY7E9/g8UUASRDAiTH497AMTZ3tUW1bF4AqbqjEIR8zSEHLlCC21ALPl/Ozxtre9Td19991qn3320bNHvvCFL+gB7Y899pj64Ac/GM5RwlgdvWm1pTOaNjarm7vU3KmVkfwuTM6GsEqOkduMPy21Mja09aqG6rLQfw8m15XqV/0D9ixAtxOOeFM5IsGIBCT0+w5XSbGkI4X9Dc++8z8FHsVUpda2K/Vo/udzzXF7F3QEiRIWSeOsQswEJJkgRP6/+sunqrmXX19wMCIIR+JfEN+4tZmFMUwMbHyw9Xo3t7PBcNUWBTk+qKso1RVfYb1vIRwBzJbzI7LMGxkY2Pom59RTT9XD2P/+97+r973vfeozn/lMGMcIg61p7op0x3l3ql9VJFnIMIHJLbWGL8RLO7YEJaxGGBgYVBvbwg9TN7T3qN1Vbei/B5Nrt2TeiG3zUXwhb1BTIbbUlOCFcCRcCWZtaFwPhSs0gBgdkOz4+aX664UGI0Kqi6TlF48n8TCxWsDEY/KBTYEDtxHz2rLVVyRD2/hLOAKYLedH5OLiYv2Rcdxxx+kP+Ed2Xa5u6o48jNlpRk2kvxPbk5DKhtZFsrC2ob1XzamviPtQoJRq6kqFutA5fHepDNauTPKmI262VWJ09KT1cxutMMyQ63yBXHX39as6xe7eMAXRX/sbx+6Z0+nXrlqhlhz3jnG//607/qhmzVugokSf8cIFUZ0hAYhUjGSCESGfFxKMDH/tQTgSXwsr07DwHQ8TbwtjKUuU8LxgIAkwwghH5LmB96WA2fK6hzY3N6tbb71VPf/88/rz3XffXbfYmjp1atDHB4Nt6UzpBcgoSWstwpH4rbWgaiRjXUs34Ygh1kfYik1+16Lp1ZH9PrhRiTEwOKg6U/3WvLl2nYQXNocvCKadlCwi5aJp7Uo12Df+4saWtSvVgkU7qijRVqvwzS4dvYXfX2XGiLTSGk4+L7RyJDMTpbG2vMAjhCstrEw8Jh/Y8vqN8MxMU6rCud9SNQKYL+e4+q9//atauHChuvbaa3VIIh/yb/mafA/+WN0UXUut4S1ami2oWHDduhbz541krG/b2loL/oUjMGMulW1sq3ZxvUox1PMnHAldHDtjZ86duCpk1iTfDwM7hAt/XJaqvkKMHr7+6tUXjTmkPV+t3fY937kimSjOOUQNU3FRkaqiDXQsZGaEDTv0bQlxfDOlMmnV+QIITs6v1GXOyIc+9CG1fPlyddddd+mPZcuW6dZa8j34QRab18a0QL4qhlAGIxerwurFGWZrLcRLdlR2RlhptrkzpVJpQjET2lTZxsZjdlXYlR1dIYcvUCoZQygwZ/4itc8Bh6rikpGLk/K5fH32/EVeXA8uaSsweBgdjEilSPfrd9H/Dyogkdc5iE+tQTvxZe4F7TnjY0PwYNNsFJ9I+6uqEMK1KZVUkgGmy/mV+iuvvKLOOussVTLsDYf8e8mSJfp78MO61h6VHohn4XFtS7de8EY8Xmuxp6XW8NsM/Ko2kh2mG9qoHomTLGzH9TzhW7WLq8IOL2irFc2O7jicddn1avF+B434mnwuX49DWUzXgysKCR7GCkYyLbQyQ9qDCEgkWB/g/UlsTGpjZVJQ4yMrwhELjtFXQbfWkqC0nsoRwHg5Pyq/4Q1v0LNGdtlllxFfl68tXrw4yGODweKs3pCBztIqiTkS8bAxaJAWS339A7S1iNG6GObUSIg7d2pl5L8X29og2ohwxBxhV5t18rd2NhSorq1XS2/4sVq7cplat3qFbqUVR8VIhkktf3wKRyYKRjIyAUnmdPL/fGaQyMyqjlRa1Rq0SO8Tk2Y4mBTU+MiGqowqwhFj1VUk1Zrm7kDDUmn3BsBsWT0q//vf/x769xlnnKHOPPNMXSXy5je/WX/tH//4h7r++uvVZZddFt6RwhgyhH1zR7xtilZt6SIciYEsJDV32TfzRd6wSkDCQnl8t5vW7ujbTWxs3zpvJkEoFgtbQwbaapmjK4ABzJPNHJGd3sW8aQ1NWWm8j78SiMQZiphyPfgatg8mEmqgtHTcYGSsgEROLz+X73ESjsTDrHDEnGPxUVWZ2WE0M2nMVh9wCyyqRgA7ZPXMvffee+tysOGD8M4+++ztTnf88cerD3/4w8EeIYyzuin+yoFNHb26HYb0hUR0bGyplSE7QAhH/KkaGT5vhiA1HrbuypfqxN50Pzu9YyahRVcEba+kOoVdvuGp4HWaxsyR/Mn8sHxb4KWn1qsV37xAFaXTk1aCZAISCUbk5/IdHK8UrzniYNLjuEnH4qOaslLjwxtm0pirriLgcCTg8wMQYzgiw9cBIQHZagMGostxrGnuUq9rrIn7ULzyWoAlpnEEaix4xmNtxPNGhlvX0k04EhNbK0dEZy+PFXGTYGT4ppwwb6csZIWHTSxbrwOqk+J7Lskl6Mi1lZYr7SRdmW8k97W4Z0lJ+xyqAuJVXlqs/w6mziitCmHgN4IjbbhlJkxQ72OCDlsAhCOrR+b58+eH9Othmy2dqdB7gOdSwUI4Eh1pi1TIQMy4ySKbLNIvnFYV96F4pTvVH2srtg1tvfrNEb1eo2dr5Ujm2KdWUQYfp607sCNqo1YXya/ydubI6Opz3xAQ2fFYEATaMsZLWprFHY5I2E5VQLzk+peZHm0xtPTNBvNGzCeBRhDhiNwWawlHACvkVeP96quvqtNPP10dccQR+kPmkMjX4L4gh1MVShbqWyycf2ErqdSxnQuXwTZrY2qplZEeGNCzRxB9S6TOVLwLFL5WvbgiqkXGdv7WoZKFAd9ba1Wyi9ybagx57vA5CIybCbM+ZPgy4ic7/01lwu0UEwsq0KguK2GDHuBqOHLvvfeq3XffXT366KNqr7320h///Oc/1etf/3p13333hXOUMILsvl5r2MwJE+af+EDe6NncUiujSSqfWAiLlAmPGSYcg2+iaokUFh4n4tcWVThi0cKrrXwPB3wPh3x6PB4YHFRdFm8MsJ0J7Wto02gGk8MRKkfMF1SAxeMBYI+c7/XnnHOO+sIXvqAuu+yy7b7+5S9/Wb397W8P8vhg2FDlvv4BZZLXWrrU62fX0ss5gnZq3TGXqQc5VH7nGbRji4K0NpBAKm7SWksqGXiciI5Ni1ljoXIkflG1cZSWPRLk0QYlPBWehyO+h0OFMqWdby7Pfyx+xtdWK261FfztTWByOGLysSHYUIMqIcDhypHnn39enXTSSdt9/ZOf/KR67rnngjouGMjEKo3etLTM6Y37MJxnUju1QrlQAWMLUyo2JNTlcSJatocLMpAd8VaqRlXRoX+X5bdX01V5PnyWhfL8SXBp2+Ox7c9/NqsuT8QedJsQ0MDcACJZUswcKgtUJUtUcQCPJabeDgEEEI5Mnz5dPfXUU9t9Xb7W2NiY69nBoh3gmzrMXFxkjkS4ZMf9OkMWuYPajdzaZeaAPtesazVn1kfcs09802XZYtZYs2riHurqMxmiGmVbNp4TwuV75YTvl78QUrUsrapsYluY4xLp7V8T42JkWaKEhW+DgjITmXpcGElC1iCCjZoywlLAFjnf408++WT16U9/Wi1btkwdeOCB+mt/+9vf1OWXX66WLFkSxjHCkFZEpvaPlwXYVHpAJRM5Z33Iwob2HpUyrJ1aoda0dKm6yrq4D8NpsrAs7dhMsaG1h9ZaEXJh56y0RmGRIx4t3dGGFS1dfWru1Eh/pVd83jkpCyxVnlfO+BY0dFnWBsw10tYqqraMY/1umKH0vxUapm108fn50Maqz0IfS6rKeB8B2CLnR+cLLrhA1dTUqCuvvFKde+65+muzZ89W//d//6fOOOOMMI4RBjC5rZLsKFvf2qPmNVTGfShOcrENlVym3WfVxl567zK5T5oUqErAt7mjVzXWlsd9KF6wfeZIZlGuoTruo/BT1LOKmrrMCXJd5HNbqcrSEkJ5z4IGBrIrA9paxfPehZZaZpEqItPCEQZ026PQYEMqyRIlbN4FbJHTvTWdTqsf/vCH6vjjj1dr1qxRra2t+kP+feaZZ7LQ6PAO4BbDFw5orRXerIb1bea0RgqyTYNJVQ0uMrGNlUltvlwmFTpdhr0Z9WEIsEuaI358bu3u07NHEA6p7C3ztLrX52DI16CB54541VWUevm7YUcQwYBue1QVWPVJlRBgl5zeqSQSCfXZz35W9fRsXWCSChL5gNtsCB5kHoppO0Nc2f3v6oKRKcPCXSRt7jZ3pIwMR0yqZnGVLAy5cD27UP1iI3kuj3pxUW6vUVer+Kba077bLIT5F47I6+betH3H7YraGAOKOH837Hj8ZcHcHpUFVo5UMG8MsErO27j2228/9eSTT4ZzNDCSLW2VZC4KguVygCCXzYUFXBNtaDMzhJDFChZAw2djj3hX56bYSNrfxWFLZzy/1xe+DqFlIaww3RaGIzYftwtkzoS0s4lacVG8w+BhfjiSKC5WlSyYW6OywMoR5o0Adsn5Hv+5z31OnXXWWbqV1r777quqqqpGfH+vvfYK8vgQM2mnZcsCkcxF2XE6DeKD3P2/sd3dxaLe9ICuOGqsYQZF0ExuxSbVIw3VZXEfhtNcaSniSshjmy0xVZ3F9Xt9YdoiVVR8DYWCYmtVeE/fQNyH4DVpb7WxvT/yqhHmC5nFtLZa8jxIG3q7ZoYV9vM8/wM2yfkee9xxx+n/Dx++Lg/ysktY/t/fb+eLWNg3iH28IIddesHt/pdh9y5b29JDOBJCOwm57ZjcKm6POXVxH4bTXGlHlR4Y0AtzsgsV0dkUUygvVWXp/gGGZ4bE1x3VvoZCQc6Is5Gtx+1WOBLta1HmjZg576qitMSY+yNt1+wiYae8B8g3pKetFmCXnF+xL1++PJwjgZFsa6u0rqVb7TSDOThB8KFN2frWbjW4Qx27eAJe2DR5To1UNbT19Klaw3aTucSWasNsLwvhSLTBWlyVR7IZQGYlzawjMPdhB28UZAh9HO19XCGtMG3dpGNrxYsr6iqjf7whHDGTBBLGhCOE5daRcI1wBPBDzo/Q8+fPD+dIYBzZRWnKi4lcFvQJRwrX1z8Q2+7dqFtryWLY9BraLPnQUmt49QjhSHg6etJOLdZPow1bZOKuOpOdxoQj4ZBFgtKSYv36whc+BkJBsrk1FeFIvOIIKghHzCSv9+N+bZFB5Yidr12au/L8WTZXAVbJq3fAiy++qE477TR1+OGH6w/5t3wNbrGtakS0dvc5tWs5LjJrxNbdevkslCMY0l7RhuvThmO0lVQN2RaqT4TnE7/CVR4bwuVbiylC+MIrR2xlc7Djgqr/hrFRoirATHFUEY2H5wT75BtwJEuKVQkziACr5Pyq4Ze//KXaY4891OOPP64WL16sP5544gn9Nfke3GFjOJJprYXC2035Yp1HlzVsLV19VixmNHel2NUZEtfCBJeqYEwnFQVxD0WXYK+1qy/WY3CZb5UUvoVBQeu1OGBIeVQhZSJplxvlQrTc15lXZSZTKnoqkwk9AwV2ybe1bjkttQDr5Pyq/eyzz1bnnnuuuvjii0d8fenSpfp7xxxzTJDHhxiHm9u6+3dtaw+ttQrc/b+xzf2WWiMWw7r7jHnxbLO4d33nQkrs5zdUxX0YznFlGHtGXPMvfCT3SRMqFte1dRu109QlvoUFvl3eMFqf2qrX0vdQLpHX9Vs6o3k/w3sIs6uIEsXFKj0Q7+MJtxE7lZfmF2iVM28MsE7O9/Z169apE044Ybuvf/SjH9XfgxvWttizyDlWsNPFglbetnSmvNvxttGiRX2TmdLTNxsbPAoAo+Rc5UhvvxoYiH/B3gfrDGlptc7i1z+m8y0s8K1SJmgpm8MRi4/dFfURhtx1FcnIfhdyryIyIZiI8vaI+NtqMYwd8CAcOeyww9RDDz203dcffvhhdfDBBwd1XIjZ+ja7Ww2ZsshiI5+qRjJYKC9cz38rcGyxSebqsOgduHbH2lBJJV0XO4BDl+4fMCZcbevp0x8Ink/91qUVBy1UCmPzRh2pgpPHNfgx/NqExXeYHUzUcxvxqq0Ww9gB++S8het973uf+vKXv6xnjrz5zW/WX/vHP/6hfvGLX6iLLrpI3X333SNOC/u09/RZv8AlQ1V3nF4d92FYaVOHf0FBU1dK97uPenijS0xZ2MyWlNdv7uxVjTXlcR+KU1yrHMnMHaku82vHexwt+foNCitl5lrtTBYywlhkKEsUe7Gr3qcgKCw2V45kwh3mUMSnpiyhiouKImnXSDhiNhP+PrTrtFO+IUe+7bgAxCfnd/uf+9zn9P9vuOEG/THW9zIljP397La0NVhwoTWUDIYuo99jzm9EpS2Zb2R3uAwCnlnHQrlP1TdSJUU4EizXZo5kNgzw2BCu15q7jTueXWfWxn0Yzraa6vVgE4ZvLcTCYH04kh5QlXRbik1xcZGuHgn7fQ2Dts0Xd+WILLCzJmHv40g+mzqoHAHsk/Mz+cDAQFYfBCP2smmo8nh8GyoelKZO/4KRjKiGNrpI2lNJmyrbbGy3/7HOtNZqUoHlGherYUy73Www7PFD/uY+Px+GyZeKChN2KtvO9ucTm9uCuSKKVkbc180n1b9xdgeYWkVK6ltrrXJmjgDWYZsDRpBqC1cWBGxr82OCzR7s5hyPK7f7uNqSSZsq20j7wK4UC99BcXVOg+1tJk0nLaxkQ4NpVjd1xX0ITvKlosKXyxkm28OFvn7zHtd8E0VwEXdVAiYnHU3inPlRTwmZ1fKpAqFyBLAP4QhGcKnaYiMDl3PW7GFLrYyWrj6jet7bxObHDZuP3cTZHC6iciRcqwwNISS04TkheL6EBtI+DH5XjvRZ3hbMBVGEI1SO2GFKjNUbBGh2q8ixCiRRXMwcU8BC3GvhbJsZeVPl82J/rmTnbmu3mzu/syEDG2W2AHK3weLHDQlREQxXQwR5LpHWTwhea1efsc87smt9XatZs1Bc4ENoUJVMqJLiorgPw2oSTNoeTtoe7rhAZo5I1UCYCEfsMCWm6g25/cX1uxGMXKtAKmmpBViJcAQjFsdtnBswERY+s9fWk7b+jWihmrvMXKQzmSwatxm6uJltKzkqzILhcvspV1uGxW1lU6cy2aotZla12EwGF+fTv9smvlTHhMmFYIG2WvGTkLK6LLzHmzIPHs9cEVf1Rm05YblvlSM8JgB2IhzBENm92etYCThzR7Jn8wJ3ULgOcmd7oCoLMDIzBYVzufLK5eAnLhLGr2k2uzJjU0ev6nS0IipOrocHslsdhXEjHLH/MrggzMoO7uv2kAXrqmT0zz0MY7cflSOAH7J6hmhra8v6DGtraws5HsTI9kXO8QOfflWW4EnK15Y4ueA68LMVnzz2Tasui/swrCaPs66F6z7MU4nTa83dViwertzSpXafzWvbINWWlzr5mtOX8CcKaQeqLtID5j+++RKOhBXE01LLvrkjnaloX8/RUst+lTmGaoQjgJ2yuqfX19dn3a+zv5++3LZy9Y3qlo6Uml1fEfdhGI+d0W7vfA+DK634pP3ebrPiPgq7uf744frli4PpLbUyVjV1ql1n1qhi2mIEGo64zIe5KmGzITidTCptf8DjgjCrO1x/LHNNQ1VSrWmOtl0mlSP2Ky8tVsVFRXo+aRhtuABYFI488MADQ/9esWKFOuecc9QnPvEJdcABB+ivPfLII+r2229Xl156aXhHitDbW7jaWkYWbwlHJhf1ThoTyc53eUNeWkLHwWy0daedqBZo6UpRYVYg18MDgtPgB7E3ddrxmkMe49a19ag5vI4IjMuVFbKZrKbM3csXlT4HZoFROWKGMAOMupjmWCD/ypEoyfuKKp4PnHhel2qQbDtM5FppAsAMWd1zDz300KF/X3zxxeqqq65SH/nIR4a+9r73vU/tueee6qabblIf//jHwzlShL446OowblsWYOLWk6LqS3T39ROOeNRSK2NzR4rFzwK4Hh6k+gdUT18/QxYDsmKLHVUjGSs2d/L4EKBqh8MRGf5MlVHh+hzYeOFC9YsL5HlbFqllE0yQZCd5NYugVpHh6PIeL6r7ZkM1VSOuqMgpHOG9AmCjnFcApUrkjW9843Zfl689+uijQR0XIrbF4QChrWfr3BGML90/oBf/QEiUCxdaamVsbHMn6ImD65UjvlzGKMiihOmD2Efb3NGrX0sgGLI45erOSlpqBcOFqgvaapm1KB5GyEsQal8FQJQzQGip5Y6qLF+zJIqL2UgF+BKOzJ07V918883bff2WW27R34Od5I2/y6gemZgLrZGCwnWRfaDmUqjqUtATB9crR3y5jFFY3dRl5cKnVI8gOK621nL1ckXNhWDBxsc5V4Uxd4R5I3aKMrCQGSdwQ7bt0SrLCEYAW+X8Cv5b3/qWOuaYY9Qf/vAHtf/+++uvScXIyy+/rH75y1+GcYyIYKhyS1ef8+HIrDpaYoyH0v9tqKDJjgQj2Q6ms6Wdmix+s+s3d1KZ50OoSOWIny21MlY3davdZtXSdjHAEGFDm3IOzyHBcOF1qbQrlo8SqgtiF0aQEUY1CtwJR+R+T4DmjqosQ49qZswA1sr5Hd673/1uHYTInJGmpib9cdRRR6mXXnpJfw/2ae9NO/EmZCLNnW6HP4UiENjG9ftCUFystNjo4GWKgi+hgS+XM+zHDVuvR9kFbls7MJO5umhE5UgwXHkt5srlsF0Y98swqlEQTTgi7bVC/z2VSdqueVg5UuVoy1DABznde/v6+tQ73/lOdeONN6qvfe1r4R0VItXsUGuc8bR0p3SFTBQvhmxE5f82XBf+hiNymXacXh33YVjH1sXuXNFWy9+qkeGttRZOq4r7MJzgYojAgObguLJpRy4H/efjJ/NBAj9PdohbSSo66itKVXNXuOsfUxnG7pSqLJ/bs60wAWB55Uhpaan697//Hd7RIBaut9QSUtbe5skCXj5cao9UKK6LyfX09Ts5nHhLR0oNDPD3z5UvoYEscsltH/npTvWrda09ymbyuOf6jLaouNh+ShZL2SkcjJQjrRr7HLkctpN2iBUBhlSywF6ZZBHUVlG01mIYu1vkPp/NYwihKeBRW62PfvSj6tZbbw3naBCLlm4/FrZaPQiB8sVy8DZkI35WjWTa5jSFvJPMRb5UjggXQ8GorGzq1BWctmMwe3ALDa4tItRWuHV54tTXb/9jhUsVMC4IsnpEHrvoRmCvhpCrOuS2IW214BaZXyuh10Qf2bbfAmCenO+96XRa3XbbbepPf/qT2nfffVVV1cj2AldddVWQx4eQyS7pNk/CEWmtNU9Vxn0YRuLl/Ta81/F7NofsCp9WXRb3YVjFl8oR0dGTVo01cR+Fna81Vm7pUi5Y29qjK4holRNM9UhHrzvhqovVMHFxpXLElcvhypyjoDb3uNgW0CdhV3XUVZSqREnOe5BhuD13qIv7EACEKOdn9meeeUa94Q1v0P+WIezDsYPCPh2ptDdthNq63XkDHkafbGzFVTE5l9vKyBvnXWfGfRT26E33q16PFn98qpIJ0vq2rYGCC6T6ZVVTl9p5BilZEJUW61qVM1wdMh9HK1yp5HSBT8+PpgtyR3d1Gfd1m5UlSvTjdVjVwA201AIA6+T8KuGBBx4I50gQC1+qRgTtUCZub4GtEsXs9JnsfuTKIudYmrv6VF//gO5Pjcn5Fhb4dnmDYvsg9tGkCmanxmo2BRXItTCBtlrBhe6uoHLEHEG28QtjwDuirx4JLRxhGDsAWIfVH8/5VE0hC54yEBbbKy1hgScjwXXh5byR4bvCZTA7sm8z5ROfWogFpbM37dzjRlfKvcsUh9oKd8IRCdQrkyyYBqG3z51AwaWgx3aBhiPc160XZmutKcwbAQDr5PXM/thjj6mf//znatWqVSqVGrmIdNdddwV1bIiAS72es13YqkjSJ3w0+qJuU0rlyIQ2e7AgKIueM+vK4z4MK/hWSSHDdZk3kRtpQeWilU1dqrGWx4lCVCVLdLWmCy2UpMc8guFSKyqXgh7blZcW6zbCQbSTrizjNYDtwqrukHk0vEYEAPvkvAp4xx13qAMPPFA9//zz6le/+pXq6+tTzz77rPrzn/+s6uoYUmQb33bBtnsWBmWrLEEgkFFWynUxYVVFp/tVFS7PVAlae69fzyE+bioIYj6Hi9a39rArvEDSlsyVUMG1FmFxcql1Zw+PEUY93lQFEGrIeyZar9pPKv3CCDGmVpUFfp4AgPDl/Mz+9a9/XX3rW99Sv/3tb1UymVTXXHONeuGFF9SHPvQhNW/evHCOEqEYGBhUnZ61mfKtBUy25EU+c0e2Kk+w22c8Lf+dx+E61+eqBMnHx1QfL3MhVViu3pdk9/Ga5u64D8N6roQj9ZVuXA4TuBQo9FA5YpSqANphBTnYHfEKY3D6VFpqAYAf4cirr76q3vOe9+h/SzjS2dmpd2J84QtfUDfddFMYx4iQdPX1612dvvU+x9gqKAHWqBwZn08VFT5UyBQqLXOcHF34ngiVI9lb3exm1UjGakerYqLkSjji0vyUuLkUKMiGEnmuhBmCmAtUSXtmZ4Qxd2Qqw9gBwEo5rwJOmTJFtbe363/PmTNHPfPMM/rfLS0tqquLN4k26fJwgYdFrfExi0Xp6hn6xI5vs0eDyn2YrVKozl7/ghHB80j2i4LrWnuUy1q7+3SlGfJX50DFhbx2qC1nN3lQulLhP8a+tnKZevzhP6u1K5eF/rt83ERgqiBmhVSUcl93RUPALbDKEiWqmsoiALBSzo/ehxxyiLrvvvvUnnvuqf7nf/5HnXnmmXreiHzt8MMPD+coEQofF3jkDYq0EyumhdQ4u6n8XhBmN9j4pMqsyaNqii2dft8XstERwQKWiahAzH4mR/+A+9Wpa5q61e6z7V/gj4uEChIu2HxbkeoXqaJHMMJsxdfe2qyuOvc09eQjDw59bZ8DDlVnXXa9qq6tD+V3dqf6VQ0zaZx5nc97BXfUViRUorhYpQcGjK1EAQAYWjny7W9/Wx133HH63+edd55asmSJ2rBhgzrmmGPUrbfemtdBXH/99WrBggWqvLxc7b///urRRx8d97SHHXaYfgMy+iPT6gvZ6/Js3sjwdmLYXhUv9gPpRezyDumg3jzYoL0nzbDlSfg6e0NmdUnIjom91uLHPI61nlzOsMhr+PoKuxeUptBj3pr3JxKMPP3owyO+Jp9fec6pof1OX99vmagygKoPwhG3nn+mBFi9SDgCAPbK+RXC1KlTh/5dXFyszjnnnIIO4Gc/+5kOWG688UYdjFx99dXqyCOPVC+++KJqbGzc7vR33XWXSqW27V7esmWLWrx4sa5iQW58fbEu5fqUvG6vmpYQDFmcgI8zOKRSZlZdRdyHYSwfqw8zVVQSsvM8Mr5UekAPY/dBZyqtWrpSqp4F8oKGmdtcrccw9mCrRsKqIpJWWsMrRjIG+vv116XF1uz5iwL/vb6+3zJRebLwuYK0IXaLzAjZFNBMRcIRALBXzq8QTjjhBPW9731PD2YPwlVXXaVOPvlkdeKJJ6rdd99dhySVlZXqtttuGzecmTlz5tCHtPOS0xOOmNnT10RdnvbJnwwLfUrVEBCNy6eWWhlbPJqxYttzSJT94sfi48yuXGxo61EDg/5U17g+WyVsti8o2X78JgkzSFi/esWE3183yffz5ev7LRPJTIjiAlvgMZvQLVMD2tggtytpsQgAsFPOK4HJZFJdeuml6qSTTtID2Q899FDd6kr+v9NOO+V0XlIB8vjjj6tzzz13RDXKEUccoR555JGszkNaeUmbr6qqqjG/39vbqz8y2tracjpGl4XZ09dkDEYcPxyRF3b5LmgV2oJo7aoVasOalWrmDvPVrHkLCnrjky96Qo/Px3Ckucu/y2z67I04+sWPVzWzfW0rMta39Xg3X2W3WbVxH4a1bA4XZKF068w2mP68MnPuxK8tZ03y/UJaMcIcFaUluuIvH6UlxfoD7giq6lOCEZmfBQCwU86v5m+55Rb9/9dee0399a9/VQ8++KC68sor1Wc+8xk1a9YstWbNmqzPa/Pmzaq/v1/NmDFjxNfl8xdeeGHSn5fZJM8888yEs04kyLnooouyPiZfpPsHVG/an/kBwxGOjN93VVprtXX35fXzZ9/5nwCOYqpSa9uVejT/87rmuL3z/lkqR8YfJupjmNrS1adnSxTzZseY55CJ+sUvveHHkR0HbVLGJ/eZjW32tkjKR1tPn17UpTVj/gFDVTKR94JlRqKpRRWl06qvcdqkpy3duFkNJhIqPbWwULXB4mDHRIXeBiYyZ/4iHabLc4a00sooLilRi/c7KJSWWnFtJMDEbbHyvZ2VlxKMuCaZKNbv/2TWoK8hPwAgj7ZaGVOmTFENDQ36//X19SqRSKjp06erKEkosueee6r99ttv3NNIVUpra+vQx+rVqyM9RlP5HBDIQi/GVutx5YTs/GQ32Nh8raCQKqpC3yy5Ko6dsJl+8cMXtUb3i48Ki13ja+pKqfSAf5svfJmxEmbf90KDkQVfukQt/OLFOviYiHxfTienl58rBAtiweoMufWtVBlKEDKcfC5fD0uf3kzAew9TFBJw0FLLTUFUjzB7CgDslvMWt6985SvqL3/5i3ryySfVbrvtpttpyVD2Qw45RAcluZg2bZoqKSlRGzZsGPF1+VzmiUyks7NT3XHHHeriiy+e8HRlZWX6AyP19Pm3cJHh4w74XEqC1zTn97PfOHbPvFppLTnuHeN+/1t3/LGgFlu5oE/sxBUUPgdDdbzhMSJkzqZffFg7f0eTgewYm29VIxkb23vVgmljt3jF5KZVlanVTV15/7xUjBT39ankuo06+Fh+xYVjVpBkghE5XWpWo/65QjRU8x4j6JaFYZL2i1JlKGG6PGdIK60onjc6etKqrJqFdRMU0n63kJ+FuaZUJgt6/smcBwDAo3Dksssu0xUiS5cuVR/84AfVzjvvnPcvl/kl++67r7r//vvV0Ucfrb82MDCgPz/ttNMm/Nlf/OIXepbIRz/60bx/v898Dgh8rpqZTG1FItI3DE1rV6rBvvEX0rasXakWLNpRmX7ZXdfS7WfliGjNs82c6+J4HI2rX/xYeqhAHNfmDj/DkS0dvWpwcFC3qETuptUUtrAkQYgEIpngY6yAZHQwMl6Akq2yRLGqpR1n4CFCFCQQiSpMz4Q+BGkuVI5QYe6iKQVugpLnAtpqAoDdcn6Gl4qR8847T8/7eMtb3qKHsh9//PHqpptuUi+99FLOB7BkyRJ18803q9tvv109//zz6pRTTtFVISeeeKL+/gknnDBiYPvwlloSqEhrL+TO53Ckf2BQpTydt2Ja9YRJi51Ujowv3zk0LiAcGVtXiH3hJ+sXL/3hh5PP5etRLnSl+gd0qxRsP4umJcb7jLRee/zhP0faYm34baKNNnwFtbasKnCweSYgkeAjE5BkWmwFHYwIWewmDAu2ItHVlny06DRHIdUftNVyt610cQGP5XUVVI0AgHfhyOLFi9UZZ5yh7rrrLrVp0yb1+9//XleAnHrqqbrNVq4+/OEPqyuuuEJdeOGFau+991ZPPfWUuueee4aGtK9atUqtW7duxM+8+OKL6uGHH1YnnXRSzr8PW/ncVkv00Pt33DcMFRG+8DdpsbOeF7bjBqlxDN42adCy7AaHGQF7HP3ix0MV4vaau+K5v7S3NquLPve/6tSjD1GXnH6C+tzRh+jPO9oKmyeRq6ZOf6vsgjCtpvCd9WMFJBXPvhh4MCKmUwkQqPYedzcjEI6Yo6yA6o8kswmdVFxcVNAmuSlVbLADANvlvEVL3vRK9YjMHZEPCSna2trUXnvtpeeP5ENaaI3XRkt+x2i77LILi1UF8j0ckIU9n4ePTzaUrru1O7LfJ4uaV55zqh6oHNdip5RDVyTZDTYW39/QS6VZV6qfcnlDAva4+sWPheeR7bV0xRMOXHXuaerpRx8e8TX5XJ5b5PYS5YyihYq5I/maXlOmVm7pLPh8RrfY2vHzS/XXgwxGMseL4ORSeWXKgPNsqxBcDn68mjlCWy1nyUB1eQ7P62fZYAcA1st5tWfq1Kmqo6NDV5BIGHLyySergw8+WNXX14dzhAiFz221RK/nlTMTkZ0z6yIMR0xY7Kylpda4eEO/NSAiHDHrOSTqfvFj6UnxPDJaHC21pJXW8HA9Y6C/X39dnluiuq3EFQ65Yvp/21QFsQFKApDVXz51KBgR8nlQwUiVtAHjeSHwSs1snX3nf5QJrjlu76wrDaWlbzLB4nrcZENU/j/LRipXbQ04OvMOVgAAdsv5Vf2PfvQjHYbU1taGc0SIhO9ttUzZcWaiuGZvxLnYyY6f8XX2cl/pjGG+hul8fw4RPI+YMZ9o/eoVE35fQveonls6evt1tVlJMXMo8iELxzIYN4j2ZDJjZO7lIytQ5fOgKkdm1JYXfB4YyfX5ZhL+TKMVW+wKaY1VSLACs9XlGXBIYMYsGgDwMBx5z3veo///yiuvqFdffVUdcsghqqKiQu/yYiihPeLe9Rs3FvbG5+Pul3xfEPuAYEACIq6D0UO3XR2amwufZ/GMd7voiOG+MnPuggm/L9WIUZHXwh09aZ5TCgwdCg1HRg9fl4oRCUYyM0iCCEhm1LLIHfR9J5c2nt84dk9lY/hDOGLGfAkJSFL9uT+HM3PEXTVlCT2UfSDHysW4NhUCAGIOR7Zs2aI+9KEPqQceeECHIS+//LJatGiRHo4+ZcoUdeWVVwZ8iAialHXn+sTvGt/DoYnI7hfZGeXTwh8vbMfXRThC9cwoQTw2mFB1UWh7DBMug0niup/Mmb9I7XPAoXrGiLTSyiguKdHzq6KuSGzv7SMcKcCMmnL1/Lq2wIKRTBAyfAZJoQGJVAY1sMgdqPbedE7vTWxsb5TLTBWEX6WWazhSWlKsgxW4Sf620mY51/aYPm4qBAAX5RyOfOELX1ClpaVq1apVarfddhv6+oc//GG1ZMkSwhELsKDDjt/JyIvDTe29ygeJ4mJVxTD2cXUzV0H18Jg5Ql8euy1N7Befba/48fA8EnyVWb6vT07/6nXq2guXqKcffWjoa3vtd7A6/eKrcj7PQhddu1I8XhRCgqWK0hI9oyGoYEQEGZA01pTTOi1grV1ut9QSzCQyh579kuPbHFpq+bFZLtf7KRvsAMDTcOSPf/yjuvfee9UOO+ww4us77bSTWrlyZZDHhpCwoENANJnacn/CkdqKBC0BJ6gyo32SDN7m8WL07QJcD2GEAgWFZgd9Xs076PNDnzYrpS7646rIQzPCkWBaa63Y0hlYMJIRVEBCS63gtTo+b0RI27CBgUGqDwyQT3ssHajAafkEHbKhEADgYTjS2dmpKisrt/t6U1OTKivjzYINCEeU6mXmyIR82gUjQRDGRoi4lbReYEFjm3z6dLvQL360dL/f7SlHo13lVlwPhZtVl3s4MphIqIHS0nGDkbECEjm9/FyuGMYePB/CEWkbJgEJbffil0/QIW214Lba8tyeD+g+AADuyPkdwcEHH6x+8IMfqEsuuUR/LjuuBwYG1De+8Q311re+NYxjRMB6Y37j/trKZWr96hV6SGrUvcAzWOycmE+BQU2OL4R9ws74kaFyBW+AtL4AQgEb+8WH0V7MJUGEqS6EZoQjhZOh1bIQmct9LD21Xq345gWqKJ2etBIkE5BIMCI/l4uGqjI9mw3BDmP3IRwRcjkJR+KXT9BB5Yj7anJ8/yvvIek+AABuyHlVUEKQww8/XD322GMqlUqps88+Wz377LO6cuRvf/tbOEcJ43b95qO9tVldde5p6slHHhz6mgxRPeuy61V1bW5vToO6HsqLeYM7lur/vtiTN6yuy/WFsE/ieqwwNSgiHNkqze1C6xtw//Ex6qpUF0IzQuXCycYVaV21prk7p5/LJejIdxj7zDqqRoLWmer3Jmxu6U6peWr7DgyIVj7zQ/JpxQW7SACWy8wrWmoBgDtyfpbfY4891EsvvaQOOugg9f73v1+32frgBz+onnzySbXjjjuGc5RwoqWUBCNPP/rwiK/J51eec2osx0NrrfHJoFFfyoSpHBkfbYO26WP2ypA0oYAm4XE/18UQroutuB6CMauuQpna8gvB8mlQeYsHg+dtkE8VCJUjfsgl8Mi1DRcAwFw5PaL39fWpd77znerGG29U5513XnhHBed2g0srreEVIxkD/f3662tXLou8xRa74idWXZZQHb1p5TLZBUZ7jPH5spMzGwRF27D4u016YECVUIGocR/ZioqiYDTWlOmNGiY93sg8tqoyFsOC5lNg0NbTR1tfW9tqUTnizaa5DW3ZnpbKEQBwRU6v8EtLS9W///3v8I4G1rR8yLW3+OqVK1RRadm431+1coVqmDM/0vYbhCMT82EBwIfLWOjwUGzVz3UxhMqRbSgo2obHi20VRfJBH/LCJEqK9eDztS25tdYK05x6M6tZbOfLvBEhYV97b1oHbYgPlSMIYu4m3QcAwB05P6J/9KMfVbfeequ67LLLwjkihC6IUODsO/+T409MVfOW/HLc7/50rVI/zfE8rzlub1UI+oJPXjniOsKRiZEfbiM7PbEVi+DbEJptw11kG7lZkI0E08LKpHBkFuFI4Hwaxp7R2tVHOBIzwhEUGnjQfQAA3JLzymA6nVa33Xab+tOf/qT23XdfVVVVNeL7V111VZDHhxD0EQpoDBWeWGWZ+y/4qjy4jIVgEXwbrottCIq24XaxDVkAgiaVI8VFRUbcz6QPvQ+bRqLm0zD2DIayxy+fFln5tOKCuxvnaKkFAG7J+VX+M888o97whjfof8tg9uFoIeBPS5RvHLtnzj/T2daqrr1wiXr60YeGvrZ4v4PVGRdfpapq61TUaKs1scqk+4sAVR5cRiBoZCPbDPI0MoSXgNswTyAYshgpAcm61virR2ipFQ6fhrH7OGPFpXCkjMoRb553KkpLVHffxC3Eq2mpBQBOyflR/YEHHgjnSBBZ+XoQO7TymfdRNnWq+r9vf18PX1+3eoWaNXdB5EPYh2N47MQqPSgVrki6fxkBhGdQ8TwSVyCQaGpRRem06mucNulpSzduVoOJhEpPrQ/9uNgoFKzZ9WaEI7MJR0LhW0utzFB25hLF/3wli+C5vCdmILs/JPiYNByhkhAAnMKjumdkEGDcJBCJMxTJYKjw5G8cJATrTU/84tBmsjMI4+N9+zZFNA0aIos6wGiJCMMRCUYWfOkSVdzXp5ZfceGEAYkEIwu/eLEaKC1VK755QegBSSlVI8611qKlVrjzN3x8L9bWw1D2uCVzCEckSKEi0B/yeL+pvXfS0wAA3MEWCM8QCJgVFJnO9coKBulNTBaksBVXBcZCTrRNoji6l5RSMSLBSHLdRh18SAAyUTAip5PTy8+FLcHu4lBaa8WJllrh8bFyRLR5erlNksuAdapG/JJN8EFbLQBwC8/0nmEhZxvCkcmVO9xfV97olLALbEJcPduwY3AbWoFsw1WR30JToaRSRCpGUrMaxw1IhgcjcrrJKkxsvB58Mauu3Ovf76ruVL+38/98DYWsDUd4XPfKZOGIvA72of00APiEZ3rPxNmWwDT0ip9cmcMv/MpKefibDJUj25RwXQzhqtiGdmvxDaudKCCJKxgR7DAO3sy6ra214mqpVVNO+6Mw+BwQ+HzZbXzOIhzxS9Uk4YgEI2yaAgC38EzvGeKAYbgyjFvsipLMU4E5bXLG89rKZerxh/+s1q5cFutxUGW0DdfENkXx30WMUR5D4DxWQFLx7IuxBSNxXQ8+tNZqrCmL5XfPrqOlVpiDyX3V7vFlN0UugYfL74ewvcpkyYRV0pOFJwAA+/DI7hkG6W7DNeH3mwF2gU2upKTwZfDedH9eP9fR2qKuW3qWevrRh4a+tni/g9UZF1+lqmrrIg/DSgO4LlzBbrltqK7apiIZz0vKTECSCUR2/PxS/fU4ghFRGdP14LrZ9RVqfVtP5L93Vj0ttcLi89yN3vSA6unrZ/ZdjHJ5XciGKr9IMFKVLFEdvWPPKasq4/YAAK7hHZxnWMjZhqsiu92arqL1STSBwNl3/if/Hz7o82reQZ8f+rRZKXXRH1fldVbXHLd3/sfBkOUReB7ZhnZr21TEuMgnAcjqL586FIwI+TzqYCTu68FlMpRdFqyi3ORTU55QtbTUCk17z9gLjz5VzhCO2LEBjFa8/qmYIBxhEwQAuIdnes+wqLUNveL9rq5wOfgJSqkBbbVMkaBaYgjXxTbcRczYSSkzRuZefv2Ir8nno4e0R4EdpeG9HplWnYz0d86spaVWWCTkGm/h0RcdnodDVs0c4T2Dd6omCEB4ngcA9xB7e4ZsZJsEbXK8DhCSCf7+kykNIBz7xrF75vwzT/79QXX5F08e9/tfvuJmtc+Bh6oo8cZ4G+avmDWXxxTSdkTuJ6n+gUh/7+jh61IxIsFIZgZJ1K216EUe7vyPTe290f0+WmqFpjPVrwY8b/XrezgUt7IcqnaoHPHPRAEIlSMA4B6e6T3DAt827H72O0BiUTOaxwtZMM31Y+78BWqwr3fcj3nzF+R8noWGhMzZ2IbHzq2kxQ9B0UjV5YlYgxEJQrpfv8t2Q9qjqiCRxwra5IRnZl10YYX8HesqaKkVFqomuA5sqhzhcd0/E81Ro30mALiH1UHPyAIfrbXcr4oIisttlVwOfoKcOSILwFGbM3+R2ueAQ1Vxycg3H/K5fH32/EWRHg+PFSMxf2WrUoKR7dREOJ9hrGAkUyGSGdIedUDCfIpwyQLllMpoWmvNqts64wTh6EoRDHSl+uM+BOV7OJLtfTyXIAVuqBwnAJH3BC63nQYAX/HI7iGe0Lfiepicy7uiWfCenLxpTMYUIp112fVq8X4HjfiafC5fjxqPFduHZuAxZCy1EVWOTBSMZMQRkMgAb7hRPTKzlpZaYSIYUKqrr18NDPjdWiz+17jFgZ0O7g1kz+XrAAC78S7OQ1IK2tPHm5LyAlvt+MDl9jkuBz9BBwO96WhnCIjq2nq19IYfq7Url6l1q1eoWXMXRF4xksGb4pG4Prai+mx7UbUhGkwk1EBp6bjByOiARIIROb38XJjqK6kcCduM2nL1/Lq20NtuNlSXhfo7fEc4snUofU+6n/kFMSovlde4E98Wy3OoMIE7pFpIum2Mno1ESy0AcBOvxjxE39StypMs8GXbhs3FoZkuBz9Bknkd7Sq+9hcSiMQVimQwiHMkKia2oqJoe7URhSPpqfVqxTcvUEXp9KTD1jMBiQQj8nNhYkZF+OQ6lsWp7hA3+UyvKWMDRcjC/PvZpDtFOBL3e+LW7r7ABrfDHRKIyXNN56gWgIQjAOAm3tl7qJJyUI0XN36HCCx8ZIc+y1wHoxEKbMXtYuzgLKrWUhJ0TBaMZMjpwg5GZCMBM0eiqx4J9/ypGgkbFexb9cRQmYvcNgzyftFfY90+aKsFAG7inb2HqsrYoSS7QarYqeV1iODq5QoaC+Fbq2ewDbeJrZIl3C7GEtXAbNNISy2ptkT4GkMOLxprmDcStjjadZooxfUQe1utIE4DN431t6ctNwC4iWd7D1UTjqiqZAmLGFlyta8+4Uh2CAaoEBirOoD7Dwsm45la5Wc44msoFIdp1WWhzQCQ6h92Boerr39Az9sA4Ujcslnoph21v8b629OWGwDcxKO7h6JqeWGyGlpf5NQqxEUycBWTIxhg5shY2DlHcDgeX8ORhmo/L3dcAe3UkMIomTeC8MMRbMV1Ea9sglDaavlrrHCE134A4CZWfDx9ovf9hZ60v4DfIQIb37NDMMAbobGwk5LKkYk2H/gYqvoaCrnWWquRcCR06QGqRjK4Lsx/LcPrYH+N9VqG134A4CYe3T1VV+F3OFDv+eXPhYvZiLQECqslh2sIBqieGQtvDqW1AveN8TRU+7XALK2YeKyMvrVW0OR1ASFX+AYIBIb0c10Y/1rG9w2FPhsdjMlzRLKE178A4CIe3T3l+5u/OipHvK4cSVA2kjWCARm8zXUwGpUjtBaLeuHaZL5dXlM2uUh7rSBJq64Ej/ehIxDYZoDZK7GSUHuy9sGEI/4avelB3g+wuQ4A3MTwCU/5tqtzuNoKdnjmwsV1AlfnqIQh6Xk4Im+EignTtlPpedWELMr6ft+YiG9zG6bV+L3hJA7yuCwbfTa09QR2nvwdAf+8bddGNVFERWDqr9EbxGixBgDuIhzxeMedtBbycffWtCq/Fm0KVeJg5UjQu01dJteVr48VgjdCY6tM+v3yIZshrj6rLkvo20hXKq1cJ7tIqRyJx7TqYMORBl4fAt6pKvP79Qyyrxwv4/0jADiLR3jPd9z5iJ2BuXGxBZUs9iN7PreVSpawCD4W38OBStpsTMqX6hFpxUTgHo8gwwypKPX1dXHUeA22DVcFYPZ6yfDndyqGAcBdPMJ7bEZtufKNvPllh2duEiXuvXNzMfAJk89vBqgcGVuV5+EIO00nN6PWj+daXy6nier+WwUdhPrK4M4LE+N6dnuuH+DqBjGf3w8BgOt4hPdYoye7OodrqGKHZ65cfONG/+Dc+PxmwOeqmcnuQz4PZSccmZxsRPBhvlOjhxtNjKqCrgym2oOqkei4+LoyXwRFgNlKh70HYg0BANzFI7zHaspLdV9wn7CIkTsXqyx4M1rYQEKf8EZofL49fwxXVeZvMJTLfaeh2u0F54rSEl29gPhMDeg2RjgSHZ83XIzGdQGYrXRYBwXeEwCAu3iE99zMOr/CglmeXd6gd8y4gmqA3Pg8d4OFi/H5HI7UlLEgno2Zjm9I8O01lImoHLFzgwqLjFuVJ/x9fQXYYPhj1fCgBADgFl6Zem5WXYXyRW1FKa1Q8uDiC8HShHuXKUw+X18EaeOrLk942xLG94H02XL9NQbhSPzqAwhHJOgtY5E6Uj5XpA7HXDPAnnCEtswA4C4e4T03pbJUt4XwwWzHF2nC4uLiMDsWc+Pz9UXlyPhqPA1HfL3c+ZAQKYjFa1OfG6dV+Te7zcTH6ELvk67eRk1WmeRxVFQStAPWtJcupS0zADiLVR/PFRUVqdn1foQGc6b4cTmD5uLCuIuBT5h8vr4SDlZOBaW23M/WUoQjuZntaHXFjLpyPRAc8ZtSYLhBS63oMbdpK0IiwJ73AVSOAIC7eISHmuNBOCIttXzuj18IF3fO084hNy4GZNny+bJPpry0xMvgrMbTUChfsxx9jUE1qjvhiFRRI1q8Jt8ajMj8FQB2VI5wfwUAd/m3qoHtTKlKOr9zaQdHF2eiWhwuLnLrxaCLgU+YfK6e8HHxPxd1Ff4tKvp4mQtdBHXtOpPnxcYaWmqZor6AcENe3/haBRf3piXfufa4CLiopHjYzBHCEQBwFqs+0HZwvOUULbUK41qlBYNXc+Nz9YTPwVA2fFzgYkErd669xphFSy2jSLiR7yYOeQzjbxk9Hke5DgAblAx7bqFyBADc5e+KF7wJDxqqypyvjImifY5LXAt7wlbqcUDALrGJ+ba4I88lVJ7lzrXZZi6/ZrKRhBv5PhbRUiu+TRe+t9YqpOIJQDRKhr0HIhwBAHfxDh9Du+5c3QHMIkbhXApHJBhhl2huEsNKyn1bvClyrKVc0Hxb3PHt8gYZKslGBVcqD6dXu3FZXJLvfbO+gmHscZla5fd1X+isHAARV47wngAAnOXnihe8mcshC5uz68vjPgzrlZe681BR5lDQExVfK0eoGpmc7Pz1qe0au8zzN3dqhTMtwghNzZNvyFHHfTo2rgSm+ZANaVQhAuYbvj+MzXUA4C5elWHIDlMqlWtkYCrzJQpX4VCg4NJliYosBPpYSu7Ton8htw2fqinq2embt1l1FXnPhTDJ3KnuvVZyQT4hh9weazxv7RSnaTX+Pp5O8zgYAmySed3i4/sgAPAJKz8YUpEscW4Xl2tDYOO8bbii0qHLEiUfW2sxjD07vrRGkSCINij5k13SMsjc9t3evs3ZsYWEHLmGbwxjj7/dXk25n+HUjFq33m8Brso8r7iwuQMAMD7/VrvgzXwO2eExs9buhRhTuDTQnnAkPz621mKXWHZ8CUdkUZzbRGHmWV51Yfvxu0xCjlxn59UTdMWusca/1+nyPNLA3CLACpk5I7z8AwC3EY5gBNnV6Uov7Rm15SpBW5xAuBQoVDgU9ETJx/sSbbWyI9UUrjxvTKTBkxAoTNNryqxtbSi7RqlGNVuuVT1UAcVvpuXVZPkGQgTtgB2K/vtWwIfXuQDgM1Z+MEJ5aYma5sgC0GwHB8zHebtw5Y1cNeFIXnwcTu7jZc43RPJhkXEaO30LJosL8xoqrd08wgwzs+X6OJRrpQnCCZ3LPBtMbnt7QcAnmXcCvCMAALf59WoUWZnlQKggC/kzaljIClKVI0NLK8tY3MqHj0GBj3NW8uVDVYUv7cPCZmtrKltDHZ/U5jC/QoI6H0Jd08nfYVad/e87cqlAk8p2AHbIVIwwcwQA3MbKD5zc0SQl6z62AQp72KkLFTC0SsqPj/cnBrJnr9HxMLq+MqkHiiOYGVa2zRmoSibUdCqHjJdLJUh1mTsVsbbzqV2dtBHjuQSwsHKEpwsAcBqvzjDmAnJDld2LAC4EPKapzmFHpqlcCHji4uNAdh8vcyFVFWHtqks0tajSjZuzOq2cTk4fNBbGg7Vgml1VGPMbKuk3bgHZ/FCVZevM2nKqRkx6/qjypOWpT0EQ4ILMa1teAgCA2whHMKaZdfYuBMkCBiXrwat2IFhwIeCJi48tpny8zIVUFoXRdkqCjgVfukQt/OLFkwYk8n05nZw+6IBkWg0ttYI0s7Zcb8SwZWFkrqWtwHyUbfUI80bMet2+w1T3QwOZrTLDsqo5AFsVMXUEAJzGyg/GZHO4IL3vKVkPXo0DuyzZKZo/H6soSnkcib21VlE6rYr7+lRy3cYJA5JMMCKnk9PLzwVFWu9Ms7ya0sTF0AUNVcqWSlRbghxI6EHliI3mT61yvjpLQtZiWrkBVnH8YQkA8F9so8a4C+FVyYTqTAW3wBQVm4Md01tSyQ7agcFBZasaKkfy5uOsllIWMXLSWFuunlvXFuh59jVOU8uvuHAo+JD/y+fy9bGCkdSsxu2+H0RLLRa0wmlV9eKGdjVo+HPKwml2hDjYateZtfoDdqlIluiAfUNbj3LVfEsCYQBj4GUgADjNv9UuZK2x1s6dsrYet+lkcdD2tlS00TC7isKE2RK+B0KFqKsoVRUh7LDPBCQSfIyuIAk7GMmEPgieVGPMNnw+mDxnNDBvBoiEy0Hk9JoyJ9rTAgAAuIiVH4yr0cK+uLLYQquE8NRbHC7Im1IWu81tq2XKbIkRv4e2WsZU7o0VkFQ8+2LowUhmPgbCscDwxdCF7PQGItPocICwaFp13IcAoAAUjgCA21j5wbgaqpPW9f+VnVkId2e4rWw+dhMkQw6WTJgtsd3v8nDOSqFmhlgJMDog2fHzS0MPRnQ1TJJ5E2GZVl1mbEWfhOk7THF/SDRgCnnP4WL1SFUyoWZQ1Q5YybKlEABAnghHMOHCwJRKMxctJuoNj/DUVyatbZ8U1LH7KhlyFcVErZMyomihNHyRJuxAyNXF7kRxeNeb/L1Xf/nUEV+Tz8O6HcyqY3E8bIsMXQydN7VSJXgMACIfWu5ale+i6e4PmwcAALCZW68+EbiGqjLrFuYQHtlFLUPZbWyfZFvQZ5oogoK4Z0sMlywpYjEjDyXFRaHukJXbwdzLrx/xNfk827A1V7PqaakVth2mVBoZRLq4gx0wnQQjCxxqZyePbRK0AgAAwFzmvRuFUaZV27PbvjKZoP1JBAufhbaniqN9kixyUzlSGNlBLX//sMU5WyLKShmXzaoPp9pidED26tUXTVhpVCjpfc8Mq/DJ48q8BrMWD2XOTJWjsw8AGyotCt2IY9JcJSrQAAAAzMarNUxoSpU9C8pTLTpWmxV6PcfRPkkGyUexsO+68kQ04WMcsyXiuqwumlFTFvj9bazHhO7X7zLpY0khZocU8mDsKg2TKrUWTWd4MhCX8tIS3V7LdvI8KEEPAAAAzEY4gknL200dljpaA+GINSFU1O2TCM6CUVYa3VNG1LMl4rysrpFdsrLzPigTPSZkE7bmi3Ak2srPWXVmtDCTaqHpNbToBOL0usZqowLTfMyfWqXK2GgBAABgPFZ/MKmpBbQjinLwtk1VLjZrCKjVWpTtk4I6Zt/Jbs6oRD1bIs7L6qKggoVswtIwApKa8kTBLQRh54wPU44D8Jm0NZxj8cwnaQsmAQ8AN9ge1gIAJkY4gklNyTMciXLwtpSu15bTHzwKsgsuqGqiKNonyYvZhip2AQehIqLAIOrZEnFeVlfNqC3XlYeFGkwk1EBp6aSPCcMfS+T08nOFmFNvf0sX20yrLos9kJLhyS608wFc8LrGGmUreRxhDiIAAIAdYg9Hrr/+erVgwQJVXl6u9t9/f/Xoo49OePqWlhZ16qmnqlmzZqmysjK18847q9///veRHa+P6qtKjR+8XV+RZEdHhKZXl1nTPkkW2xiuHYwo3ujHMVtiLCxqFEYC65kBtElKT61XK755QVZhaSYgkdPLzxVizhRaasVh0bR4d1rLYHjmUwFmkNdvs+rseyyW9yM7UTUCAABgjVhXDH/2s5+pJUuWqKVLl6onnnhCLV68WB155JFq48aNY54+lUqpt7/97WrFihXqzjvvVC+++KK6+eab1Zw5cyI/dp/UlCVUorjY6MHb9ZW0P4lSkP3Yw26fFGSQ47vKkAODuGZLjKWylEq0Qu0QUMAgQUe2zwtyukKDkfrKpG7pguhJKFUWU5gtC5pxhzMARtplRo2Vz31VPIcATihSbJgAAB/EGo5cddVV6uSTT1Ynnnii2n333dWNN96oKisr1W233Tbm6eXrTU1N6te//rV6y1veoitODj30UB2qINwFg3zDh6gGbxOORKuhKqn7KdvQPqmxlnDEhsAgrtkS46FyJJhg0sbZLXOpGomNVG3Mb4hn5ocMhOd+D5ilrrJUzawtt+o9084WBjoAAAA+iy0ckSqQxx9/XB1xxBHbDqa4WH/+yCOPjPkzd999tzrggAN0W60ZM2aoPfbYQ339619X/f394/6e3t5e1dbWNuIDuSukD3gUg7dlpy+ikygpLnjIeRTtk6TiaSq3jcBUlYW3cBjXbImxyM51WrEFs0g0J6DB7JEeM+FIrBY0VMXSJpNB7ICZdplpT9ggz3lUHgIAANglttWfzZs361BDQo7h5PP169eP+TPLli3T7bTk52TOyAUXXKCuvPJK9dWvfnXc33PppZequrq6oY+5c+cGfll8UGhlRpiDt2WAKm9E4hm4bHr7JKkaKaZ/fKChWFiVAHHNlhgL7TCCY9tw6xk1ZaosQfVAnKR6Q6o4olRbXqoHwgMwj2yAKuQ1Z7RVI7TmA1zEu0kAcJtVW2MHBgZUY2Ojuummm9S+++6rPvzhD6vzzjtPt+Maz7nnnqtaW1uHPlavXh3pMbsiiMqMsAZvF1LVgvzl+0Y1yvZJNrVisGkGUViini0xHsLW4Mjjs02P0TKQG/GLuoqDqhHAbLtaUD0iVSM15fY83wGYXAyFrAAAn8KRadOmqZKSErVhw4YRX5fPZ86cOebPzJo1S+2888765zJ22203XWkibbrGUlZWpmpra0d8IHdVyRJVWlJs5OBt6UeM6MkCck15wtj2SbKDj3kjwfPhjb8PlzFK8yypHpF2ajNqCFRNIFUctRGFavLaRgYoAzCXDdUjVI0A7ikpKlJ7zqlTOzZy/wYAl8UWjiSTSV39cf/994+oDJHPZa7IWGQI+yuvvKJPl/HSSy/p0ETODyEPZS9goSLMwdvMG4nPrLoKY9snydB42uMEL59AzDa1HlzGKMkMj2ILtt7tMKWSNnwGWRjRYHYJ76RlIACz7WLwoHMJWNlYAbhHXhcuml5t3Qw9AEBuYn03uGTJEnXzzTer22+/XT3//PPqlFNOUZ2dnerEE0/U3z/hhBN0W6wM+X5TU5M688wzdSjyu9/9Tg9klwHtCF++FRphD94uJLRBYWbnEY5E1T4p6p71vrCpRVK+otqx7gsJKW24P9o2H8V1sthYaMVqNhbQUguwwpSqpGo0tLpvJ4ODGwAAABgcjsjMkCuuuEJdeOGFau+991ZPPfWUuueee4aGtK9atUqtW7du6PQyTP3ee+9V//rXv9Ree+2lzjjjDB2UnHPOOTFeCn/kU6ER9uBtGcbO8OR4A7OqpJnX/2x2+IQWHEglmatk4HxYQ+d9ZnprLdtmo/ggEUG7q+nVZcwYAiyyi4GzR2RHeS1VIwAAANYqGhwcHFQeaWtrU3V1dXo4O/NHctOVSqv7nhs5I6bQwdu5nG4ssoPsgB0bcrocCNbz69rUSxvalWn96t/yuuxuQ8jdAy9uVG3dfcpFM2vL1f6LeEwJmrzUkOeP7r5+ZaK9dqhnKLeB2nr61AMvbAzt/N+4YCqtMgDL/P2VzWpTR68yxWG7NBKuAwAQMdZ2ESSaLCNrlclETjMcohi8PaWKNyNxM7FCw8RjcskUh+f8SNsOBE+qjUxtW1VSXMQCuaFkN/bUkO6Tut2b4QOeAWxvZ4OqR2T2HsEIAACA3eglgJxMqSxV69v6cxq8XZROZz14W4KRXOZLTHV4kdYW8qZQFrBkh68pi7Cz61nwCvtxYOUW5aT6PGcrIbvWWqZVmWUWt5IJ9oqYav7UKtXUmQrl9iiDVgHYRaqDG6rK1JbO+KtHdp5RHfchAAAAoECsBiAnDdVJowZv5zMHBcGbO9WcXdczaspyqnBC7sLayW1CsEbgGh6ZDyUzHkwzv8HMihZsJWF3GIPZ5/F3B6xlQighrX15HwIAAGA/whFY205HBkOz29cMc+rNWWTawdDWPS6pKS91MoCqryjVQ6ARHtMWpGUYt+xChrnkPhl0q0T5mzOIHbBXY2157O2sdjIgoAEAAEDhWAVCzuFIcZEZbSjY4W2OimSJml4T/wJjsqRYD9RG+KblWEXmYmUc8mxhZVAAJa2VYL6g/05zp/B3B2y304yaWCtoCdYBAADcYM4KBawg/blNaakzzYDFeJi1yDhnSoUerozwmRCGBc3Fy2QauX/uYMjCtMlD4jGSvO6oKQ+m0iNRLJUohOiA7WbXlauqZDwVYK9rpGoEAADAFYQjyJkpO6UaDAlpsG1HeBh94W0LaHzhWpAgi/Yy4BX+tNaS+UTlpe61h3NVUNUeM+vKaZ8HOEAC7h1jCCmkJR9VygAAAO7g3SGsbD1TW17KopaRO8IrYp1Bw2DM6FQmE/p+6FLoS9VRNOoMua/Ob6iK+xCQY2VgEOZOje95CkCw5k6JvlXjjtOrdTADAAAANxCOIK9ZH9KWIk6u7Vp3xfyp8S02zqdqJHKNte7cD2ewCzRScd9fyxIlaoZDt19fAtlCq7vk7z7dkOpXAIWTKrAog24JYmjHCAAA4BbCEeQ1dyTuYcyNhCNGqquMZ0e4SXMMfOJSoMBCuV/zgaR6gJ2//lWPzKnn7w64ZtH0qsju1wumVVFlCgAA4BjCEeSlMcZF0eKiItXAzk9jLYhhnsDs+gqVTPBwFsfcnzIHrncJ9GRXOqIj84lkTlFcmE9kp1l15QUtgjKIHXCPtNmdE8F9Wx57FtCOEQAAwDn2r2rBu13WzAYwm+zMjbrtWtwtenwlCwUzY1zgDnLBFf4EFFOrkqrGoXk5vi2CTqtK5v2z8rcH4J4oQgt5rVCRZN4hAACAawhHkP8w5op4FpdmspBpfP/nKAezy1BwKoni48JObKk8QvSkPWMcFTtzacFntXxfAxRadQLAXPI6MOz3JVSNAAAAuIlwBHmbURPPouhMh+YcuCrKN5DS/xnxkeHGNrfWqqsoVdVltNSKgyxUy+yPKEnVIWGY3eTvV1OeyPmDvzvgtjBfe8rrhOnMOwQAAHASK0IoaMf4yxvbI58NQEm7HYPZp1QmVXNXKoJB7Cx4xb3ALYuOyzd3Khtx+4nXDlMq1Yvro3sekeoB5hPZTdpjvW3XGXEfBgADn8+fXduq+gcGAz/v+VSNAAAAOIsVAhQWVJRGG1QwG8AeUVSPyMKqDHZGvOTvYKs59fYeuwtkN25DVXS7cWmpBQBukteDMvcuaMUxVDkCAAAgOqwqoiCzIh7GTDhijzlTKlQy5OBiQQMLnSaQIcc2tqaSlmBUovlTvVOWKKEtCgA4bN7UylDmHMnzBwAAANxEOAJrhjHL4O2a8niGwCPflleVoc6KkOolmGFuCAsSYbPxmF0kbdlkZ24UIQwDuQHA7cHsVclgN2tQcQgAAOA2whEUvGNc+n9HgWGq9pk/rdKJoe9wb/FA2m/wmGIGmQEyozb8oJ35MgDgviA3PpQlilUjFYcAAABOs68PCowiu3Clv++rmzqcqlJBcNU+sgDd1t0X6PnKLnNp2wVzSHuqxppytbG9R9lAHrekuglmkPvzutbu0M5f2r5RaQYAfjyfvLC+LbjKRl4rAAAAOI1wBIG8cQg7HJEWSrTUstObFkyN+xAQkQXTKq0JR6g8MsvM2nKVKC5W6YGBUM6fMBUA/JAJw1u6UgWfVxgD3gEAAGAW2mohkNZaVQH39x2NdiiA+WbUlEfWZq8QsmhSV0nYahKp4plZF17rElqoAYA/ggg1KkpL9HscAAAAuI1wBFYsPLGwBZhPWk/MbzB/9shCqkaMFNbjvLT3kw8AgB+CaMUrz0nSPhgAAABuo60WAmtZ8vLG9lDOu6GqTFWGXJkCIBjzp1aplzZ0qMHBQWWiZEkxLZYMJTNrSkuKVV9/sK21CNcBwC/yvmHH6dWqp68/7/OYO8X8zR4AAAAoHCvOCGwmiOzMbesJdvC2YCETsGswu8yPCHO4diHmTq1kELuh5O8yo7ZMrWkO9rYzK4AdxAAAu+wxpy7uQwAAAIAFaKsFo+eCSDl7EKXxAKKzcJq5basWGHxsUGpmXUXgg3lpqQUAAAAAAMZCOAKjW5dMry5TZQnzBzwD2GZ6TZmRC9Izasv1YjnMNaOmTBUH2ON9VsBhCwAAAAAAcAfhCAJTVZZQU6uSxlejAPCzemSRgceEkRIlxTpcC8rMOioPAQAAAADA2AhHEK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\"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"# Inspect full SVI posterior shape per subject (not just posterior means)\\n\",\n \"z_samples = np.array(svi_samples[\\\"z\\\"])\\n\",\n \"\\n\",\n \"reward_prob_samples = 0.5 + 0.5 / (1.0 + np.exp(-z_samples[..., 0])) # [draws, agents]\\n\",\n \"true_reward_prob = np.array(0.5 + 0.5 * nn.sigmoid(ground_truth_z[:, 0]))\\n\",\n \"posterior_mean = reward_prob_samples.mean(axis=0)\\n\",\n \"\\n\",\n \"subject_ids = np.arange(num_agents)\\n\",\n \"sort_idx = np.argsort(true_reward_prob)\\n\",\n \"subject_ids_sorted = subject_ids[sort_idx]\\n\",\n \"true_reward_prob_sorted = true_reward_prob[sort_idx]\\n\",\n \"posterior_mean_sorted = posterior_mean[sort_idx]\\n\",\n \"reward_prob_samples_sorted = reward_prob_samples[:, sort_idx]\\n\",\n \"\\n\",\n \"plot_positions = np.arange(num_agents)\\n\",\n \"\\n\",\n \"fig, axes = plt.subplots(2, 1, figsize=(16, 10), constrained_layout=True)\\n\",\n \"\\n\",\n \"# 1) Violin plot: per-subject posterior distributions + true values (sorted by true reward prob)\\n\",\n \"parts = axes[0].violinplot(\\n\",\n \" [reward_prob_samples_sorted[:, i] for i in range(num_agents)],\\n\",\n \" positions=plot_positions,\\n\",\n \" showmeans=False,\\n\",\n \" showmedians=True,\\n\",\n \" showextrema=False,\\n\",\n \")\\n\",\n \"for pc in parts['bodies']:\\n\",\n \" pc.set_alpha(0.35)\\n\",\n \"\\n\",\n \"axes[0].scatter(plot_positions, true_reward_prob_sorted, color='crimson', marker='x', s=80, label='true reward prob')\\n\",\n \"axes[0].scatter(plot_positions, posterior_mean_sorted, color='black', s=20, label='posterior mean')\\n\",\n \"axes[0].set_ylabel('reward probability')\\n\",\n \"axes[0].set_xlabel('subject id (sorted by true reward probability)')\\n\",\n \"axes[0].set_ylim(0.5, 1.0)\\n\",\n \"axes[0].set_xticks(plot_positions)\\n\",\n \"axes[0].set_xticklabels(subject_ids_sorted)\\n\",\n \"axes[0].set_title('SVI posterior distribution per subject (violin, sorted)')\\n\",\n \"axes[0].legend(loc='upper left')\\n\",\n \"\\n\",\n \"# 2) Density heatmap: posterior mass over probability bins by subject (same sorted order)\\n\",\n \"bins = np.linspace(0.0, 1.0, 60)\\n\",\n \"density = np.stack([\\n\",\n \" np.histogram(reward_prob_samples_sorted[:, i], bins=bins, density=True)[0]\\n\",\n \" for i in range(num_agents)\\n\",\n \"], axis=1) # [num_bins-1, num_agents]\\n\",\n \"\\n\",\n \"im = axes[1].imshow(\\n\",\n \" density,\\n\",\n \" aspect='auto',\\n\",\n \" origin='lower',\\n\",\n \" extent=[-0.5, num_agents - 0.5, bins[0], bins[-1]],\\n\",\n \" cmap='viridis',\\n\",\n \")\\n\",\n \"axes[1].plot(plot_positions, true_reward_prob_sorted, color='crimson', linestyle='--', marker='x', label='true reward prob')\\n\",\n \"axes[1].set_ylabel('reward probability')\\n\",\n \"axes[1].set_xlabel('subject id (sorted by true reward probability)')\\n\",\n \"axes[1].set_ylim(0.5, 1.0)\\n\",\n \"axes[1].set_xticks(plot_positions)\\n\",\n \"axes[1].set_xticklabels(subject_ids_sorted)\\n\",\n \"axes[1].set_title('SVI posterior density by subject (sorted)')\\n\",\n \"axes[1].legend(loc='upper left')\\n\",\n \"fig.colorbar(im, ax=axes[1], label='density')\\n\",\n \"\\n\",\n \"plt.show()\\n\",\n \"\\n\",\n \"\\n\"\n ]\n }\n ],\n \"metadata\": {},\n \"nbformat\": 4,\n \"nbformat_minor\": 5\n}\n" }, { "path": "examples/model_fitting/tmaze_recoverability.py", "content": "\"\"\"Fast recoverability diagnostics for pybefit + pymdp TMaze fitting.\n\nThis module provides a lightweight alternative to running the full\n`fitting_with_pybefit.ipynb` notebook when evaluating identifiability.\nIt focuses on synthetic recovery sweeps with fixed per-agent latent grids,\nthen reports parameter correlation and a simple bimodality diagnostic.\n\"\"\"\n\nfrom __future__ import annotations\n\nimport argparse\nimport json\nfrom dataclasses import asdict, dataclass\nfrom pathlib import Path\nfrom typing import Any\n\nimport jax.numpy as jnp\nimport jax.tree_util as jtu\nimport matplotlib.pyplot as plt\nimport numpy as np\nfrom jax import lax, nn\nfrom jax import random as jr\nfrom numpyro.infer import Predictive\n\nfrom pybefit.inference import (\n NumpyroGuide,\n NumpyroModel,\n Normal,\n NormalPosterior,\n default_dict_numpyro_svi,\n run_svi,\n)\nfrom pybefit.inference.numpyro.likelihoods import pymdp_likelihood as likelihood\n\nfrom pymdp.agent import Agent\nfrom pymdp.envs import TMaze\n\n\n@dataclass(frozen=True)\nclass RecoverabilityConfig:\n \"\"\"Configuration for synthetic TMaze recoverability diagnostics.\"\"\"\n\n parameterization: str = \"three_param\"\n seed: int = 0\n num_agents: int = 9\n num_blocks: int = 80\n num_trials: int = 5\n svi_steps: int = 300\n num_particles: int = 5\n num_samples: int = 80\n reward_probability: float = 0.98\n punishment_probability: float = 0.0\n cue_validity: float = 1.0\n dependent_outcomes: bool = True\n save_plot: str | None = None\n save_json: str | None = None\n\n\ndef _assert_parameterization(parameterization: str) -> None:\n valid = {\"three_param\", \"reward_only\"}\n if parameterization not in valid:\n raise ValueError(f\"parameterization must be one of {sorted(valid)}, got {parameterization!r}\")\n\n\ndef _build_task(cfg: RecoverabilityConfig) -> TMaze:\n return TMaze(\n reward_probability=cfg.reward_probability,\n punishment_probability=cfg.punishment_probability,\n cue_validity=cfg.cue_validity,\n reward_condition=None,\n dependent_outcomes=cfg.dependent_outcomes,\n )\n\n\ndef _latent_grid(cfg: RecoverabilityConfig, num_params: int) -> jnp.ndarray:\n \"\"\"Construct deterministic per-agent latent values for reproducible recovery checks.\"\"\"\n\n base = jnp.linspace(-2.5, 2.5, cfg.num_agents)\n if num_params == 1:\n return base[:, None]\n\n key = jr.PRNGKey(cfg.seed + 13)\n key_1, key_2 = jr.split(key)\n z_1 = 0.8 * jr.normal(key_1, (cfg.num_agents,))\n z_2 = 0.8 * jr.normal(key_2, (cfg.num_agents,))\n return jnp.stack([base, z_1, z_2], axis=-1)\n\n\ndef _build_three_param_transform(task: TMaze):\n \"\"\"Notebook-aligned transform with free reward probability, lambda, and initial reward-state prior.\"\"\"\n\n def transform(z: jnp.ndarray) -> Agent:\n num_agents, _ = z.shape\n reward_prob = nn.sigmoid(z[..., 0])\n lam = nn.softplus(z[..., 1])\n d = nn.sigmoid(z[..., 2])\n\n A = lax.stop_gradient(task.A)\n A = jtu.tree_map(lambda x: jnp.broadcast_to(x, (num_agents,) + x.shape), A)\n B = lax.stop_gradient(task.B)\n B = jtu.tree_map(lambda x: jnp.broadcast_to(x, (num_agents,) + x.shape), B)\n\n one_minus = 1.0 - reward_prob\n reward_left = jnp.stack([reward_prob, one_minus], -1)\n punish_left = jnp.stack([one_minus, reward_prob], -1)\n reward_right = jnp.stack([one_minus, reward_prob], -1)\n punish_right = jnp.stack([reward_prob, one_minus], -1)\n zeros = jnp.zeros_like(reward_left)\n\n side = jnp.broadcast_to(jnp.array([[1.0, 1.0], [0.0, 0.0], [0.0, 0.0]]), (num_agents, 3, 2))\n left_col = jnp.stack([zeros, reward_left, punish_left], axis=-2)\n right_col = jnp.stack([zeros, reward_right, punish_right], axis=-2)\n A[1] = jnp.stack([side, left_col, right_col, side, side], axis=-2)\n\n C = [\n jnp.zeros((num_agents, A[0].shape[1])),\n jnp.expand_dims(lam, -1) * jnp.array([0.0, 1.0, -1.0]),\n jnp.zeros((num_agents, A[2].shape[1])),\n ]\n D = [\n jnp.zeros((num_agents, B[0].shape[1])).at[:, 0].set(1.0),\n jnp.stack([d, 1.0 - d], -1),\n ]\n\n return Agent(\n A,\n B,\n C=C,\n D=D,\n policy_len=2,\n A_dependencies=task.A_dependencies,\n B_dependencies=task.B_dependencies,\n batch_size=num_agents,\n )\n\n return transform\n\n\ndef _build_reward_only_transform(task: TMaze):\n \"\"\"Constrained transform with only reward probability free (lambda and D fixed).\n\n This removes the strongest confounds in the 3-parameter notebook setup and\n provides a cleaner recoverability baseline.\n \"\"\"\n\n def transform(z: jnp.ndarray) -> Agent:\n num_agents, _ = z.shape\n reward_prob = nn.sigmoid(z[..., 0])\n lam = jnp.full((num_agents,), 1.2)\n\n A = lax.stop_gradient(task.A)\n A = jtu.tree_map(lambda x: jnp.broadcast_to(x, (num_agents,) + x.shape), A)\n B = lax.stop_gradient(task.B)\n B = jtu.tree_map(lambda x: jnp.broadcast_to(x, (num_agents,) + x.shape), B)\n\n one_minus = 1.0 - reward_prob\n reward_left = jnp.stack([reward_prob, one_minus], -1)\n punish_left = jnp.stack([one_minus, reward_prob], -1)\n reward_right = jnp.stack([one_minus, reward_prob], -1)\n punish_right = jnp.stack([reward_prob, one_minus], -1)\n zeros = jnp.zeros_like(reward_left)\n\n side = jnp.broadcast_to(jnp.array([[1.0, 1.0], [0.0, 0.0], [0.0, 0.0]]), (num_agents, 3, 2))\n left_col = jnp.stack([zeros, reward_left, punish_left], axis=-2)\n right_col = jnp.stack([zeros, reward_right, punish_right], axis=-2)\n A[1] = jnp.stack([side, left_col, right_col, side, side], axis=-2)\n\n C = [\n jnp.zeros((num_agents, A[0].shape[1])),\n jnp.expand_dims(lam, -1) * jnp.array([0.0, 1.0, -1.0]),\n jnp.zeros((num_agents, A[2].shape[1])),\n ]\n D = [\n jnp.zeros((num_agents, B[0].shape[1])).at[:, 0].set(1.0),\n jnp.full((num_agents, 2), 0.5),\n ]\n\n return Agent(\n A,\n B,\n C=C,\n D=D,\n policy_len=2,\n A_dependencies=task.A_dependencies,\n B_dependencies=task.B_dependencies,\n batch_size=num_agents,\n )\n\n return transform\n\n\ndef _build_model_and_truth(cfg: RecoverabilityConfig) -> tuple[NumpyroModel, jnp.ndarray, int]:\n _assert_parameterization(cfg.parameterization)\n task = _build_task(cfg)\n\n if cfg.parameterization == \"three_param\":\n num_params = 3\n transform = _build_three_param_transform(task)\n else:\n num_params = 1\n transform = _build_reward_only_transform(task)\n\n prior = Normal(num_params, cfg.num_agents, backend=\"numpyro\")\n opts_task = {\n \"task\": task,\n \"num_blocks\": cfg.num_blocks,\n \"num_trials\": cfg.num_trials,\n \"num_agents\": cfg.num_agents,\n }\n model = NumpyroModel(prior, transform, likelihood, opts={\"prior\": {}, \"transform\": {}, \"likelihood\": opts_task})\n z_true = _latent_grid(cfg, num_params)\n return model, z_true, num_params\n\n\ndef _simulate_measurements(model: NumpyroModel, z_true: jnp.ndarray, seed: int) -> dict[str, Any]:\n pred = Predictive(model, posterior_samples={\"z\": z_true[None, ...]}, return_sites=[\"z\", \"outcomes\", \"multiactions\"])\n samples = pred(jr.PRNGKey(seed))\n observations = samples[\"outcomes\"]\n return {\n \"samples\": samples,\n \"measurements\": {\n \"outcomes\": [obs[0] for obs in observations],\n \"multiactions\": samples[\"multiactions\"][0],\n },\n }\n\n\ndef _fit_svi(\n model: NumpyroModel,\n measurements: dict[str, Any],\n num_params: int,\n cfg: RecoverabilityConfig,\n) -> dict[str, Any]:\n posterior = NumpyroGuide(NormalPosterior(num_params, cfg.num_agents, backend=\"numpyro\"))\n opts_svi = default_dict_numpyro_svi | {\n \"seed\": cfg.seed,\n \"iter_steps\": cfg.svi_steps,\n \"elbo_kwargs\": {\"num_particles\": cfg.num_particles, \"max_plate_nesting\": 1},\n \"svi_kwargs\": {\"progress_bar\": False, \"stable_update\": True},\n \"sample_kwargs\": {\"num_samples\": cfg.num_samples},\n }\n svi_samples, _, _ = run_svi(model, posterior, measurements, opts=opts_svi)\n return svi_samples\n\n\ndef _pearson(x: np.ndarray, y: np.ndarray) -> float:\n if np.std(x) < 1e-12 or np.std(y) < 1e-12:\n return float(\"nan\")\n return float(np.corrcoef(x, y)[0, 1])\n\n\ndef _bimodality_score(probabilities: np.ndarray) -> float:\n \"\"\"Simple threshold-bimodality score in [0, 1], higher means more mass near extremes.\"\"\"\n\n low_or_high = np.mean((probabilities < 0.2) | (probabilities > 0.8))\n middle = np.mean((probabilities >= 0.35) & (probabilities <= 0.65))\n score = low_or_high - middle\n return float(np.clip(score, 0.0, 1.0))\n\n\ndef run_recoverability(cfg: RecoverabilityConfig) -> dict[str, Any]:\n \"\"\"Run one synthetic recoverability sweep and return diagnostics.\"\"\"\n\n model, z_true, num_params = _build_model_and_truth(cfg)\n simulation = _simulate_measurements(model, z_true, cfg.seed + 1)\n svi_samples = _fit_svi(model, simulation[\"measurements\"], num_params, cfg)\n\n true_z = np.array(z_true)\n inferred_z = np.array(svi_samples[\"z\"].mean(0))\n latent_corr = [_pearson(true_z[:, idx], inferred_z[:, idx]) for idx in range(num_params)]\n\n true_reward_prob = 1.0 / (1.0 + np.exp(-true_z[:, 0]))\n inferred_reward_prob = 1.0 / (1.0 + np.exp(-inferred_z[:, 0]))\n\n results = {\n \"config\": asdict(cfg),\n \"num_params\": num_params,\n \"corr_latent\": latent_corr,\n \"corr_reward_probability\": _pearson(true_reward_prob, inferred_reward_prob),\n \"bimodality_score_reward_probability\": _bimodality_score(inferred_reward_prob),\n \"true_z\": true_z.tolist(),\n \"inferred_z\": inferred_z.tolist(),\n \"true_reward_probability\": true_reward_prob.tolist(),\n \"inferred_reward_probability\": inferred_reward_prob.tolist(),\n }\n return results\n\n\ndef _save_scatter(results: dict[str, Any], path: Path) -> None:\n true_prob = np.array(results[\"true_reward_probability\"])\n inferred_prob = np.array(results[\"inferred_reward_probability\"])\n\n plt.figure(figsize=(7, 5))\n plt.scatter(true_prob, inferred_prob, label=\"reward probability\")\n lower = float(min(true_prob.min(), inferred_prob.min()))\n upper = float(max(true_prob.max(), inferred_prob.max()))\n plt.plot((lower, upper), (lower, upper), \"k--\", linewidth=1.0)\n plt.xlabel(\"true value\")\n plt.ylabel(\"posterior mean (SVI)\")\n plt.title(\"TMaze Recoverability\")\n plt.legend(loc=\"best\")\n plt.tight_layout()\n path.parent.mkdir(parents=True, exist_ok=True)\n plt.savefig(path, dpi=150)\n plt.close()\n\n\ndef _to_jsonable(results: dict[str, Any]) -> str:\n return json.dumps(results, indent=2, sort_keys=True)\n\n\ndef parse_args() -> argparse.Namespace:\n parser = argparse.ArgumentParser(description=__doc__)\n parser.add_argument(\"--parameterization\", choices=[\"three_param\", \"reward_only\"], default=\"three_param\")\n parser.add_argument(\"--seed\", type=int, default=0)\n parser.add_argument(\"--num-agents\", type=int, default=9)\n parser.add_argument(\"--num-blocks\", type=int, default=80)\n parser.add_argument(\"--num-trials\", type=int, default=5)\n parser.add_argument(\"--svi-steps\", type=int, default=300)\n parser.add_argument(\"--num-particles\", type=int, default=5)\n parser.add_argument(\"--num-samples\", type=int, default=80)\n parser.add_argument(\"--save-plot\", type=str, default=None)\n parser.add_argument(\"--save-json\", type=str, default=None)\n return parser.parse_args()\n\n\ndef main() -> None:\n args = parse_args()\n cfg = RecoverabilityConfig(\n parameterization=args.parameterization,\n seed=args.seed,\n num_agents=args.num_agents,\n num_blocks=args.num_blocks,\n num_trials=args.num_trials,\n svi_steps=args.svi_steps,\n num_particles=args.num_particles,\n num_samples=args.num_samples,\n save_plot=args.save_plot,\n save_json=args.save_json,\n )\n results = run_recoverability(cfg)\n\n print(f\"parameterization={cfg.parameterization}\")\n print(f\"corr_reward_probability={results['corr_reward_probability']:.3f}\")\n print(f\"bimodality_score_reward_probability={results['bimodality_score_reward_probability']:.3f}\")\n for idx, corr in enumerate(results[\"corr_latent\"]):\n print(f\"corr_latent_{idx}={corr:.3f}\")\n\n if cfg.save_plot:\n _save_scatter(results, Path(cfg.save_plot))\n print(f\"saved_plot={cfg.save_plot}\")\n\n if cfg.save_json:\n out_path = Path(cfg.save_json)\n out_path.parent.mkdir(parents=True, exist_ok=True)\n out_path.write_text(_to_jsonable(results))\n print(f\"saved_json={cfg.save_json}\")\n\n\nif __name__ == \"__main__\":\n main()\n" }, { "path": "examples/sparse/sparse_benchmark.ipynb", "content": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"# Sparse Array Benchmarking\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"%load_ext autoreload\\n\",\n \"%autoreload 2\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"import jax.numpy as jnp\\n\",\n \"from jax import tree_util as jtu\\n\",\n \"from jax.experimental import sparse\\n\",\n \"from pymdp.agent import Agent\\n\",\n \"import matplotlib.pyplot as plt\\n\",\n \"import seaborn as sns\\n\",\n \"import time\\n\",\n \"\\n\",\n \"from pymdp.inference import smoothing_ovf\\n\",\n \"import numpy as np\\n\",\n \"\\n\",\n \"import tracemalloc\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"def sizeof(x):\\n\",\n \" return np.prod(x.shape)\\n\",\n \"\\n\",\n \"\\n\",\n \"def sizeof_sparse(x):\\n\",\n \" return np.prod(x.data.shape) + np.prod(x.indices.shape)\\n\",\n \"\\n\",\n \"\\n\",\n \"def get_matrices(n_batch, num_obs, n_states):\\n\",\n \"\\n\",\n \" A_1 = jnp.ones((num_obs[0], n_states[0]))\\n\",\n \" A_1 = A_1.at[-1, :-1].set(0)\\n\",\n \" A_2 = jnp.ones((num_obs[0], n_states[1]))\\n\",\n \" A_2 = A_2.at[-1, 1:].set(0)\\n\",\n \"\\n\",\n \" A_tensor = A_1[..., None] * A_2[:, None]\\n\",\n \" A_tensor /= A_tensor.sum(0)\\n\",\n \"\\n\",\n \" A = [jnp.broadcast_to(A_tensor, (n_batch, *A_tensor.shape))]\\n\",\n \"\\n\",\n \" # create two transition matrices, one for each state factor\\n\",\n \" B_1 = jnp.eye(n_states[0])\\n\",\n \" B_1 = B_1.at[:, 1:].set(B_1[:, :-1])\\n\",\n \" B_1 = B_1.at[:, 0].set(0)\\n\",\n \" B_1 = B_1.at[-1, 0].set(1)\\n\",\n \" B_1 = jnp.broadcast_to(B_1, (n_batch, n_states[0], n_states[0]))\\n\",\n \"\\n\",\n \" B_2 = jnp.eye(n_states[1])\\n\",\n \" B_2 = B_2.at[:, 1:].set(B_2[:, :-1])\\n\",\n \" B_2 = B_2.at[:, 0].set(0)\\n\",\n \" B_2 = B_2.at[-1, 0].set(1)\\n\",\n \" B_2 = jnp.broadcast_to(B_2, (n_batch, n_states[1], n_states[1]))\\n\",\n \"\\n\",\n \" B = [B_1[..., None], B_2[..., None]]\\n\",\n \" C = [jnp.zeros((n_batch, num_obs[0]))] # flat preferences\\n\",\n \" D = [jnp.ones((n_batch, n_states[0])) / n_states[0], jnp.ones((n_batch, n_states[1])) / n_states[1]] # flat prior\\n\",\n \" E = jnp.ones((n_batch, 1))\\n\",\n \"\\n\",\n \" return A, B, C, D, E\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": null,\n \"metadata\": {},\n \"outputs\": [],\n \"source\": [\n \"def profile(fun, *args): \\n\",\n \" tracemalloc.start()\\n\",\n \" tracemalloc.reset_peak()\\n\",\n \" bt = time.time()\\n\",\n \" res = fun(*args)\\n\",\n \" et = time.time()\\n\",\n \" size, peak = tracemalloc.get_traced_memory()\\n\",\n \"\\n\",\n \" stats = {'time': et - bt}\\n\",\n \" return res, stats\\n\",\n \"\\n\",\n \"def experiment(n_states):\\n\",\n \" results = {}\\n\",\n \"\\n\",\n \" n_batch = 1\\n\",\n \" num_obs = [2]\\n\",\n \"\\n\",\n \" A, B, C, D, E = get_matrices(n_batch=n_batch, num_obs=num_obs, n_states=n_states)\\n\",\n \"\\n\",\n \" # for the single modality, a sequence over time of observations (one hot vectors)\\n\",\n \" obs = [\\n\",\n \" jnp.broadcast_to(\\n\",\n \" jnp.array(\\n\",\n \" [\\n\",\n \" [1.0, 0.0], # observation 0 is ambiguous with respect state factors\\n\",\n \" [1.0, 0], # observation 0 is ambiguous with respect state factors\\n\",\n \" [1.0, 0], # observation 0 is ambiguous with respect state factors\\n\",\n \" [0.0, 1.0],\\n\",\n \" ]\\n\",\n \" )[:, None],\\n\",\n \" (4, n_batch, num_obs[0]),\\n\",\n \" )\\n\",\n \" ] # observation 1 provides information about exact state of both factors\\n\",\n \"\\n\",\n \" agents = Agent(\\n\",\n \" A=A,\\n\",\n \" B=B,\\n\",\n \" C=C,\\n\",\n \" D=D,\\n\",\n \" E=E,\\n\",\n \" pA=None,\\n\",\n \" pB=None,\\n\",\n \" policy_len=3,\\n\",\n \" control_fac_idx=None,\\n\",\n \" policies=None,\\n\",\n \" gamma=16.0,\\n\",\n \" alpha=16.0,\\n\",\n \" use_utility=True,\\n\",\n \" categorical_obs=True,\\n\",\n \" action_selection=\\\"deterministic\\\",\\n\",\n \" sampling_mode=\\\"full\\\",\\n\",\n \" inference_algo=\\\"ovf\\\",\\n\",\n \" num_iter=16,\\n\",\n \" learn_A=False,\\n\",\n \" learn_B=False,\\n\",\n \" batch_size=1,\\n\",\n \" )\\n\",\n \"\\n\",\n \" jtu.tree_map(lambda b: sparse.BCOO.fromdense(b, n_batch=n_batch), agents.B)\\n\",\n \"\\n\",\n \"\\n\",\n \" prior = agents.D\\n\",\n \" qs_hist = None\\n\",\n \" action_hist = []\\n\",\n \" for t in range(len(obs[0])):\\n\",\n \" first_obs = jtu.tree_map(lambda x: jnp.moveaxis(x[:t+1], 0, 1), obs)\\n\",\n \" beliefs = agents.infer_states(first_obs, past_actions=None, empirical_prior=prior, qs_hist=qs_hist)\\n\",\n \" actions = jnp.broadcast_to(agents.policies[0, 0], (n_batch, 2))\\n\",\n \" prior = agents.update_empirical_prior(actions, beliefs)\\n\",\n \" qs_hist = beliefs\\n\",\n \" action_hist.append(actions)\\n\",\n \"\\n\",\n \" beliefs = jtu.tree_map(lambda x, y: jnp.concatenate([x[:, None], y], 1), agents.D, beliefs)\\n\",\n \"\\n\",\n \" take_first = lambda pytree: jtu.tree_map(lambda leaf: leaf[0], pytree)\\n\",\n \" beliefs_single = take_first(beliefs)\\n\",\n \"\\n\",\n \" # ======\\n\",\n \" # Dense implementation\\n\",\n \" smoothed_beliefs_dense, run_stats = profile(\\n\",\n \" smoothing_ovf, *(beliefs_single, take_first(agents.B), jnp.stack(action_hist, 1)[0])\\n\",\n \" )\\n\",\n \" results.update({k+'_dense': v for k, v in run_stats.items()})\\n\",\n \" results[\\\"size_dense\\\"] = sum([sizeof(sB) for sB in agents.B])\\n\",\n \" # ======\\n\",\n \"\\n\",\n \" sparse_B_single = jtu.tree_map(lambda b: sparse.BCOO.fromdense(b[0]), agents.B)\\n\",\n \" actions_single = jnp.stack(action_hist, 1)[0]\\n\",\n \"\\n\",\n \" # ======\\n\",\n \" # Sparse implementation\\n\",\n \" smoothed_beliefs_sparse, run_stats = profile(\\n\",\n \" smoothing_ovf, *(beliefs_single, sparse_B_single, actions_single)\\n\",\n \" )\\n\",\n \" results.update({k+'_sparse': v for k, v in run_stats.items()})\\n\",\n \" results[\\\"size_sparse\\\"] = sum([sizeof_sparse(sB) for sB in sparse_B_single])\\n\",\n \" # ======\\n\",\n \"\\n\",\n \" return results, [beliefs_single, smoothed_beliefs_dense, smoothed_beliefs_sparse]\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Running the experiment and visualizing the results\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 1,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_3558/2542277956.py:35: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agents = Agent(\\n\"\n ]\n },\n {\n \"data\": {\n \"text/plain\": [\n \"Text(0.5, 1.0, 'smoothed beliefs sparse')\"\n ]\n },\n \"execution_count\": 1,\n \"metadata\": {},\n \"output_type\": \"execute_result\"\n },\n {\n \"data\": {\n \"image/png\": 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\",\n \"text/plain\": [\n \"
\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"res, (beliefs, smoothed_dense, smoothed_sparse) = experiment([2, 3])\\n\",\n \"\\n\",\n \"fig, axes = plt.subplots(2, 3, figsize=(8, 4), sharex=True)\\n\",\n \"\\n\",\n \"sns.heatmap(beliefs[0].mT, ax=axes[0, 0], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"sns.heatmap(beliefs[1].mT, ax=axes[1, 0], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"\\n\",\n \"sns.heatmap(smoothed_dense[0][0].mT, ax=axes[0, 1], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"sns.heatmap(smoothed_dense[0][1].mT, ax=axes[1, 1], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"\\n\",\n \"sns.heatmap(smoothed_sparse[0][0].mT, ax=axes[0, 2], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"sns.heatmap(smoothed_sparse[0][1].mT, ax=axes[1, 2], cbar=False, vmax=1., vmin=0., cmap='viridis')\\n\",\n \"\\n\",\n \"axes[0, 0].set_title('Filtered beliefs')\\n\",\n \"axes[0, 1].set_title('smoothed beliefs dense')\\n\",\n \"axes[0, 2].set_title('smoothed beliefs sparse')\\n\"\n ]\n },\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {},\n \"source\": [\n \"### Benchmarking runtime and memory performance\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 2,\n \"metadata\": {},\n \"outputs\": [\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"Step 1\\n\",\n \"\\t [100, 300]\\n\"\n ]\n },\n {\n \"name\": \"stderr\",\n \"output_type\": \"stream\",\n \"text\": [\n \"/var/folders/_f/1qqqnkyd5k5g2b1pgfwzzrqm0000gn/T/ipykernel_3558/2542277956.py:35: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\\n\",\n \" agents = Agent(\\n\"\n ]\n },\n {\n \"name\": \"stdout\",\n \"output_type\": \"stream\",\n \"text\": [\n \"\\t {'time_dense': 0.4508378505706787, 'size_dense': 100000, 'time_sparse': 0.5985698699951172, 'size_sparse': 1600}\\n\",\n \"Step 2\\n\",\n \"\\t [200, 600]\\n\",\n \"\\t {'time_dense': 0.5454308986663818, 'size_dense': 400000, 'time_sparse': 0.5894217491149902, 'size_sparse': 3200}\\n\",\n \"Step 3\\n\",\n \"\\t [300, 900]\\n\",\n \"\\t {'time_dense': 0.36173391342163086, 'size_dense': 900000, 'time_sparse': 0.5830059051513672, 'size_sparse': 4800}\\n\",\n \"Step 4\\n\",\n \"\\t [400, 1200]\\n\",\n \"\\t {'time_dense': 0.44315290451049805, 'size_dense': 1600000, 'time_sparse': 0.7388842105865479, 'size_sparse': 6400}\\n\",\n \"Step 5\\n\",\n \"\\t [500, 1500]\\n\",\n \"\\t {'time_dense': 0.418179988861084, 'size_dense': 2500000, 'time_sparse': 0.5743489265441895, 'size_sparse': 8000}\\n\",\n \"Step 6\\n\",\n \"\\t [600, 1800]\\n\",\n \"\\t {'time_dense': 0.3202641010284424, 'size_dense': 3600000, 'time_sparse': 0.5391190052032471, 'size_sparse': 9600}\\n\",\n \"Step 7\\n\",\n \"\\t [700, 2100]\\n\",\n \"\\t {'time_dense': 0.44112205505371094, 'size_dense': 4900000, 'time_sparse': 0.6291599273681641, 'size_sparse': 11200}\\n\",\n \"Step 8\\n\",\n \"\\t [800, 2400]\\n\",\n \"\\t {'time_dense': 0.44248127937316895, 'size_dense': 6400000, 'time_sparse': 0.6097638607025146, 'size_sparse': 12800}\\n\",\n \"Step 9\\n\",\n \"\\t [900, 2700]\\n\",\n \"\\t {'time_dense': 0.3552210330963135, 'size_dense': 8100000, 'time_sparse': 0.639538049697876, 'size_sparse': 14400}\\n\"\n ]\n }\n ],\n \"source\": [\n \"n_steps = 10\\n\",\n \"\\n\",\n \"res = []\\n\",\n \"for i in range(1, n_steps):\\n\",\n \" print(f\\\"Step {i}\\\")\\n\",\n \" num_states = [100 * i, 300 * i]\\n\",\n \" print('\\\\t', num_states)\\n\",\n \" results, bel = experiment(num_states)\\n\",\n \" res += [results]\\n\",\n \" print('\\\\t', res[-1])\"\n ]\n },\n {\n \"cell_type\": \"code\",\n \"execution_count\": 3,\n \"metadata\": {},\n \"outputs\": [\n {\n \"data\": {\n \"image/png\": 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\"\n ]\n },\n \"metadata\": {},\n \"output_type\": \"display_data\"\n }\n ],\n \"source\": [\n \"keys = list(set(r.replace(\\\"_dense\\\", \\\"\\\").replace(\\\"_sparse\\\", \\\"\\\") for r in res[0].keys())) \\n\",\n \"n_plots = len(keys)\\n\",\n \"\\n\",\n \"fig, ax = plt.subplots(n_plots, 1, figsize=(6, 3 * n_plots))\\n\",\n \"for i, a in enumerate(ax.flatten()):\\n\",\n \" k = keys[i]\\n\",\n \" a.plot([r[k + \\\"_dense\\\"] for r in res], label=f\\\"{k.replace('_', ' ').capitalize()} dense\\\")\\n\",\n \" a.plot([r[k + \\\"_sparse\\\"] for r in res], label=f\\\"{k} sparse\\\")\\n\",\n \" a.set_xticks(list(range(0, len(res))))\\n\",\n \" a.set_xticklabels([f\\\"[{1000*i}, {3000*i}]\\\" for i in range(1, n_steps)], rotation=45)\\n\",\n \" m = max([r[k + \\\"_dense\\\"] for r in res] + [r[k + \\\"_sparse\\\"] for r in res]) * 1.05\\n\",\n \" a.set_ylim([0, m])\\n\",\n \"\\n\",\n \"plt.tight_layout()\\n\",\n \"[a.legend() for a in ax.flatten()]\\n\",\n \"plt.show()\"\n ]\n }\n ],\n \"metadata\": {},\n \"nbformat\": 4,\n \"nbformat_minor\": 2\n}\n" }, { "path": "mkdocs.yml", "content": "site_name: pymdp\nsite_description: JAX-first Active Inference in discrete state spaces\nsite_url: https://pymdp-rtd.readthedocs.io/en/latest/\nrepo_url: https://github.com/infer-actively/pymdp\nrepo_name: infer-actively/pymdp\ndocs_dir: docs-mkdocs\nexclude_docs: |\n overrides/**\nsite_dir: !ENV [MKDOCS_SITE_DIR, site]\nstrict: true\nvalidation:\n omitted_files: ignore\ntheme:\n name: dracula\n custom_dir: docs-mkdocs/overrides\n logo: assets/pymdp-logo.png\n favicon: assets/pymdp-favicon.png\nmarkdown_extensions:\n - admonition\n - attr_list\n - footnotes\n - pymdownx.arithmatex:\n generic: true\n - toc:\n permalink: true\nextra_css:\n - styles/crisp-api.css\nextra_javascript:\n - javascripts/mathjax.js\n - javascripts/sidebar-accessibility.js\n - https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js\nplugins:\n - search\n - mkdocs-jupyter:\n execute: false\n include_source: true\n ignore_h1_titles: true\n theme: dark\n - mkdocstrings:\n handlers:\n python:\n options:\n show_source: false\n show_signature_annotations: true\n show_root_heading: true\n docstring_style: numpy\n heading_level: 2\nnav:\n - Home: index.md\n - Getting Started:\n - Installation: getting-started/installation.md\n - Quickstart (JAX): getting-started/quickstart-jax.md\n - Guides:\n - Using rollout() for compiled active inference loops: guides/rollout-active-inference-loop.md\n - PymdpEnv and Custom Environments: guides/pymdp-env.md\n - Generative Model Structure: guides/generative-model-structure.md\n - Migration:\n - NumPy/legacy to JAX: migration/numpy-to-jax.md\n - Tutorials:\n - Overview: tutorials/index.md\n - Notebook Gallery: tutorials/notebooks/index.md\n - API Reference:\n - Overview: api/index.md\n - Agent: api/agent.md\n - Inference: api/inference.md\n - Control: api/control.md\n - Learning: api/learning.md\n - Algorithms: api/algos.md\n - Utils: api/utils.md\n - Maths: api/maths.md\n - Environment: api/envs-env.md\n - Env Rollout: api/envs-rollout.md\n - Sophisticated Inference Planning: api/planning-si.md\n - MCTS Planning: api/planning-mcts.md\n - Legacy:\n - Legacy/NumPy Archive: legacy/index.md\n - Development:\n - Viewing Docs Locally: development/viewing-docs.md\n - Release Notes: development/release-notes.md\n" }, { "path": "nbval_sanitize.cfg", "content": "# nbval sanitization configuration\n# This file contains regex patterns to sanitize notebook outputs before comparison\n# Format: regex to match [replacement]\n\n# Sanitize file paths with line numbers\n*.py:[0-9]+ *.py:LINE\n\n# Sanitize temporary paths\n/tmp/.* /tmp/...\n/var/.* /var/...\n\n# Sanitize memory addresses\n0x[0-9a-fA-F]+ 0x...\n\n# Sanitize timestamps\n[0-9]{4}-[0-9]{2}-[0-9]{2} [0-9]{2}:[0-9]{2}:[0-9]{2} TIMESTAMP" }, { "path": "paper/paper.bib", "content": "@article{friston_reinforcement_2009,\n\ttitle = {Reinforcement learning or active inference?},\n\tauthor = {Friston, Karl J. and Daunizeau, Jean and Kiebel, Stefan J.},\n\tjournal = {PLoS ONE},\n\tyear = {2009},\n\tvolume = {4},\n\tnumber = {7},\n\tpages = {e6421},\n\tdoi = {10.1371/journal.pone.0006421}\n}\n\n@article{vanderbroeck2019active,\n title={Active inference for robot control: A factor graph approach},\n author={Vanderbroeck, Mees and Baioumy, Mohamed and van der Lans, Daan and de Rooij, Rens and van der Werf, Tiis},\n journal={Student Undergraduate Research E-journal!},\n volume={5},\n pages={1--5},\n year={2019}\n}\n\n@inproceedings{ergul2020learning,\n title={Learning Where to Park},\n author={Ergul, Burak and van de Laar, Thijs and Koudahl, Magnus and Roa-Villescas, Martin and de Vries, Bert},\n booktitle={International Workshop on Active Inference},\n pages={125--132},\n year={2020},\n organization={Springer}\n}\n\n@article{10.1162/neco_a_01427,\n author={van de Laar, Thijs and Senoz, Ismail and {\\\"O}z{\\c{c}}elikkale, Ay{\\c{c}}a and Wymeersch, Henk},\n title = {Chance-Constrained Active Inference},\n journal = {Neural Computation},\n volume = {33},\n number = {10},\n pages = {2710-2735},\n year = {2021},\n month = {09},\n issn = {0899-7667},\n doi = {10.1162/neco_a_01427},\n url = {https://doi.org/10.1162/neco\\_a\\_01427},\n eprint = {https://direct.mit.edu/neco/article-pdf/33/10/2710/1963501/neco\\_a\\_01427.pdf},\n }\n\n@misc{heins2022pymdp_arxiv,\n title={pymdp: A Python library for active inference in discrete state spaces},\n author={Heins, Conor and Millidge, Beren and Demekas, Daphne and Klein, Brennan and Friston, Karl and Couzin, Iain and Tschantz, Alexander},\n eprint={2201.03904v1},\n archivePrefix={arXiv},\n primaryClass={cs.AI}, \n year={2022}\n}\n\n@article{millidge2021whence,\n title = {Whence the expected free energy?},\n author = {Millidge, Beren and Tschantz, Alexander and Buckley, Christopher L.},\n journal = {Neural Computation},\n year = {2021},\n volume = {33},\n number = {2},\n pages = {447--482},\n doi = {10.1162/neco_a_01354}\n}\n\n@article{friston2015active,\n title = {Active inference and epistemic value},\n author = {Friston, Karl J. and Rigoli, Francesco and Ognibene, Dimitri and Mathys, Christoph and Fitzgerald, Thomas and Pezzulo, Giovanni},\n journal = {Cognitive Neuroscience},\n year = {2015},\n volume = {6},\n number = {4},\n pages = {187--214},\n doi = {10.1080/17588928.2015.1020053}\n}\n\n@article{parr2019neuronal,\n title = {Neuronal message passing using Mean-field, Bethe, and Marginal approximations},\n author = {Parr, Thomas and Markovic, Dimitrije and Kiebel, Stefan J. and Friston, Karl J.},\n journal = {Scientific Reports},\n year = {2019},\n volume = {9},\n number = {1},\n pages = {1--18},\n doi = {10.1038/s41598-018-38246-3}\n}\n\n@article{penny2004modelling,\n title = {Modelling functional integration: A comparison of structural equation and dynamic causal models},\n author = {Penny, Will D. and Stephan, Klaas E. and Mechelli, Andrea and Friston, Karl J.},\n journal = {NeuroImage},\n year = {2004},\n volume = {23},\n pages = {S264--S274},\n doi = {10.1016/j.neuroimage.2004.07.041}\n}\n\n@article{friston_active_2012,\n\ttitle = {Active inference and agency: Optimal control without cost functions},\n\tauthor = {Friston, Karl J. and Samothrakis, Spyridon and Montague, Read},\n\tjournal = {Biological Cybernetics},\n\tyear = {2012},\n\tvolume = {106},\n\tnumber = {8-9},\n\tpages = {523--541},\n doi = {10.1007/s00422-012-0512-8}\n}\n\n@article{montague2012computational,\n title = {Computational psychiatry},\n author = {Montague, P. Read and Dolan, Raymond J. and Friston, Karl J. and Dayan, Peter},\n journal = {Trends in Cognitive Sciences},\n year = {2012},\n volume = {16},\n number = {1},\n pages = {72--80},\n doi = {10.1016/j.tics.2011.11.018}\n}\n\n@inproceedings{tschantz2020reinforcement,\n title = {Reinforcement learning through active inference},\n author = {Tschantz, Alexander and Millidge, Beren and Seth, Anil K. and Buckley, Christopher L.},\n booktitle = {Bridging AI and Cognitive Science at the International Conference on Learning Representations},\n year = {2020},\n url = {https://baicsworkshop.github.io/pdf/BAICS_37.pdf}\n}\n\n@article{sajid2021active,\n title = {Active inference: Demystified and compared},\n author = {Sajid, Noor and Ball, Philip J. and Parr, Thomas and Friston, Karl J.},\n journal = {Neural Computation},\n year = {2021},\n volume = {33},\n number = {3},\n pages = {674--712},\n doi = {10.1162/neco_a_01357}\n}\n\n@inproceedings{tschantz2020scaling,\n title = {Scaling active inference},\n author = {Tschantz, Alexander and Baltieri, Manuel and Seth, Anil K. and Buckley, Christopher L.},\n booktitle = {2020 International Joint Conference on Neural Networks (IJCNN)},\n year = {2020},\n pages = {1--8},\n organization = {IEEE},\n doi = {10.1109/IJCNN48605.2020.9207382}\n}\n\n@article{friston2017process,\n title = {Active inference: A process theory},\n author = {Friston, Karl J. and FitzGerald, Thomas and Rigoli, Francesco and Schwartenbeck, Philipp and Pezzulo, Giovanni},\n journal = {Neural Computation},\n year = {2017},\n volume = {29},\n number = {1},\n pages = {1--49},\n doi = {10.1162/NECO_a_00912}\n}\n\n@article{baltieri2019pid,\n title = {PID control as a process of active inference with linear generative models},\n author = {Baltieri, Manuel and Buckley, Christopher L.},\n journal = {Entropy},\n year = {2019},\n volume = {21},\n number = {3},\n pages = {257},\n doi = {10.3390/e21030257}\n}\n\n@inproceedings{fountas2020deep,\n title = {Deep active inference agents using Monte-Carlo methods},\n author = {Fountas, Zafeirios and Sajid, Noor and Mediano, Pedro A.M. and Friston, Karl J.},\n booktitle = {Advances in Neural Information Processing Systems},\n year = {2020},\n url = {https://proceedings.neurips.cc/paper/2020/hash/865dfbde8a344b44095495f3591f7407-Abstract.html}\n}\n\n@article{van2019simulating,\n title = {Simulating active inference processes by message passing},\n author = {van de Laar, Thijs W. and de Vries, Bert},\n journal = {Frontiers in Robotics and AI},\n year = {2019},\n volume = {6},\n pages = {20},\n doi = {10.3389/frobt.2019.00020}\n}\n\n@article{ueltzhoffer2018deep,\n title = {Deep active inference},\n author = {Ueltzh{\\\"o}ffer, Kai},\n journal = {Biological Cybernetics},\n year = {2018},\n volume = {112},\n number = {6},\n pages = {547--573},\n doi = {10.1007/s00422-018-0785-7}\n}\n\n@article{tschantz2020learning,\n title = {Learning action-oriented models through active inference},\n author = {Tschantz, Alexander and Seth, Anil K. and Buckley, Christopher L.},\n journal = {PLoS Computational Biology},\n year = {2020},\n volume = {16},\n number = {4},\n pages = {e1007805},\n doi = {10.1371/journal.pcbi.1007805}\n}\n\n@inproceedings{ccatal2020learning,\n title = {Learning perception and planning with deep active inference},\n author = {{\\c{C}}atal, Ozan and Verbelen, Tim and Nauta, Johannes and De Boom, Cedric and Dhoedt, Bart},\n booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},\n year = {2020},\n pages = {3952--3956},\n organization = {IEEE},\n doi = {10.1109/ICASSP40776.2020.9054364}\n}\n\n@book{penny2011statistical,\n title = {Statistical parametric mapping: The analysis of functional brain images},\n author = {Penny, William D. and Friston, Karl J. and Ashburner, John T. and Kiebel, Stefan J. and Nichols, Thomas E.},\n year = {2007},\n isbn = {978-0-12-372560-8},\n doi = {10.1016/B978-0-12-372560-8.X5000-1}\n}\n\n@article{friston2010free,\n title = {The free-energy principle: A unified brain theory?},\n author = {Friston, Karl J.},\n journal = {Nature Reviews Neuroscience},\n year = {2010},\n volume = {11},\n number = {2},\n pages = {127--138},\n doi = {10.1038/nrn2787}\n}\n\n@article{da2020active,\n title = {Active inference on discrete state-spaces: A synthesis},\n author = {Da Costa, Lancelot and Parr, Thomas and Sajid, Noor and Veselic, Sebastijan and Neacsu, Victorita and Friston, Karl J.},\n journal = {Journal of Mathematical Psychology},\n year = {2020},\n volume = {99},\n pages = {102447},\n doi = {10.1016/j.jmp.2020.102447}\n}\n\n@article{kaelbling1998planning,\n title = {Planning and acting in partially observable stochastic domains},\n author = {Kaelbling, Leslie Pack and Littman, Michael L. and Cassandra, Anthony R.},\n journal = {Artificial Intelligence},\n year = {1998},\n volume = {101},\n number = {1-2},\n pages = {99--134},\n doi = {10.1016/S0004-3702(98)00023-X}\n}\n\n@article{friston2021sophisticated,\n title = {Sophisticated inference},\n author = {Friston, Karl J. and Da Costa, Lancelot and Hafner, Danijar and Hesp, Casper and Parr, Thomas},\n journal = {Neural Computation},\n year = {2021},\n volume = {33},\n number = {3},\n pages = {713--763},\n doi = {10.1162/neco_a_01351}\n}\n\n@article{schwartenbeck2015dopaminergic,\n title = {The dopaminergic midbrain encodes the expected certainty about desired outcomes},\n author = {Schwartenbeck, Philipp and FitzGerald, Thomas and Mathys, Christoph and Dolan, Ray and Friston, Karl J.},\n journal = {Cerebral Cortex},\n year = {2015},\n volume = {25},\n number = {10},\n pages = {3434--3445},\n doi = {10.1093/cercor/bhu159}\n}\n\n@article{smith2020imprecise,\n title = {Imprecise action selection in substance use disorder: Evidence for active learning impairments when solving the explore-exploit dilemma},\n author = {Smith, Ryan and Schwartenbeck, Philipp and Stewart, Jennifer L. and Kuplicki, Rayus and Ekhtiari, Hamed and Paulus, Martin P. and {Tulsa 1000 Investigators}},\n journal = {Drug and Alcohol Dependence},\n year = {2020},\n volume = {215},\n pages = {108208},\n doi = {10.1016/j.drugalcdep.2020.108208}\n}\n\n@article{smith2021greater,\n title = {Greater decision uncertainty characterizes a transdiagnostic patient sample during approach-avoidance conflict: A computational modelling approach},\n author = {Smith, Ryan and Kirlic, Namik and Stewart, Jennifer L. and Touthang, James and Kuplicki, Rayus and Khalsa, Sahib S. and Feinstein, Justin and Paulus, Martin P. and Aupperle, Robin L.},\n journal = {Journal of Psychiatry \\& Neuroscience},\n year = {2021},\n volume = {46},\n number = {1},\n pages = {E74},\n doi = {10.1503/jpn.200032}\n}\n\n@article{smith2022step,\n title={A step-by-step tutorial on active inference and its application to empirical data},\n author={Smith, Ryan and Friston, Karl J and Whyte, Christopher J},\n journal={Journal of Mathematical Psychology},\n volume={107},\n pages={102632},\n year={2022},\n publisher={Elsevier},\n doi={10.1016/j.jmp.2021.102632}\n}\n\n@article{friston2008variational,\n title = {DEM: A variational treatment of dynamic systems},\n author = {Friston, Karl J. and Trujillo-Barreto, N. and Daunizeau, Jean},\n journal = {NeuroImage},\n volume = {41},\n number = {3},\n pages = {849--885},\n year = {2008},\n doi = {10.1016/j.neuroimage.2008.02.054}\n}\n\n@misc{friston2019free,\n title={A free energy principle for a particular physics},\n author={Friston, Karl},\n eprint={1906.10184v1},\n archivePrefix={arXiv},\n primaryClass={q-bio.NC}, \n year={2019}\n}\n\n@article{millidge2020deep,\n title = {Deep active inference as variational policy gradients},\n author = {Millidge, Beren},\n journal = {Journal of Mathematical Psychology},\n year = {2020},\n volume = {96},\n pages = {102348},\n doi = {10.1016/j.jmp.2020.102348}\n}\n\n@inproceedings{millidge2020relationship,\n title = {On the relationship between active inference and control as inference},\n author = {Millidge, Beren and Tschantz, Alexander and Seth, Anil K. and Buckley, Christopher L.},\n booktitle = {International Workshop on Active Inference},\n year = {2020},\n pages = {3--11},\n organization = {Springer},\n doi = {10.1007/978-3-030-64919-7_1}\n}\n\n@article{ForneyLab2019,\n\ttitle = {A factor graph approach to automated design of {Bayesian} signal processing algorithms},\n\tvolume = {104},\n\tissn = {0888-613X},\n\turl = {http://www.sciencedirect.com/science/article/pii/S0888613X18304298},\n\tdoi = {10.1016/j.ijar.2018.11.002},\n\tabstract = {The benefits of automating design cycles for Bayesian inference-based algorithms are becoming increasingly recognized by the machine learning community. As a result, interest in probabilistic programming frameworks has much increased over the past few years. This paper explores a specific probabilistic programming paradigm, namely message passing in Forney-style factor graphs (FFGs), in the context of automated design of efficient Bayesian signal processing algorithms. To this end, we developed “ForneyLab”2 as a Julia toolbox for message passing-based inference in FFGs. We show by example how ForneyLab enables automatic derivation of Bayesian signal processing algorithms, including algorithms for parameter estimation and model comparison. Crucially, due to the modular makeup of the FFG framework, both the model specification and inference methods are readily extensible in ForneyLab. In order to test this framework, we compared variational message passing as implemented by ForneyLab with automatic differentiation variational inference (ADVI) and Monte Carlo methods as implemented by state-of-the-art tools “Edward” and “Stan”. In terms of performance, extensibility and stability issues, ForneyLab appears to enjoy an edge relative to its competitors for automated inference in state-space models.},\n\turldate = {2018-11-16},\n\tjournal = {International Journal of Approximate Reasoning},\n\tauthor = {Cox, Marco and van de Laar, Thijs and de Vries, Bert},\n\tmonth = jan,\n\tyear = {2019},\n\tkeywords = {Bayesian inference, Message passing, Factor graphs, Julia, Probabilistic programming},\n\tpages = {185--204}\n}\n\n@article{gregory1980perceptions,\n title={Perceptions as hypotheses},\n author={Gregory, Richard Langton},\n journal={Philosophical Transactions of the Royal Society of London. B, Biological Sciences},\n volume={290},\n number={1038},\n pages={181--197},\n year={1980},\n publisher={The Royal Society London},\n doi={10.1098/rstb.1980.0090}\n}\n\n@misc{brockman2016openai,\n title={Openai gym},\n author={Brockman, Greg and Cheung, Vicki and Pettersson, Ludwig and Schneider, Jonas and Schulman, John and Tang, Jie and Zaremba, Wojciech},\n eprint={1606.01540v1},\n archivePrefix={arXiv},\n primaryClass={cs.LG},\n year={2016}\n}\n\n@article{friston2016active,\n title = {Active inference and learning},\n author = {Friston, Karl J. and FitzGerald, Thomas and Rigoli, Francesco and Schwartenbeck, Philipp and O'Doherty, John and Pezzulo, Giovanni},\n journal = {Neuroscience \\& Biobehavioral Reviews},\n year = {2016},\n volume = {68},\n pages = {862--879},\n doi = {10.1016/j.neubiorev.2016.06.022}\n}\n\n@article{dayan1995helmholtz,\n title = {The Helmholtz Machine},\n author = {Dayan, Peter and Hinton, Geoffrey E. and Neal, Radford M. and Zemel, Richard S.},\n journal = {Neural Computation},\n year = {1995},\n volume = {7},\n number = {5},\n pages = {889--904},\n doi = {10.1162/neco.1995.7.5.889}\n}\n\n@misc{von1910treatise,\n title = {Treatise on physiological optics (Vol. 3)},\n author = {Von Helmholtz, Herman and Southall, JPC},\n year = {1910},\n publisher = {Dover, New York},\n doi = {10.1037/13536-000}\n}\n\n@inproceedings{hinton1983optimal,\n title = {Optimal perceptual inference},\n author = {Hinton, Geoffrey E. and Sejnowski, Terrence J.},\n booktitle = {Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition},\n volume = {448},\n year = {1983},\n organization = {Citeseer},\n url = {http://www.cs.toronto.edu/~hinton/absps/optimal.pdf}\n}\n\n@inproceedings{baioumy2021towards,\n title={Towards Stochastic Fault-Tolerant Control Using Precision Learning and Active Inference},\n author={Baioumy, Mohamed and Pezzato, Corrado and Corbato, Carlos Hernandez and Hawes, Nick and Ferrari, Riccardo},\n booktitle={Machine Learning and Principles and Practice of Knowledge Discovery in Databases},\n year={2022},\n publisher={Springer International Publishing},\n pages={681--691},\n isbn={978-3-030-93736-2},\n doi = {10.1007/978-3-030-93736-2_48}\n}\n\n@article{ccatal2021robot,\n title = {Robot navigation as hierarchical active inference},\n author = {{\\c{C}}atal, Ozan and Verbelen, Tim and Van de Maele, Toon and Dhoedt, Bart and Safron, Adam},\n journal = {Neural Networks},\n year = {2021},\n volume = {142},\n pages = {192--204},\n doi = {10.1016/j.neunet.2021.05.010}\n}\n\n@article{wirkuttis2021leading,\n title = {Leading or following? Dyadic robot imitative interaction using the active inference framework},\n author = {Wirkuttis, Nadine and Tani, Jun},\n journal = {IEEE Robotics and Automation Letters},\n year = {2021},\n volume = {6},\n number = {3},\n pages = {6024--6031},\n doi = {10.1109/LRA.2021.3090015}\n}\n\n@article{martinez2021probabilistic,\n title = {Probabilistic modeling for optimization of bioreactors using reinforcement learning with active inference},\n author = {Mart{\\'i}nez, Ernesto C. and Kim, Jong Woo and Barz, Tilman and Bournazou, Mariano N. Cruz},\n journal = {Computer Aided Chemical Engineering},\n year = {2021},\n volume = {50},\n pages = {419--424},\n doi = {10.1016/B978-0-323-88506-5.50066-8}\n}\n\n@misc{moreno2021pid,\n title = {PID control as a process of active inference applied to a refrigeration system},\n author = {Moreno, Adri{\\'a}n Rocandio},\n year = {2021},\n url = {https://projekter.aau.dk/projekter/files/415131289/1034_PID_Control_as_Active_Inference.pdf}\n}\n\n@article{parr2019generalised,\n title = {Generalised free energy and active inference},\n author = {Parr, Thomas and Friston, Karl J.},\n journal = {Biological Cybernetics},\n year = {2019},\n volume = {113},\n number = {5},\n pages = {495--513},\n doi = {10.1007/s00422-019-00805-w}\n}\n\n@article{fox2021active,\n title = {Active inference: Applicability to different types of social organization explained through reference to industrial engineering and quality management},\n author = {Fox, Stephen},\n journal = {Entropy},\n year = {2021},\n volume = {23},\n number = {2},\n pages = {198},\n doi = {10.3390/e23020198}\n}\n\n@article{tison2021communication,\n title = {Communication as socially extended active inference: An ecological approach to communicative behavior},\n author = {Tison, Remi and Poirier, Pierre},\n journal = {Ecological Psychology},\n year = {2021},\n volume = {33},\n pages = {197--235},\n doi = {10.1080/10407413.2021.1965480}\n}\n\n@article{friston2013life,\n title = {Life as we know it},\n author = {Friston, Karl J.},\n journal = {Journal of the Royal Society Interface},\n year = {2013},\n volume = {10},\n number = {86},\n pages = {20130475},\n doi = {10.1098/rsif.2013.0475}\n}\n\n@article{schwartenbeck2019computational,\n title = {Computational mechanisms of curiosity and goal-directed exploration},\n author = {Schwartenbeck, Philipp and Passecker, Johannes and Hauser, Tobias U. and FitzGerald, Thomas and Kronbichler, Martin and Friston, Karl J.},\n journal = {Elife},\n year = {2019},\n volume = {8},\n pages = {e41703},\n doi = {10.7554/eLife.41703}\n}\n\n@article{friston2017active,\n title = {Active inference, curiosity and insight},\n author = {Friston, Karl J. and Lin, Marco and Frith, Christopher D. and Pezzulo, Giovanni and Hobson, J. Allan and Ondobaka, Sasha},\n journal = {Neural Computation},\n year = {2017},\n volume = {29},\n number = {10},\n pages = {2633--2683},\n doi = {10.1162/neco_a_00999}\n}\n\n@misc{lance_lnA,\n author = \"Da Costa, Lancelot\",\n date = \"2021\",\n howpublished = \"Personal communication\"\n}\n\n@article{holmes2021active,\n title={Active inference, selective attention, and the cocktail party problem},\n author={Holmes, Emma and Parr, Thomas and Griffiths, Timothy D and Friston, Karl J},\n journal={Neuroscience \\& Biobehavioral Reviews},\n volume={131},\n pages={1288--1304},\n year={2021},\n publisher={Elsevier},\n doi={10.1016/j.neubiorev.2021.09.038}\n}\n\n@article{adams2021everything,\n title={Everything is connected: Inference and attractors in delusions},\n author={Adams, Rick A and Vincent, Peter and Benrimoh, David and Friston, Karl J and Parr, Thomas},\n journal={Schizophrenia research},\n year={2021},\n publisher={Elsevier},\n doi={10.1016/j.schres.2021.07.032}\n}\n\n@article{parr2020prefrontal,\n title={Prefrontal computation as active inference},\n author={Parr, Thomas and Rikhye, Rajeev Vijay and Halassa, Michael M and Friston, Karl J},\n journal={Cerebral Cortex},\n volume={30},\n number={2},\n pages={682--695},\n year={2020},\n publisher={Oxford University Press},\n doi={10.1093/cercor/bhz118}\n}\n\n@article{smith2021long,\n title={Long-term stability of computational parameters during approach-avoidance conflict in a transdiagnostic psychiatric patient sample},\n author={Smith, Ryan and Kirlic, Namik and Stewart, Jennifer L and Touthang, James and Kuplicki, Rayus and McDermott, Timothy J and Taylor, Samuel and Khalsa, Sahib S and Paulus, Martin P and Aupperle, Robin L},\n journal={Scientific reports},\n volume={11},\n number={1},\n pages={1--13},\n year={2021},\n publisher={Nature Publishing Group},\n doi={10.1038/s41598-021-91308-x}\n}" }, { "path": "paper/paper.md", "content": "---\ntitle: 'pymdp: A Python library for active inference in discrete state spaces'\ntags:\n - Python\n - active inference\n - Markov Decision Process\n - POMDP\n - MDP\n - Reinforcement Learning\n - Artificial Intelligence\n - Bayesian inference\n - free energy principle\nauthors:\n - name: Conor Heins^[corresponding author]\n affiliation: \"1, 2, 3, 4\"\n - name: Beren Millidge\n affiliation: \"4, 5\"\n - name: Daphne Demekas\n affiliation: \"6\"\n - name: Brennan Klein\n orcid: 0000-0001-8326-5044\n affiliation: \"4, 7, 8\"\n - name: Karl Friston\n affiliation: \"9\" \n - name: Iain D. Couzin\n affiliation: \"1, 2, 3\" \n - name: Alexander Tschantz^[corresponding author]\n affiliation: \"4, 10, 11\"\naffiliations:\n - name: Department of Collective Behaviour, Max Planck Institute of Animal Behavior, 78457 Konstanz, Germany\n index: 1\n - name: Centre for the Advanced Study of Collective Behaviour, 78457 Konstanz, Germany\n index: 2\n - name: Department of Biology, University of Konstanz, 78457 Konstanz, Germany\n index: 3\n - name: VERSES Research Lab, Los Angeles, California, USA\n index: 4\n - name: MRC Brain Networks Dynamics Unit, University of Oxford, Oxford, UK\n index: 5\n - name: Department of Computing, Imperial College London, London, UK\n index: 6\n - name: Network Science Institute, Northeastern University, Boston, MA, USA\n index: 7\n - name: Laboratory for the Modeling of Biological and Socio-Technical Systems, Northeastern University, Boston, USA\n index: 8\n - name: Wellcome Centre for Human Neuroimaging, Queen Square Institute of Neurology, University College London, London WC1N 3AR, UK\n index: 9\n - name: Sussex AI Group, Department of Informatics, University of Sussex, Brighton, UK\n index: 10\n - name: Sackler Centre for Consciousness Science, University of Sussex, Brighton, UK\n index: 11\n \ndate: 14 January 2022\nbibliography: paper.bib\n---\n\n# Statement of Need\n\nActive inference is an account of cognition and behavior in complex systems which brings together action, perception, and learning under the theoretical mantle of Bayesian inference [@friston_reinforcement_2009; @friston_active_2012; @friston2015active; @friston2017process]. Active inference has seen growing applications in academic research, especially in fields that seek to model human or animal behavior [@parr2020prefrontal; @holmes2021active; @adams2021everything]. The majority of applications have focused on cognitive neuroscience, with a particular focus on modelling decision-making under uncertainty [@schwartenbeck2015dopaminergic; @smith2020imprecise; @smith2021greater]. Nonetheless, the framework has broad applicability and has recently been applied to diverse disciplines, ranging from computational models of psychopathology [@montague2012computational; @smith2021greater], control theory [@baltieri2019pid; @millidge2020relationship; @baioumy2021towards] and reinforcement learning [@tschantz2020reinforcement; @tschantz2020scaling; @sajid2021active; @fountas2020deep; @millidge2020deep], through to social cognition [@adams2021everything; @wirkuttis2021leading; @tison2021communication] and even real-world engineering problems [@martinez2021probabilistic; @moreno2021pid; @fox2021active]. While in recent years, some of the code arising from the active inference literature has been written in open source languages like Python and Julia [@ueltzhoffer2018deep; @van2019simulating; @tschantz2020learning; @ccatal2020learning; @millidge2020deep], to-date, the most popular software for simulating active inference agents is the `DEM` toolbox of `SPM` [@friston2008variational; @smith2022step], a MATLAB library originally developed for the statistical analysis and modelling of neuroimaging data [@penny2011statistical]. `DEM` contains a reliable, reproducible set of functions for studying active inference, but the use of the toolbox can be restrictive for researchers in settings where purchasing a MATLAB license is financially costly. And although active inference researchers have relied heavily on `DEM` for simulating and fitting models of behavior, most of its functionality is restricted to single MATLAB scripts or functions, particularly one called `spm_MDP_VB_X.m`, that lack modularity and often must be customized for applications on a domain-specific basis. Increasing interest in active inference, manifested both in terms of sheer number of cited research papers as well as diversifying applications across disciplines, has thus created a need for generic, widely-available, and user-friendly code for simulating active inference in open-source scientific computing languages like Python. The software we present here, [`pymdp`](https://github.com/infer-actively/pymdp), represents a significant step in this direction: namely, we provide the first open-source package for simulating active inference with discrete state-space generative models. The name `pymdp` derives from the fact that the package is written in the **Py**thon programming language and concerns discrete, Markovian generative models of decision-making, which take the form of Markov Decision Processes or **MDP**s.\n\n`pymdp` is a Python package that is directly inspired by the active inference routines contained in `DEM`. However, `pymdp` is has a modular, flexible structure that allows researchers to build and simulate active inference agents quickly and with a high degree of customization. We developed `pymdp` in the hopes that it will increase the accessibility and exposure of the active inference framework to researchers, engineers, and developers with diverse disciplinary backgrounds. In the spirit of open-source software, we also hope that it spurs new innovation, development, and collaboration in the growing active inference and wider Bayesian modelling communities. For additional pedagogical and technical resources on `pymdp`, we refer the reader to the package's github repository. We also encourage more technically-interested readers to consult a companion preprint article that includes technical material covering the mathematics of active inference in discrete state spaces [@heins2022pymdp_arxiv].\n\n# Summary\n\n`pymdp` offers a suite of robust, tested, and modular routines for simulating active inference agents equipped with *partially-observable Markov Decision Process* (POMDP) generative models. Mathematically, a POMDP comprises a joint distribution over observations $o$, hidden states $s$, control states $u$ and hyperparameters $\\phi$: $P(o, s, u, \\phi)$. This joint distribution further factorizes into a set of categorical and Dirichlet distributions: the likelihoods and priors of the generative model. With `pymdp`, one can build a generative model using a set of prior and likelihood distributions, initialize an agent, and then link it to an external environment to run active inference processes - all in a few lines of code. The `Agent` and `Env` (environment) APIs of `pymdp` are built according to the standardized framework of OpenAIGym commonly used in reinforcement learning, where an agent and environment object recursively exchange observations and actions over time [@brockman2016openai].\n\n# Introduction\n\nSimulations of active inference are commonly performed in discrete time and space [@friston2015active; @da2020active]. This is partially motivated by the mathematical tractability of performing inference with discrete probability distributions, but also by the intuition of modelling choice behavior as a sequence of discrete, mutually-exclusive choices in, e.g., psychophysics or decision-making experiments. The most popular generative models -- used to realize active inference in this context -- are partially-observable Markov Decision Processes or *POMDPs* [@kaelbling1998planning]. POMDPs are state-space models that model the environment in terms of hidden states that stochastically change over time, as a function of both the current state of the environment as well as the behavioral output of an agent (control states or actions). Crucially, the environment is *partially-observable*, i.e. the hidden states are not directly observed by the agent, but can only be inferred through observations that relate to hidden states in a probabilistic manner, such that observations are modelled as being generated stochastically from the current hidden state. This necessitates both \"perceptual\" inference of hidden states as well as control.\n\nAs such, in most POMDP problems, an agent is tasked with inferring the hidden state of its environment and then choosing a sequence of control states or actions to change hidden states in a way that leads to desired outcomes (maximizing reward, or occupancy within some preferred set of states). \n\n# Usage \n\nIn order to enhance the user-friendliness of `pymdp` without sacrificing flexibility, we have built the library to be highly modular and customizable, such that agents in `pymdp` can be specified at a variety of levels of abstraction with desired parameterisations. The methods of the `Agent` class can thus be called in any particular order, depending on the application, and furthermore they can be specified with various keyword arguments that entail choices of implementation details at lower levels.\n\nBy retaining a modular structure throughout the package's dependency hierarchy, `pymdp` also affords the ability to flexibly compose different low level functions. This allows users to customize and integrate their active inference loops with desired inference algorithms and policy selection routines. For instance, one could sub-class the `Agent` class and write a customized `step()` function, that combines whichever components of active inference one is interested in. \n\n# Related software packages\n\nThe `DEM` toolbox within `SPM` in MATLAB is the current gold-standard in active inference modelling. In particular, simulating an active inference process in `DEM` consists of defining the generative model in terms of a fixed set of matrices and vectors, and then calling the `spm_MDP_VB_X.m` function to simulate a sequence of trials. `pymdp`, by contrast, provides a user-friendly and modular development experience, with core functionality split up into different libraries that separately perform the computations of active inference in a standalone fashion. Moreover, `pymdp` provides the user the ability to write an active inference process at different levels of abstraction depending on the user's level of expertise or skill with the package -- ranging from the high level `Agent` functionality, which allows the user to define and simulate an active inference agent in just a few lines of code, all the way to specifying a particular variational inference algorithm (e.g., marginal-message passing [@parr2019neuronal]) for the agent to use during state estimation. In the `DEM` toolbox of `SPM`, this would require setting undocumented flags or else manually editing the routines in `spm_MDP_VB_X.m` to enable or disable bespoke functionality. There has been one recent attempt at creating a comprehensive user-guide for building active inference agents in `DEM` [@smith2022step], though to our knowledge there has not been a package devoted to the open source development of these powerful software tools.\n\nA recent related, but largely non-overlapping project is [ForneyLab](https://github.com/biaslab/ForneyLab.jl), which provides a set of Julia libraries for performing approximate Bayesian inference via message passing on Forney Factor Graphs [@ForneyLab2019]. Notably, this package has also seen several applications in simulating active inference processes, using ForneyLab as the backend for the inference algorithms employed by an active inference agent [@van2019simulating; @vanderbroeck2019active; @ergul2020learning; @10.1162/neco_a_01427]. While ForneyLab focuses on including a rigorous set of message passing routines that can be used to simulate active inference agents, `pymdp` is specifically designed to help users quickly build agents (regardless of their underlying inference routines) and plug them into arbitrary environments to run active inference in a few easy steps.\n\n# Funding Statement\nCH and IDC acknowledge support from the Office of Naval Research grant (ONR, N00014- 64019-1-2556), with IDC further acknowledging support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement (ID: 860949), the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy-EXC 2117- 422037984, and the Max Planck Society. KF is supported by funding for the Wellcome Centre for Human Neuroimaging (Ref: 205103/Z/16/Z) and the Canada-UK Artificial Intelligence Initiative (Ref: ES/T01279X/1). CH, DD, and BK acknowledge the support of a grant from the John Templeton Foundation (61780). The opinions expressed in this publication are those of the author(s) and do not necessarily reflect the views of the John Templeton Foundation.\n\n# Acknowledgements\n\nThe authors would like to thank Dimitrije Markovic, Arun Niranjan, Sivan Altinakar, Mahault Albarracin, Alex Kiefer, Magnus Koudahl, Ryan Smith, Casper Hesp, and Maxwell Ramstead for discussions and feedback that contributed to development of `pymdp`. We would also like to thank Thomas Parr for pointing out a technical error in an earlier version of the arXiv preprint for this work. Finally, we are grateful to the many users of `pymdp` whose feedback and usage of the package have contributed to its continued improvement and development.\n\n# References" }, { "path": "pymdp/__init__.py", "content": "" }, { "path": "pymdp/agent.py", "content": "#!/usr/bin/env python\n# -*- coding: utf-8 -*-\n\n\"\"\"Agent API for Active Inference with the modern JAX backend.\"\"\"\nimport math as pymath\nimport warnings\nimport jax.numpy as jnp\nimport jax.tree_util as jtu\nfrom jax import nn, vmap\nfrom pymdp import inference, control, learning, utils\nfrom pymdp.distribution import Distribution, get_dependencies\nfrom equinox import Module, field, tree_at\n\nfrom typing import Any, Callable, Optional, Sequence, Union\nfrom jaxtyping import Array\nfrom functools import partial\nfrom jax import lax\n\nclass Agent(Module):\n \"\"\"\n The Agent class, the highest-level API that wraps together processes for action, perception, and learning under active inference.\n\n Examples\n --------\n A single timestep of active inference:\n\n from jax import random as jr\n\n my_agent = Agent(A=A, B=B, C=C, )\n observation = env.step(initial_action)\n qs = my_agent.infer_states(observation, empirical_prior=my_agent.D)\n q_pi, neg_efe = my_agent.infer_policies(qs)\n keys = jr.split(rng_key, my_agent.batch_size + 1)\n next_action = my_agent.sample_action(q_pi, rng_key=keys[1:])\n next_observation = env.step(next_action)\n\n This represents one timestep of an active inference process. Wrapping this step in a loop with an `Env()` class that returns\n observations and takes actions as inputs, would entail a dynamic agent-environment interaction.\n\n Observation Formats\n -------------------\n Observations can be provided in two formats:\n\n 1. **Discrete observations** (default, categorical_obs=False):\n Each `observations[m]` is an integer observation index for modality `m`.\n These are converted to one-hot vectors internally.\n\n 2. **Categorical observations** (categorical_obs=True):\n Each `observations[m]` is a probability vector over observations for\n modality `m`.\n\n Advanced preprocessing\n ----------------------\n You can override default preprocessing with `preprocess_fn` (set on the\n agent or per `infer_states` call). If provided, this function should\n return categorical observations and takes precedence over default\n discrete/categorical handling.\n \"\"\"\n\n A: list[Array]\n B: list[Array]\n C: list[Array]\n D: list[Array]\n E: Array\n pA: list[Array]\n pB: list[Array]\n gamma: Array\n alpha: Array\n\n # matrix of all possible policies (each row is a policy of shape (num_controls[0], num_controls[1], ..., num_controls[num_control_factors-1])\n policies: control.Policies = field(static=True)\n\n # threshold for inductive inference (the threshold for pruning transitions that are below a certain probability)\n inductive_threshold: Array\n # epsilon for inductive inference (trade-off/weight for how much inductive value contributes to EFE of policies)\n inductive_epsilon: Array\n # H vectors (one per hidden state factor) used for inductive inference -- these encode goal states or constraints\n H: list[Array]\n # I matrices (one per hidden state factor) used for inductive inference -- these encode the 'reachability' matrices of goal states encoded in `self.H`\n I: list[Array]\n # static parameters not leaves of the PyTree\n A_dependencies: Optional[list[list[int]]] = field(static=True)\n B_dependencies: Optional[list[list[int]]] = field(static=True)\n B_action_dependencies: Optional[list[list[int]]] = field(static=True)\n # mapping from multi action dependencies to flat action dependencies for each B\n action_maps: list[dict] = field(static=True)\n batch_size: int = field(static=True)\n num_iter: int = field(static=True)\n num_obs: list[int] = field(static=True)\n num_modalities: int = field(static=True)\n num_states: list[int] = field(static=True)\n num_factors: int = field(static=True)\n num_controls: list[int] = field(static=True)\n # Used to store original action dimensions in case there are multiple action dependencies per state\n num_controls_multi: list[int] = field(static=True)\n control_fac_idx: Optional[list[int]] = field(static=True)\n # depth of planning during roll-outs (i.e. number of timesteps to look ahead when computing expected free energy of policies)\n policy_len: int = field(static=True)\n # number of past timesteps (including current) to use for sequence inference (mmp, vmp, exact)\n inference_horizon: Optional[int] = field(static=True)\n # depth of inductive inference (i.e. number of future timesteps to use when computing inductive `I` matrix)\n inductive_depth: int = field(static=True)\n # flag for whether to use expected utility (\"reward\" or \"preference satisfaction\") when computing expected free energy\n use_utility: bool = field(static=True)\n # flag for whether to use state information gain (\"salience\") when computing expected free energy\n use_states_info_gain: bool = field(static=True)\n # flag for whether to use parameter information gain (\"novelty\") when computing expected free energy\n use_param_info_gain: bool = field(static=True)\n # flag for whether to use inductive inference (\"intentional inference\") when computing expected free energy\n use_inductive: bool = field(static=True)\n categorical_obs: bool = field(static=True)\n preprocess_fn: Optional[Callable] = field(static=True)\n # determinstic or stochastic action selection\n action_selection: str = field(static=True)\n # whether to sample from full posterior over policies (\"full\") or from marginal posterior over actions (\"marginal\")\n sampling_mode: str = field(static=True)\n # fpi, vmp, mmp, ovf, exact\n inference_algo: str = field(static=True)\n # whether to perform learning online or offline (options: \"online\", \"offline\")\n learning_mode: str = field(static=True, default=\"online\")\n\n learn_A: bool = field(static=True)\n learn_B: bool = field(static=True)\n learn_C: bool = field(static=True)\n learn_D: bool = field(static=True)\n learn_E: bool = field(static=True)\n\n def __init__(\n self,\n A: Union[list[Array], list[Distribution]],\n B: Union[list[Array], list[Distribution]],\n C: Optional[list[Array]] = None,\n D: Optional[list[Array]] = None,\n E: Optional[Array] = None,\n pA: Optional[list[Array]] = None,\n pB: Optional[list[Array]] = None,\n H: Optional[list[Array]] = None,\n I: Optional[list[Array]] = None,\n A_dependencies: Optional[list[list[int]]] = None,\n B_dependencies: Optional[list[list[int]]] = None,\n B_action_dependencies: Optional[list[list[int]]] = None,\n num_controls: Optional[list[int]] = None,\n control_fac_idx: Optional[list[int]] = None,\n policy_len: int = 1,\n policies: Optional[Union[Array, control.Policies]] = None,\n gamma: float | Array = 1.0,\n alpha: float | Array = 1.0,\n inductive_depth: int = 1,\n inductive_threshold: float | Array = 0.1,\n inductive_epsilon: float | Array = 1e-3,\n use_utility: bool = True,\n use_states_info_gain: bool = True,\n use_param_info_gain: bool = False,\n use_inductive: bool = False,\n categorical_obs: bool = False,\n preprocess_fn: Optional[Callable] = None,\n action_selection: str = \"deterministic\",\n sampling_mode: str = \"full\",\n inference_algo: str = \"fpi\",\n inference_horizon: Optional[int] = None,\n num_iter: int = 16,\n batch_size: int = 1,\n learning_mode: str = \"online\", # TODO: or should this be an argument to `self.infer_parameters()` or even `env/rollout.py:rollout()`\n learn_A: bool = False,\n learn_B: bool = False,\n learn_C: bool = False,\n learn_D: bool = False,\n learn_E: bool = False,\n ) -> None:\n if B_action_dependencies is not None:\n assert num_controls is not None, \"Please specify num_controls if you're also using complex action dependencies\"\n\n if learn_A:\n assert pA is not None, \"pA is required for A learning\"\n\n # extract high level variables\n self.num_modalities = len(A)\n self.num_factors = len(B)\n self.num_controls = num_controls\n self.num_controls_multi = num_controls\n\n # extract dependencies for A and B matrices\n (\n self.A_dependencies,\n self.B_dependencies,\n self.B_action_dependencies,\n ) = self._construct_dependencies(A_dependencies, B_dependencies, B_action_dependencies, A, B)\n\n # extract A, B, C and D tensors from optional Distributions\n A = [jnp.array(a.data) if isinstance(a, Distribution) else a for a in A]\n B = [jnp.array(b.data) if isinstance(b, Distribution) else b for b in B]\n if C is not None:\n C = [jnp.array(c.data) if isinstance(c, Distribution) else c for c in C]\n if D is not None:\n D = [jnp.array(d.data) if isinstance(d, Distribution) else d for d in D]\n if E is not None:\n E = jnp.array(E.data) if isinstance(E, Distribution) else E\n if H is not None:\n H = [jnp.array(h.data) if isinstance(h, Distribution) else h for h in H]\n\n if pA is not None:\n pA = [jnp.array(pa) for pa in pA]\n\n if pB is not None:\n pB = [jnp.array(pb) for pb in pB]\n\n self.batch_size = batch_size\n\n # flatten B action dims for multiple action dependencies\n self.action_maps = None\n if (\n policies is None and B_action_dependencies is not None\n ): # note, this only works when B_action_dependencies is not the trivial case of [[0], [1], ...., [num_factors-1]]\n policies_multi = control.construct_policies(\n self.num_controls_multi,\n self.num_controls_multi,\n policy_len,\n control_fac_idx,\n )\n B, pB, self.action_maps = self._flatten_B_action_dims(B, pB, self.B_action_dependencies)\n policies = self._construct_flattend_policies(policies_multi, self.action_maps)\n self.sampling_mode = \"full\"\n \n # extract shapes from A and B\n self.num_states = self._get_num_states_from_B(B, self.B_dependencies)\n self.num_controls = [b_f.shape[-1] for b_f in B] # dimensions of control states for each hidden state factor\n\n # check that batch_size is consistent with shapes of given A and B\n for m, a_m in enumerate(A):\n a_m_state_factors = tuple([self.num_states[f] for f in self.A_dependencies[m]])\n if a_m.ndim > (len(a_m_state_factors) + 1): # this indicates there's a leading batch dimension\n if a_m.shape[0] == 1 and batch_size > 1:\n A[m] = jnp.broadcast_to(a_m, (batch_size,) + a_m.shape[1:])\n if pA is not None:\n pA[m] = jnp.broadcast_to(pA[m], (batch_size,) + a_m.shape[1:])\n if C is not None:\n C[m] = jnp.broadcast_to(C[m], (batch_size,) + C[m].shape[1:])\n elif a_m.shape[0] != batch_size:\n raise ValueError(\n f\"Batch size {batch_size} does not match the first dimension of A[{m}] with shape {a_m.shape}\"\n )\n elif a_m.ndim == (len(a_m_state_factors) + 1): # this indicates no leading batch dimension\n A[m] = jnp.broadcast_to(a_m, (batch_size,) + a_m.shape)\n if pA is not None:\n pA[m] = jnp.broadcast_to(pA[m], (batch_size,) + a_m.shape)\n if C is not None:\n C[m] = jnp.broadcast_to(C[m], (batch_size,) + C[m].shape)\n \n for f, b_f in enumerate(B):\n b_f_state_factors = tuple([self.num_states[f] for f in self.B_dependencies[f]])\n if b_f.ndim > (len(b_f_state_factors) + 2): # this indicates there's a leading batch dimension\n if b_f.shape[0] == 1 and batch_size > 1:\n B[f] = jnp.broadcast_to(b_f, (batch_size,) + b_f.shape[1:])\n if pB is not None:\n pB[f] = jnp.broadcast_to(pB[f], (batch_size,) + b_f.shape[1:])\n if D is not None:\n D[f] = jnp.broadcast_to(D[f], (batch_size,) + D[f].shape[1:])\n elif b_f.shape[0] != batch_size:\n raise ValueError(\n f\"Batch size {batch_size} does not match the first dimension of B[{f}] with shape {b_f.shape}\"\n )\n elif b_f.ndim == (len(b_f_state_factors) + 2): # this indicates no leading batch dimension\n B[f] = jnp.broadcast_to(b_f, (batch_size,) + b_f.shape)\n if pB is not None:\n pB[f] = jnp.broadcast_to(pB[f], (batch_size,) + b_f.shape)\n if D is not None:\n D[f] = jnp.broadcast_to(D[f], (batch_size,) + D[f].shape)\n\n # now that shapes of A/B have been made consistent and have (batch_size,)-sized leading dimension applied, we can infer num_obs from the first dimension of A\n self.num_obs = [a_m.shape[1] for a_m in A] # dimensions of observations for each modality\n\n # static parameters\n self.num_iter = num_iter\n self.inference_algo = inference_algo.lower() if isinstance(inference_algo, str) else inference_algo\n self.inference_horizon = inference_horizon\n self.inductive_depth = inductive_depth\n\n if self.inference_horizon is not None and self.inference_horizon < 1:\n raise ValueError(\"`inference_horizon` must be >= 1 when provided\")\n if use_inductive and self.inductive_depth < 1:\n raise ValueError(\"`inductive_depth` must be >= 1 when `use_inductive` is True\")\n\n # policy parameters\n self.policy_len = policy_len\n self.action_selection = action_selection\n self.sampling_mode = sampling_mode\n self.use_utility = use_utility\n self.use_states_info_gain = use_states_info_gain\n self.use_param_info_gain = use_param_info_gain\n self.use_inductive = use_inductive\n\n # learning parameters\n self.learning_mode = learning_mode\n self.learn_A = learn_A\n self.learn_B = learn_B\n self.learn_C = learn_C\n self.learn_D = learn_D\n self.learn_E = learn_E\n\n # construct control factor indices\n if control_fac_idx is None:\n self.control_fac_idx = [f for f in range(self.num_factors) if self.num_controls[f] > 1]\n else:\n msg = \"Check control_fac_idx - must be consistent with `num_states` and `num_factors`...\"\n assert max(control_fac_idx) <= (self.num_factors - 1), msg\n self.control_fac_idx = control_fac_idx\n\n # construct policies\n if policies is None:\n policies_array = control.construct_policies(\n self.num_states,\n self.num_controls,\n self.policy_len,\n self.control_fac_idx,\n )\n self.policies = control.Policies(policies_array)\n else:\n if not isinstance(policies, control.Policies):\n self.policies = control.Policies(jnp.array(policies))\n else:\n self.policies = policies\n\n if C is None:\n C = [jnp.ones((self.batch_size, self.num_obs[m])) / self.num_obs[m] for m in range(self.num_modalities)]\n \n if D is None:\n D = [jnp.ones((self.batch_size, self.num_states[f])) / self.num_states[f] for f in range(self.num_factors)]\n\n if E is None:\n E = jnp.ones((self.batch_size, self.policies.num_policies)) / self.policies.num_policies\n else:\n if E.ndim > 1:\n if E.shape[0] == 1 and batch_size > 1:\n E = jnp.broadcast_to(E, (batch_size,) + E.shape[1:])\n elif E.shape[0] != batch_size:\n raise ValueError(\n f\"Batch size {batch_size} does not match the first dimension of E with shape {E.shape}\"\n )\n elif E.ndim == 1:\n E = jnp.broadcast_to(E, (self.batch_size,) + E.shape)\n\n if H is not None:\n for f, h_f in enumerate(H):\n if h_f.ndim > 1:\n if h_f.shape[0] == 1 and batch_size > 1:\n H[f] = jnp.broadcast_to(h_f, (batch_size,) + h_f.shape[1:])\n elif h_f.shape[0] != batch_size:\n raise ValueError(\n f\"Batch size {batch_size} does not match the first dimension of H[{f}] with shape {h_f.shape}\"\n )\n elif h_f.ndim == 1:\n H[f] = jnp.broadcast_to(h_f, (self.batch_size,) + h_f.shape)\n\n self.A = A\n self.B = B\n self.C = C\n self.D = D\n self.E = E\n self.H = H\n self.pA = pA\n self.pB = pB\n\n self.gamma = jnp.broadcast_to(gamma, (self.batch_size,))\n self.alpha = jnp.broadcast_to(alpha, (self.batch_size,))\n\n self.inductive_threshold = jnp.broadcast_to(inductive_threshold, (self.batch_size,))\n self.inductive_epsilon = jnp.broadcast_to(inductive_epsilon, (self.batch_size,))\n\n if self.use_inductive and H is not None:\n I = vmap(\n partial(\n control.generate_I_matrix,\n depth=self.inductive_depth,\n )\n )(H, B, self.inductive_threshold)\n elif self.use_inductive and I is not None:\n I = I\n else:\n I = jtu.tree_map(lambda x: jnp.expand_dims(jnp.zeros_like(x), 1), D)\n self.I = I\n\n self.categorical_obs = categorical_obs\n self.preprocess_fn = preprocess_fn\n if (self.preprocess_fn is not None) and (self.categorical_obs is False):\n warnings.warn(\n \"preprocess_fn is set while categorical_obs=False. If your preprocess_fn returns \"\n \"categorical distributions, set categorical_obs=True so that learning/planning can \"\n \"interpret observations correctly.\",\n UserWarning,\n stacklevel=2,\n )\n\n # validate model\n self._validate()\n\n @property\n def unique_multiactions(self) -> Array:\n size = pymath.prod(self.num_controls)\n return jnp.unique(self.policies.policy_arr[:, 0], axis=0, size=size, fill_value=-1)\n\n def _get_num_states_from_B(self, B: list[Array], B_dependencies: list[list[int]]) -> list[int]:\n \"\"\" Use the shapes of B and the B_dependencies to determine the number of states for each factor.\"\"\"\n \n num_states = []\n for (f, B_deps_f) in enumerate(B_dependencies): \n if f in B_deps_f:\n self_factor_index = B_deps_f.index(f)\n else:\n raise ValueError(f\"num_states cannot be inferred from B, B_dependencies if the dynamics of hidden state {f} is not conditioned on itself\")\n \n num_states_f = B[f].shape[-(len(B_deps_f) + 1 - self_factor_index)]\n num_states.append(num_states_f)\n\n return num_states\n\n def infer_parameters(\n self,\n beliefs_A: list[Array],\n observations: list[Array],\n actions: Array | None,\n beliefs_B: list[Array] | None = None,\n lr_pA: float = 1.0,\n lr_pB: float = 1.0,\n **kwargs: Any,\n ) -> \"Agent\":\n \"\"\"Update Dirichlet parameters for `A` and/or `B` models from data.\n\n Parameters\n ----------\n beliefs_A: list[Array]\n Marginal state beliefs used when updating the observation model\n parameters.\n observations: list[Array]\n Observation histories for each modality.\n actions: Array or None\n Action history aligned to time. For multi-action agents this should be\n shaped `(batch, T, num_factors)`.\n beliefs_B: list[Array] | None, optional\n Optional sequence of beliefs used for transition updates. If `None`,\n transition updates are skipped.\n lr_pA: float, default=1.0\n Learning-rate multiplier for `A` updates.\n lr_pB: float, default=1.0\n Learning-rate multiplier for `B` updates.\n **kwargs: Any\n Reserved for future arguments.\n\n Returns\n -------\n Agent\n Agent instance with updated `pA`, `A`, `pB`, and `B` where learning is\n enabled.\n \"\"\"\n\n agent = self\n\n # ------------------------------------------------------------------\n # Prepare the sequences we'll use for A- and B- learning\n # ------------------------------------------------------------------\n # For updating A we use 'marginal_beliefs' (possibly smoothed under OVF).\n # For updating B we need a *time* sequence to construct joints or run smoothing.\n seq_beliefs = beliefs_A if beliefs_B is None else beliefs_B # (list over factors) each (B, T, Ns_f)\n\n # Normalize action shape to include time if needed\n if actions is not None and actions.ndim == 2:\n # (B, Nu) -> (B, 1, Nu) so we can slice to T-1 below\n actions = jnp.expand_dims(actions, 1)\n \n # Infer sequence length (T) from beliefs provided for B learning\n # If learn_B is False we don't need a time sequence, but computing T is cheap and safe\n T = seq_beliefs[0].shape[1] # each factor has (B, T, Ns_f)\n\n # Make actions time-conformant: always slice to T-1 along time\n if actions is not None and actions.ndim == 3:\n actions_Tm1 = actions[:, :max(T - 1, 0), :] # (B, max(T-1, 0), Nu)\n else:\n actions_Tm1 = actions # None or already time-matched\n\n if actions_Tm1 is not None:\n valid_transition_mask = jnp.all(actions_Tm1 >= 0, axis=-1)\n else:\n valid_transition_mask = None\n \n # A handy predicate: can we (meaningfully) apply sequence-based smoothing or\n # B-joint construction for this update window?\n # We need at least one valid transition.\n can_update_Beliefs = (\n actions_Tm1 is not None\n and (T > 1)\n and (actions_Tm1.shape[1] == (T - 1))\n and jnp.any(valid_transition_mask)\n )\n\n # Full B-parameter update additionally requires `self.learn_B`.\n can_update_B = (\n self.learn_B\n and can_update_Beliefs\n )\n\n def _apply_transition_mask(joint_beliefs: list[Array] | None) -> list[Array] | None:\n if valid_transition_mask is None:\n return joint_beliefs\n\n def _mask_joint(x: Array) -> Array:\n mask = valid_transition_mask.astype(x.dtype).reshape(\n valid_transition_mask.shape + (1,) * (x.ndim - 2)\n )\n return x * mask\n\n return jtu.tree_map(_mask_joint, joint_beliefs)\n\n def _empty_joint_beliefs() -> list[Array]:\n return [\n jnp.zeros(\n (\n self.batch_size,\n seq_beliefs[0].shape[1] - 1,\n self.num_states[f],\n *[self.num_states[dep] for dep in self.B_dependencies[f]],\n )\n )\n for f in range(self.num_factors)\n ]\n\n def _build_outer_product_joints() -> list[list[Array]]:\n return [\n [seq_beliefs[f][:, 1:]] + [seq_beliefs[f_idx][:, :-1] for f_idx in self.B_dependencies[f]]\n for f in range(self.num_factors)\n ]\n\n def _smooth_or_fallback(smoothing_fn: Callable[..., Any]) -> tuple[list[Array], list[Array]]:\n def update_with_smoothing(_: Any) -> tuple[list[Array], list[Array]]:\n # Use the *sequence* of filtered beliefs (seq_beliefs) for smoothing\n # vmap runs over batch: each call sees (T, Ns_f) and (T-1, Nu)\n smoothed_marginals_and_joints = vmap(smoothing_fn)(\n seq_beliefs, self.B, actions_Tm1\n )\n marginal_beliefs = smoothed_marginals_and_joints[0] # list[f] -> (B, T, Ns_f)\n joint_beliefs = _apply_transition_mask(smoothed_marginals_and_joints[1]) # list[f] -> (B, T-1, ...)\n return marginal_beliefs, joint_beliefs\n\n def use_filtered_beliefs(_: Any) -> tuple[list[Array], list[Array]]:\n # No valid transition yet (or sentinel action found):\n # - Use filtered beliefs for A-learning,\n # - and either skip B-learning or fall back to the two-frame outer-product joint.\n marginal_beliefs = seq_beliefs\n # Create empty joint_beliefs with same structure as the true branch would return\n joint_beliefs = _apply_transition_mask(_empty_joint_beliefs())\n return marginal_beliefs, joint_beliefs\n\n return lax.cond(\n can_update_Beliefs,\n update_with_smoothing,\n use_filtered_beliefs,\n operand=None\n )\n\n if self.inference_algo in inference.SMOOTHING_METHODS:\n smoothing_fn = inference.smoothing_ovf\n if self.inference_algo == inference.EXACT_METHOD:\n # Exact backward smoothing from online filtering history for single-factor HMMs.\n smoothing_fn = inference.smoothing_exact\n marginal_beliefs, joint_beliefs = _smooth_or_fallback(smoothing_fn)\n else:\n # Non-OVF: keep existing behavior (use filtered marginals and build joints from t and t-1)\n marginal_beliefs = beliefs_A\n joint_beliefs = _apply_transition_mask(_build_outer_product_joints()) if self.learn_B else None\n\n if self.learn_A:\n update_A = partial(\n learning.update_obs_likelihood_dirichlet,\n A_dependencies=self.A_dependencies,\n num_obs=self.num_obs,\n categorical_obs=self.categorical_obs,\n )\n \n lr = jnp.broadcast_to(lr_pA, (self.batch_size,))\n qA, E_qA = vmap(update_A)(\n self.pA,\n self.A,\n observations,\n marginal_beliefs,\n lr=lr,\n )\n \n agent = tree_at(lambda x: (x.A, x.pA), agent, (E_qA, qA))\n \n if self.learn_B:\n update_B = partial(learning.update_state_transition_dirichlet, num_controls=self.num_controls)\n lrB = jnp.broadcast_to(lr_pB, (self.batch_size,))\n\n def update_B_step(_: Any) -> tuple[list[Array], list[Array]]:\n qB, E_qB = vmap(update_B)(\n self.pB,\n self.B,\n joint_beliefs,\n actions_Tm1, # time-aligned actions\n lr=lrB\n )\n return qB, E_qB\n\n def skip_B_step(_: Any) -> tuple[list[Array], list[Array]]:\n return self.pB, self.B\n\n qB, E_qB = lax.cond(can_update_B, update_B_step, skip_B_step, operand=None)\n\n if self.use_inductive and self.H is not None:\n I_updated = lax.cond(\n can_update_B,\n lambda _: vmap(partial(control.generate_I_matrix, depth=self.inductive_depth))(\n self.H, E_qB, self.inductive_threshold\n ),\n lambda _: self.I,\n operand=None,\n )\n agent = tree_at(lambda x: (x.B, x.pB, x.I), agent, (E_qB, qB, I_updated))\n else:\n agent = tree_at(lambda x: (x.B, x.pB), agent, (E_qB, qB))\n\n return agent\n\n def process_obs(self, observations: list[Array] | list[int]) -> list[Array]:\n \"\"\"\n Preprocess observations into the distributional format expected by the inference routines.\n\n Parameters\n ----------\n observations: list[Array] or list[int]\n The observation input. Format depends on the default preprocessing:\n\n - If `self.categorical_obs=False` (default): Each entry `observations[m]` is an integer\n index representing the discrete observation for modality `m`.\n\n - If `self.categorical_obs=True`: Each entry `observations[m]` is a 1D array representing\n a probability distribution over observations for modality `m`.\n\n Returns\n -------\n o_vec: list[Array]\n Observations in distributional form (one-hot vectors or categorical distributions).\n\n Notes\n -----\n If `self.preprocess_fn` is set on the agent, it takes precedence over the default\n categorical/discrete handling and will be used instead of the logic based on\n `self.categorical_obs`. This override only affects preprocessing; `self.categorical_obs`\n is still used by learning and planning code paths that consume raw observations.\n Ensure `self.categorical_obs` matches the output format of your preprocessing\n (or per-call `preprocess_fn`) to keep those paths consistent.\n \"\"\"\n if self.preprocess_fn is not None:\n return self.preprocess_fn(observations)\n\n if self.categorical_obs:\n return observations\n\n return self.make_categorical(observations)\n\n def make_categorical(self, observations: list[Array] | list[int]) -> list[Array]:\n \"\"\"\n Convert discrete index observations into one-hot categorical distributions.\n\n Parameters\n ----------\n observations: list[Array] or list[int]\n Each entry `observations[m]` is an integer index for modality `m`.\n\n Returns\n -------\n o_vec: list\n One-hot categorical distributions for each modality.\n \"\"\"\n return [nn.one_hot(o, self.num_obs[m]) for m, o in enumerate(observations)]\n\n def infer_states(\n self,\n observations: list[Array] | list[int],\n empirical_prior: list[Array],\n *,\n past_actions: Array | None = None,\n qs_hist: list[Array] | None = None,\n valid_steps: int | Array | None = None,\n mask: list[Array] | None = None,\n preprocess_fn: Callable | None = None,\n return_info: bool = False,\n ) -> list[Array] | tuple[list[Array], dict[str, Any]]:\n \"\"\"\n Update approximate posterior over hidden states by solving variational inference problem, given an observation.\n\n Parameters\n ----------\n observations: list[Array] | list[int]\n Observation input in one of two formats:\n\n - Discrete observations (default): each `observations[m]` is an\n integer index for modality `m`.\n - Categorical observations: each `observations[m]` is a probability\n vector over observations for modality `m`.\n\n If `preprocess_fn` is provided, it should map the raw input to\n categorical observations and takes precedence over default handling.\n\n empirical_prior: list[Array] or tuple[Array]\n Empirical prior beliefs over hidden states. Depending on the inference algorithm chosen,\n the resulting `empirical_prior` variable may be a matrix (or list[Array]).\n of additional dimensions to encode extra conditioning variables like timepoint and policy.\n\n past_actions: Array, optional\n Action history aligned to time. For single-batch sequence inference\n this should be shaped `(T-1, num_factors)`. For batched calls it\n should be shaped `(batch, T-1, num_factors)`.\n\n qs_hist: list[Array] or tuple[Array], optional\n History of posterior beliefs over hidden states.\n\n valid_steps: Array or int, optional\n Number of valid (unpadded) timesteps when using fixed-size sequence windows.\n If provided, sequence inference methods (`mmp`, `vmp`) ignore padded prefix\n timesteps and transitions.\n\n mask: list[Array] or tuple[Array], optional\n Mask for observations.\n\n preprocess_fn: callable, optional\n Optional preprocessing function to convert observations into distributional form.\n If None, defaults to `self.process_obs`. The callable should accept\n `observations` and return distributional observations.\n\n return_info: bool, default=False\n If `True`, also return canonical VFE diagnostics for the inferred\n posterior (`vfe_t`, `vfe`, and component terms). For `ovf` / `exact`\n this remains a forward-filtering diagnostic; to score the full\n smoothed sequence, call `pymdp.inference.smoothing_ovf(...)` or\n `pymdp.inference.smoothing_exact(...)` explicitly and then pass the\n resulting pairwise joints into `pymdp.maths.calc_vfe(...,\n joint_qs=...)`.\n\n Notes\n -----\n `categorical_obs` is no longer an argument to `infer_states`. Set it when\n constructing the agent or supply a `preprocess_fn`. If you provide a custom\n preprocessing function, ensure `self.categorical_obs` matches the output format,\n since it is still used by learning and planning code paths that consume raw observations.\n\n Returns\n -------\n qs: list[Array] or tuple[list[Array], dict[str, Any]]\n Posterior beliefs over hidden states. Depending on the inference algorithm chosen,\n the resulting `qs` variable will have additional sub-structure to reflect whether\n beliefs are additionally conditioned on timepoint and policy.\n For example, in case the `self.inference_algo == 'MMP'` indexing structure is\n policy->timepoint->factor, so that `qs[p_idx][t_idx][f_idx]` refers to beliefs\n about marginal factor `f_idx` expected under policy `p_idx` at timepoint `t_idx`.\n If `return_info=True`, a second return value contains VFE diagnostics.\n\n Examples\n --------\n Discrete observations:\n\n >>> obs = [0, 1] # Modality 0 observed observation 0, modality 1 observed observation 1\n >>> qs = agent.infer_states(obs, prior)\n\n Categorical observations:\n\n >>> obs = [\n ... jnp.array([0.7, 0.2, 0.1]), # Peaked belief distribution for observation 0\n ... jnp.array([0.5, 0.5]) # Flat belief distribution for observation 1\n ... ]\n >>> agent_cat = Agent(..., categorical_obs=True)\n >>> qs = agent_cat.infer_states(obs, prior)\n \"\"\"\n\n if preprocess_fn is None:\n o_vec = self.process_obs(observations)\n else:\n o_vec = preprocess_fn(observations)\n\n if not isinstance(empirical_prior, (list, tuple)):\n raise ValueError(\n \"`empirical_prior` must be a list/tuple with one entry per hidden-state factor.\"\n )\n if len(empirical_prior) != self.num_factors:\n raise ValueError(\n f\"`empirical_prior` has {len(empirical_prior)} factor(s), expected {self.num_factors}\"\n )\n\n A = self.A\n if mask is not None:\n for i, m in enumerate(mask):\n o_vec[i] = m * o_vec[i] + (1 - m) * jnp.ones_like(o_vec[i]) / self.num_obs[i]\n A[i] = m * A[i] + (1 - m) * jnp.ones_like(A[i]) / self.num_obs[i]\n\n infer_states = partial(\n inference.update_posterior_states,\n A_dependencies=self.A_dependencies,\n B_dependencies=self.B_dependencies,\n num_iter=self.num_iter,\n method=self.inference_algo,\n distr_obs=True, # Always True because o_vec is expected to be distributional\n inference_horizon=self.inference_horizon,\n return_info=return_info,\n )\n\n if valid_steps is not None:\n valid_steps = jnp.asarray(valid_steps, dtype=jnp.int32)\n if valid_steps.ndim == 0:\n valid_steps = jnp.broadcast_to(valid_steps, (self.batch_size,))\n elif valid_steps.ndim != 1 or valid_steps.shape[0] != self.batch_size:\n raise ValueError(\n \"`valid_steps` must be a scalar or have shape `(batch_size,)`\"\n )\n \n output = vmap(infer_states)(\n A,\n self.B,\n o_vec,\n past_actions,\n prior=empirical_prior,\n qs_hist=qs_hist,\n valid_steps=valid_steps,\n )\n\n return output\n\n def update_empirical_prior(self, action: Array, qs: list[Array]) -> list[Array]:\n \"\"\"\n Compute the empirical prior used for the next state-inference step.\n\n Parameters\n ----------\n action: Array\n Action sampled at the current timestep for each control factor.\n qs: list[Array]\n Posterior beliefs over hidden states for the current timestep/history.\n\n Returns\n -------\n pred: list[Array]\n Predicted prior over hidden states for the next inference step.\n For sequence methods (`mmp`, `vmp`), this returns `self.D` to preserve sequence-inference semantics.\n \"\"\"\n # this computation of the predictive prior is correct only for fully factorised Bs.\n if self.inference_algo in inference.SEQUENCE_METHODS:\n # in the case of the 'mmp' or 'vmp' we have to use D as prior parameter for infer states\n pred = self.D\n else:\n qs_last = jtu.tree_map( lambda x: x[:, -1], qs)\n propagate_beliefs = partial(control.compute_expected_state, B_dependencies=self.B_dependencies)\n pred = vmap(propagate_beliefs)(qs_last, self.B, action)\n \n return pred\n\n def infer_policies(self, qs: list[Array]) -> tuple[Array, Array]:\n \"\"\"\n Perform policy inference by optimizing a posterior (categorical) distribution over policies.\n This distribution is computed as the softmax of `neg_efe * gamma + lnE` where\n `neg_efe` is the negative expected free energy of policies, `gamma` is a policy\n precision and `lnE` is the (log) prior probability of policies.\n In SPM-style notation this same quantity is often written as `G`, with\n `G = neg_efe = -EFE`.\n This function returns the posterior over policies as well as the negative expected free energy of each policy.\n\n Parameters\n ----------\n qs: list[Array]\n Posterior beliefs over hidden states (typically output of\n `infer_states`), including the most recent timestep.\n\n Returns\n ----------\n q_pi: Array\n Posterior beliefs over policies with shape\n `(batch_size, num_policies)`.\n neg_efe: Array\n Negative expected free energies of policies with shape\n `(batch_size, num_policies)`.\n \"\"\"\n\n latest_belief = jtu.tree_map(lambda x: x[:, -1], qs) # only get the posterior belief held at the current timepoint\n infer_policies = partial(\n control.update_posterior_policies_inductive,\n self.policies.policy_arr,\n A_dependencies=self.A_dependencies,\n B_dependencies=self.B_dependencies,\n use_utility=self.use_utility,\n use_states_info_gain=self.use_states_info_gain,\n use_param_info_gain=self.use_param_info_gain,\n use_inductive=self.use_inductive\n )\n\n q_pi, neg_efe = vmap(infer_policies)(\n latest_belief, \n self.A,\n self.B,\n self.C,\n self.E,\n self.pA,\n self.pB,\n I = self.I,\n gamma=self.gamma,\n inductive_epsilon=self.inductive_epsilon\n )\n\n return q_pi, neg_efe\n \n def multiaction_probabilities(self, q_pi: Array) -> Array:\n \"\"\"\n Compute probabilities of unique multi-actions from the posterior over policies.\n\n Parameters\n ----------\n q_pi: Array\n Posterior beliefs over policies for one batch element.\n\n Returns\n ----------\n Array\n Probability vector over unique multi-actions.\n \"\"\"\n\n if self.sampling_mode == \"marginal\":\n get_marginals = partial(control.get_marginals, policies=self.policies.policy_arr, num_controls=self.num_controls)\n marginals = get_marginals(q_pi)\n outer = lambda a, b: jnp.outer(a, b).reshape(-1)\n marginals = jtu.tree_reduce(outer, marginals)\n\n elif self.sampling_mode == \"full\":\n locs = jnp.all(\n self.policies.policy_arr[:, 0] == jnp.expand_dims(self.unique_multiactions, -2),\n -1,\n )\n get_marginals = lambda x: jnp.where(locs, x, 0.).sum(-1)\n marginals = vmap(get_marginals)(q_pi)\n\n return marginals\n\n def sample_action(self, q_pi: Array, rng_key: Array | None = None) -> Array:\n \"\"\"\n Sample or select a discrete action from the posterior over control states.\n \n Parameters\n ----------\n q_pi: Array\n Posterior over policies for each batch element (usually from\n `infer_policies`).\n rng_key: Array or sequence of keys, optional\n Required for stochastic action selection. For batched agents, pass a\n key array with one key per batch element.\n\n Returns\n ----------\n action: Array\n Action indices per batch element and control factor.\n \"\"\"\n if (rng_key is None) and (self.action_selection == \"stochastic\"):\n raise ValueError(\"Please provide a random number generator key to sample actions stochastically\")\n\n if self.sampling_mode == \"marginal\":\n sample_action = partial(control.sample_action, self.policies.policy_arr, self.num_controls, action_selection=self.action_selection)\n action = vmap(sample_action)(q_pi, alpha=self.alpha, rng_key=rng_key)\n elif self.sampling_mode == \"full\":\n sample_policy = partial(control.sample_policy, self.policies.policy_arr, action_selection=self.action_selection)\n action = vmap(sample_policy)(q_pi, alpha=self.alpha, rng_key=rng_key)\n\n return action\n \n def decode_multi_actions(self, action: Array) -> Array:\n \"\"\"Decode flattened multi-actions back to factor-wise actions.\n\n Parameters\n ----------\n action: Array\n Flattened multi-action indices.\n\n Returns\n -------\n Array\n Array of shape `(batch_size, num_controls_multi)` containing decoded\n actions per control factor.\n \"\"\"\n if self.action_maps is None:\n return action\n\n action_multi = jnp.zeros((self.batch_size, len(self.num_controls_multi))).astype(action.dtype)\n for f, action_map in enumerate(self.action_maps):\n if action_map[\"multi_dependency\"] == []:\n continue\n\n action_multi_f = utils.index_to_combination(action[..., f], action_map[\"multi_dims\"])\n action_multi = action_multi.at[..., action_map[\"multi_dependency\"]].set(action_multi_f)\n return action_multi\n\n def encode_multi_actions(self, action_multi: Array) -> Array:\n \"\"\"Encode factor-wise multi-actions into flattened actions.\n\n Parameters\n ----------\n action_multi: Array\n Array of actions per control factor.\n\n Returns\n -------\n Array\n Flattened action indices with shape `(batch_size, num_controls)`.\n \"\"\"\n if self.action_maps is None:\n return action_multi\n\n action = jnp.zeros((self.batch_size, len(self.num_controls))).astype(action_multi.dtype)\n for f, action_map in enumerate(self.action_maps):\n if action_map[\"multi_dependency\"] == []:\n action = action.at[..., f].set(jnp.zeros_like(action_multi[..., 0]))\n continue\n\n action_f = utils.get_combination_index(\n action_multi[..., action_map[\"multi_dependency\"]],\n action_map[\"multi_dims\"],\n )\n action = action.at[..., f].set(action_f)\n return action\n\n def get_model_dimensions(self) -> dict[str, Any]:\n \"\"\"\n Collect key model dimensions in a single object.\n\n Returns\n -------\n dict[str, Any]\n Dictionary containing model shape metadata. Includes:\n\n - `num_obs`: list[int]\n - `num_states`: list[int]\n - `num_controls`: list[int]\n - `num_modalities`: int\n - `num_factors`: int\n - `num_policies`: int\n - `policy_len`: int\n - `inference_horizon`: int | None\n - `A_dependencies`: list[list[int]]\n - `B_dependencies`: list[list[int]]\n \"\"\"\n return {\n \"num_obs\": self.num_obs,\n \"num_states\": self.num_states,\n \"num_controls\": self.num_controls,\n \"num_modalities\": self.num_modalities,\n \"num_factors\": self.num_factors,\n \"num_policies\": self.policies.num_policies,\n \"policy_len\": self.policy_len,\n \"inference_horizon\": self.inference_horizon,\n \"A_dependencies\": self.A_dependencies,\n \"B_dependencies\": self.B_dependencies,\n }\n\n def _construct_dependencies(\n self,\n A_dependencies: list[list[int]] | None,\n B_dependencies: list[list[int]] | None,\n B_action_dependencies: list[list[int]] | None,\n A: list[Array] | list[Distribution],\n B: list[Array] | list[Distribution],\n ) -> tuple[list[list[int]], list[list[int]], list[list[int]]]:\n if A_dependencies is not None:\n A_dependencies = A_dependencies\n elif isinstance(A[0], Distribution) and isinstance(B[0], Distribution):\n A_dependencies, _ = get_dependencies(A, B)\n else:\n A_dependencies = utils.resolve_a_dependencies(\n self.num_factors, self.num_modalities\n )\n\n if B_dependencies is not None:\n B_dependencies = B_dependencies\n elif isinstance(A[0], Distribution) and isinstance(B[0], Distribution):\n _, B_dependencies = get_dependencies(A, B)\n else:\n B_dependencies = utils.resolve_b_dependencies(self.num_factors)\n\n \"\"\"TODO: check B action shape\"\"\"\n if B_action_dependencies is not None:\n B_action_dependencies = B_action_dependencies\n else:\n B_action_dependencies = utils.resolve_b_action_dependencies(self.num_factors)\n return A_dependencies, B_dependencies, B_action_dependencies\n\n def _flatten_B_action_dims(\n self,\n B: list[Array],\n pB: list[Array] | None,\n B_action_dependencies: list[list[int]],\n ) -> tuple[list[Array], list[Array] | None, list[dict[str, Any]]]:\n assert hasattr(B[0], \"shape\"), \"Elements of B must be tensors and have attribute shape\"\n action_maps = [] # mapping from multi action dependencies to flat action dependencies for each B\n B_flat = []\n pB_flat = []\n for i, (B_f, action_dependency) in enumerate(zip(B, B_action_dependencies)):\n if action_dependency == []:\n B_flat.append(jnp.expand_dims(B_f, axis=-1))\n if pB is not None:\n pB_flat.append(jnp.expand_dims(pB[i], axis=-1))\n action_maps.append(\n {\"multi_dependency\": [], \"multi_dims\": [], \"flat_dependency\": [i], \"flat_dims\": [1]}\n )\n continue\n\n dims = [self.num_controls_multi[d] for d in action_dependency]\n target_shape = list(B_f.shape)[: -len(action_dependency)] + [pymath.prod(dims)]\n B_flat.append(B_f.reshape(target_shape))\n if pB is not None:\n pB_flat.append(pB[i].reshape(target_shape))\n action_maps.append(\n {\n \"multi_dependency\": action_dependency,\n \"multi_dims\": dims,\n \"flat_dependency\": [i],\n \"flat_dims\": [pymath.prod(dims)],\n }\n )\n if pB is None:\n pB_flat = None\n return B_flat, pB_flat, action_maps\n\n def _construct_flattend_policies(self, policies: Array, action_maps: list[dict[str, Any]]) -> Array:\n policies_flat = []\n for action_map in action_maps:\n if action_map[\"multi_dependency\"] == []:\n policies_flat.append(jnp.zeros_like(policies[..., 0]))\n continue\n\n policies_flat.append(\n utils.get_combination_index(\n policies[..., action_map[\"multi_dependency\"]],\n action_map[\"multi_dims\"],\n )\n )\n policies_flat = jnp.stack(policies_flat, axis=-1)\n return policies_flat\n\n def _get_default_params(self) -> dict[str, Any] | None:\n method = self.inference_algo\n default_params = None\n if method == \"VANILLA\":\n default_params = {\"num_iter\": 8, \"dF\": 1.0, \"dF_tol\": 0.001}\n elif method == \"MMP\":\n raise NotImplementedError(\"MMP is not implemented\")\n elif method == \"VMP\":\n raise NotImplementedError(\"VMP is not implemented\")\n elif method == \"BP\":\n raise NotImplementedError(\"BP is not implemented\")\n elif method == \"EP\":\n raise NotImplementedError(\"EP is not implemented\")\n elif method == \"CV\":\n raise NotImplementedError(\"CV is not implemented\")\n\n return default_params\n\n def _validate(self) -> None:\n for m in range(self.num_modalities):\n factor_dims = tuple([self.num_states[f] for f in self.A_dependencies[m]])\n assert (\n self.A[m].shape[2:] == factor_dims\n ), f\"Please input an `A_dependencies` whose {m}-th indices correspond to the hidden state factors that line up with lagging dimensions of A[{m}]...\"\n \n # validate A tensor is normalised\n utils.validate_normalization(self.A[m], axis=1, tensor_name=f\"A[{m}]\")\n \n if self.pA is not None:\n assert (\n self.pA[m].shape[2:] == factor_dims if self.pA[m] is not None else True\n ), f\"Please input an `A_dependencies` whose {m}-th indices correspond to the hidden state factors that line up with lagging dimensions of pA[{m}]...\"\n \n assert max(self.A_dependencies[m]) <= (\n self.num_factors - 1\n ), f\"Check modality {m} of `A_dependencies` - must be consistent with `num_states` and `num_factors`...\"\n\n for f in range(self.num_factors):\n factor_dims = tuple([self.num_states[f] for f in self.B_dependencies[f]])\n assert (\n self.B[f].shape[2:-1] == factor_dims\n ), f\"Please input a `B_dependencies` whose {f}-th indices pick out the hidden state factors that line up with the all-but-final lagging dimensions of B[{f}]...\"\n \n # validate B tensor is normalised\n utils.validate_normalization(self.B[f], axis=1, tensor_name=f\"B[{f}]\")\n \n if self.pB is not None:\n assert (\n self.pB[f].shape[2:-1] == factor_dims\n ), f\"Please input a `B_dependencies` whose {f}-th indices pick out the hidden state factors that line up with the all-but-final lagging dimensions of pB[{f}]...\"\n \n assert max(self.B_dependencies[f]) <= (\n self.num_factors - 1\n ), f\"Check factor {f} of `B_dependencies` - must be consistent with `num_states` and `num_factors`...\"\n\n for factor_idx in self.control_fac_idx:\n assert (\n self.num_controls[factor_idx] > 1\n ), \"Control factor (and B matrix) dimensions are not consistent with user-given control_fac_idx\"\n\n if self.inference_algo == inference.EXACT_METHOD:\n if self.num_factors != 1:\n raise ValueError(\"`exact` inference currently supports only a single hidden-state factor\")\n if len(self.B_dependencies) != 1 or list(self.B_dependencies[0]) != [0]:\n raise ValueError(\n \"Exact inference requires single-factor self-dynamics only \"\n \"(i.e. B_dependencies == [[0]])\"\n )\n if any(list(deps) != [0] for deps in self.A_dependencies):\n raise ValueError(\n \"Exact inference requires each observation modality to depend only on factor 0 \"\n \"(i.e. A_dependencies[m] == [0])\"\n )\n" }, { "path": "pymdp/algos.py", "content": "\"\"\"Core variational-inference and exact-HMM algorithm implementations.\n\nThis module contains lower-level routines used by high-level inference/control\nAPIs. Public entry points include fixed-point iteration, message-passing over\nsequences, and exact single-factor scan-based HMM smoothing.\n\"\"\"\n\nimport jax.numpy as jnp\nimport jax.tree_util as jtu\nfrom typing import Any, Callable, NamedTuple, Tuple\nfrom jax import jit, vmap, grad, lax, nn\nfrom jaxtyping import Array\n# from jax.config import config\n# config.update(\"jax_enable_x64\", True)\n\nfrom pymdp.maths import compute_log_likelihood, compute_log_likelihood_per_modality, log_stable, factor_dot, factor_dot_flex, MINVAL\n\ndef add(x: Array, y: Array) -> Array:\n return x + y\n\n\ndef _matmul_high_precision(lhs: Array, rhs: Array) -> Array:\n \"\"\"Use the highest available matmul precision on accelerator backends.\"\"\"\n return jnp.matmul(lhs, rhs, precision=lax.Precision.HIGHEST)\n\ndef marginal_log_likelihood(qs: list[Array], log_likelihood: Array, i: int) -> Array:\n xs = [q for j, q in enumerate(qs) if j != i]\n return factor_dot(log_likelihood, xs, keep_dims=(i,))\n\ndef all_marginal_log_likelihood(\n qs: list[Array], log_likelihoods: list[Array], all_factor_lists: list[list[int]]\n) -> list[Array]:\n qL_marginals = jtu.tree_map(lambda ll_m, factor_list_m: mll_factors(qs, ll_m, factor_list_m), log_likelihoods, all_factor_lists)\n \n num_factors = len(qs)\n\n # insted of a double loop we could have a list defining m to f mapping\n # which could be resolved with a single tree_map cast\n qL_all = [jnp.zeros(1)] * num_factors\n for m, factor_list_m in enumerate(all_factor_lists):\n for l, f in enumerate(factor_list_m):\n qL_all[f] += qL_marginals[m][l]\n\n return qL_all\n\ndef mll_factors(qs: list[Array], ll_m: Array, factor_list_m: list[int]) -> list[Array]:\n relevant_factors = [qs[f] for f in factor_list_m]\n marginal_ll_f = jtu.Partial(marginal_log_likelihood, relevant_factors, ll_m)\n loc_nf = len(factor_list_m)\n loc_factors = list(range(loc_nf))\n return jtu.tree_map(marginal_ll_f, loc_factors)\n\ndef run_vanilla_fpi(\n A: list[Array],\n obs: list[Array],\n prior: list[Array],\n num_iter: int = 1,\n distr_obs: bool = True,\n) -> list[Array]:\n \"\"\" Vanilla fixed point iteration (jaxified) \"\"\"\n\n nf = len(prior)\n factors = list(range(nf))\n # Step 1: Compute log likelihoods for each factor\n ll = compute_log_likelihood(obs, A, distr_obs=distr_obs)\n # log_likelihoods = [ll] * nf\n\n # Step 2: Map prior to log space and create initial log-posterior\n log_prior = jtu.tree_map(log_stable, prior)\n log_q = jtu.tree_map(jnp.zeros_like, prior)\n\n # Step 3: Iterate until convergence\n def scan_fn(carry: list[Array], t: Array) -> tuple[list[Array], None]:\n log_q = carry\n q = jtu.tree_map(nn.softmax, log_q)\n mll = jtu.Partial(marginal_log_likelihood, q, ll)\n marginal_ll = jtu.tree_map(mll, factors)\n log_q = jtu.tree_map(add, marginal_ll, log_prior)\n\n return log_q, None\n\n res, _ = lax.scan(scan_fn, log_q, jnp.arange(num_iter))\n\n # Step 4: Map result to factorised posterior\n qs = jtu.tree_map(nn.softmax, res)\n return qs\n\ndef run_factorized_fpi(\n A: list[Array],\n obs: list[Array],\n prior: list[Array],\n A_dependencies: list[list[int]],\n num_iter: int = 1,\n distr_obs: bool = True,\n) -> list[Array]:\n \"\"\"\n Run the fixed point iteration algorithm with sparse dependencies between factors and observations (stored in `A_dependencies`)\n \"\"\"\n\n # Exact one-pass update for single-factor models.\n if len(prior) == 1:\n log_likelihood = compute_log_likelihood(obs, A, distr_obs=distr_obs)\n log_q = log_likelihood + log_stable(prior[0])\n return [nn.softmax(log_q, axis=-1)]\n\n # Step 1: Compute log likelihoods for each factor\n log_likelihoods = compute_log_likelihood_per_modality(obs, A, distr_obs=distr_obs)\n\n # Step 2: Map prior to log space and create initial log-posterior\n log_prior = jtu.tree_map(log_stable, prior)\n log_q = jtu.tree_map(jnp.zeros_like, prior)\n\n # Step 3: Iterate until convergence\n def scan_fn(carry: list[Array], t: Array) -> tuple[list[Array], None]:\n log_q = carry\n q = jtu.tree_map(nn.softmax, log_q)\n marginal_ll = all_marginal_log_likelihood(q, log_likelihoods, A_dependencies)\n log_q = jtu.tree_map(add, marginal_ll, log_prior)\n\n return log_q, None\n\n res, _ = lax.scan(scan_fn, log_q, jnp.arange(num_iter))\n\n # Step 4: Map result to factorised posterior\n qs = jtu.tree_map(nn.softmax, res)\n return qs\n\ndef mirror_gradient_descent_step(\n tau: float, ln_A: Array, lnB_past: Array, lnB_future: Array, ln_qs: Array\n) -> Array:\n \"\"\"\n u_{k+1} = u_{k} - \\nabla_p F_k\n p_k = softmax(u_k)\n \"\"\"\n err = ln_A - ln_qs + lnB_past + lnB_future\n ln_qs = ln_qs + tau * err\n qs = nn.softmax(ln_qs - ln_qs.mean(axis=-1, keepdims=True))\n\n return qs\n\ndef update_marginals(\n get_messages: Callable[..., tuple[list[Array], list[Array]]],\n obs: list[Array],\n A: list[Array],\n B: list[Array] | None,\n prior: list[Array],\n A_dependencies: list[list[int]],\n B_dependencies: list[list[int]],\n num_iter: int = 1,\n tau: float = 1.0,\n distr_obs: bool = True,\n obs_valid_mask: Array | None = None,\n transition_valid_mask: Array | None = None,\n) -> list[Array]:\n \"\"\" Version of marginal update that uses a sparse dependency matrix for A \"\"\"\n\n T = obs[0].shape[0]\n ln_B = None if B is None else jtu.tree_map(log_stable, B)\n # log likelihoods -> $\\ln(A)$ for all time steps\n # for $k > t$ we have $\\ln(A) = 0$\n\n def get_log_likelihood(obs_t: list[Array], A: list[Array]) -> list[Array]:\n # # mapping over batch dimension\n # return vmap(compute_log_likelihood_per_modality)(obs_t, A)\n return compute_log_likelihood_per_modality(obs_t, A, distr_obs=distr_obs)\n\n # mapping over time dimension of obs array\n log_likelihoods = vmap(get_log_likelihood, (0, None))(obs, A) # this gives a sequence of log-likelihoods (one for each `t`)\n\n if obs_valid_mask is not None:\n obs_valid_mask = obs_valid_mask.astype(log_likelihoods[0].dtype)\n log_likelihoods = jtu.tree_map(\n lambda ll: ll * obs_valid_mask.reshape((T,) + (1,) * (ll.ndim - 1)),\n log_likelihoods,\n )\n\n # log marginals -> $\\ln(q(s_t))$ for all time steps and factors\n ln_qs = jtu.tree_map( lambda p: jnp.broadcast_to(jnp.zeros_like(p), (T,) + p.shape), prior)\n\n # log prior -> $\\ln(p(s_t))$ for all factors\n ln_prior = jtu.tree_map(log_stable, prior)\n\n qs = jtu.tree_map(nn.softmax, ln_qs)\n\n def scan_fn(carry: list[Array], iter: Array) -> tuple[list[Array], None]:\n qs = carry\n\n ln_qs = jtu.tree_map(log_stable, qs)\n # messages from future $m_+(s_t)$ and past $m_-(s_t)$ for all time steps and factors. For t = T we have that $m_+(s_T) = 0$\n \n lnB_future, lnB_past = get_messages(\n ln_B,\n B,\n qs,\n ln_prior,\n B_dependencies,\n transition_valid_mask=transition_valid_mask,\n )\n\n mgds = jtu.Partial(mirror_gradient_descent_step, tau)\n\n ln_As = vmap(all_marginal_log_likelihood, in_axes=(0, 0, None))(qs, log_likelihoods, A_dependencies)\n\n qs = jtu.tree_map(mgds, ln_As, lnB_past, lnB_future, ln_qs)\n\n return qs, None\n\n qs, _ = lax.scan(scan_fn, qs, jnp.arange(num_iter))\n\n return qs\n\ndef variational_filtering_step(\n prior: list[Array], Bs: list[Array], ln_As: list[Array], A_dependencies: list[list[int]]\n) -> tuple[list[Array], list[Array], list[Array]]:\n\n ln_prior = jtu.tree_map(log_stable, prior)\n \n #TODO: put this inside scan\n ####\n marg_ln_As = all_marginal_log_likelihood(prior, ln_As, A_dependencies)\n\n # compute posterior q(z_t) -> n x 1 x d\n post = jtu.tree_map( \n lambda x, y: nn.softmax(x + y, -1), marg_ln_As, ln_prior \n )\n ####\n\n # compute prediction p(z_{t+1}) = \\int p(z_{t+1}|z_t) q(z_t) -> n x d x 1\n pred = jtu.tree_map(\n lambda x, y: jnp.sum(x * jnp.expand_dims(y, -2), -1), Bs, post\n )\n \n # compute reverse conditional distribution q(z_t|z_{t+1})\n cond = jtu.tree_map(\n lambda x, y, z: x * jnp.expand_dims(y, -2) / jnp.expand_dims(z, -1),\n Bs,\n post, \n pred\n )\n\n return post, pred, cond\n\ndef update_variational_filtering(\n obs: list[Array],\n A: list[Array],\n B: list[Array],\n prior: list[Array],\n A_dependencies: list[list[int]],\n **kwargs: Any,\n) -> tuple[list[Array], list[Array], list[Array]]:\n \"\"\"Online variational filtering belief update that uses a sparse dependency matrix for A\"\"\"\n\n obs[0].shape[0]\n def pad(x: Array) -> Array:\n npad = [(0, 0)] * jnp.ndim(x)\n npad[0] = (0, 1)\n return jnp.pad(x, npad, constant_values=1.)\n \n B = jtu.tree_map(pad, B)\n \n def get_log_likelihood(obs_t: list[Array], A: list[Array]) -> list[Array]:\n # mapping over batch dimension\n return vmap(compute_log_likelihood_per_modality)(obs_t, A)\n\n # mapping over time dimension of obs array\n log_likelihoods = vmap(get_log_likelihood, (0, None))(obs, A) # this gives a sequence of log-likelihoods (one for each `t`)\n \n def scan_fn(carry: tuple[list[Array], list[Array]], iter: tuple[list[Array], list[Array]]) -> tuple[tuple[list[Array], list[Array]], list[Array]]:\n _, prior = carry\n Bs, ln_As = iter\n\n post, pred, cond = variational_filtering_step(prior, Bs, ln_As, A_dependencies)\n \n return (post, pred), cond\n\n init = (prior, prior)\n iterator = (B, log_likelihoods)\n # get q_T(s_t), p_T(s_{t+1}) and the history q_{T}(s_{t}|s_{t+1})q_{T-1}(s_{t-1}|s_{t}) ...\n (qs, ps), qss = lax.scan(scan_fn, init, iterator)\n\n return qs, ps, qss\n\ndef get_vmp_messages(\n ln_B: list[Array] | None,\n B: list[Array] | None,\n qs: list[Array],\n ln_prior: list[Array],\n B_dependencies: list[list[int]],\n transition_valid_mask: Array | None = None,\n) -> tuple[list[Array], list[Array]]:\n \n num_factors = len(qs)\n factors = list(range(num_factors))\n get_deps_forw = lambda x, f_idx: [x[f][:-1] for f in f_idx]\n get_deps_back = lambda x, f_idx: [x[f][1:] for f in f_idx]\n\n T = qs[0].shape[0]\n if transition_valid_mask is None:\n transition_valid_mask = jnp.ones((max(T - 1, 0),), dtype=bool)\n transition_valid_mask = transition_valid_mask.astype(bool)\n start_mask = jnp.concatenate(\n [jnp.ones((1,), dtype=bool), jnp.logical_not(transition_valid_mask)],\n axis=0,\n )\n\n def forward(ln_b: Array, ln_prior: Array, f: int) -> Array:\n dims = tuple((0, 2 + i) for i in range(len(B_dependencies[f])))\n msg = factor_dot_flex(ln_b, get_deps_forw(qs, B_dependencies[f]), dims, keep_dims=(0, 1))\n msg = jnp.where(transition_valid_mask[:, None], msg, 0.0)\n # Append the prior as the t=0 forward message so the result has length T.\n # With window masks, start_mask also resets masked boundary timesteps to the prior.\n msg = jnp.concatenate([jnp.expand_dims(ln_prior, 0), msg], axis=0)\n prior_msg = jnp.broadcast_to(jnp.expand_dims(ln_prior, 0), msg.shape)\n return jnp.where(start_mask[:, None], prior_msg, msg)\n \n def backward(ln_bs: list[Array], xs: list[Array]) -> Array:\n msg = 0.0\n for ln_b, x in zip(ln_bs, xs):\n msg += vmap(lambda q, b: q @ b)(x, ln_b)\n\n msg = jnp.where(transition_valid_mask[:, None], msg, 0.0)\n return jnp.pad(msg, ((0, 1), (0, 0)))\n\n def marg(inv_deps: list[int], f: int) -> list[Array]:\n ln_B_marg = []\n for i in inv_deps:\n idxs = []\n dims = []\n for j, d in enumerate(B_dependencies[i]):\n if d != f:\n idxs.append(d)\n dims.append((0, 2 + j))\n\n if idxs:\n keep_dims = (0, 1, 2 + B_dependencies[i].index(f))\n ln_B_marg.append(\n factor_dot_flex(\n ln_B[i],\n get_deps_forw(qs, idxs),\n tuple(dims),\n keep_dims=keep_dims,\n )\n )\n else:\n ln_B_marg.append(ln_B[i])\n\n return ln_B_marg\n\n if ln_B is not None:\n inv_B_deps = [[i for i, deps in enumerate(B_dependencies) if f in deps] for f in factors]\n ln_B_marg = jtu.tree_map(lambda f: marg(inv_B_deps[f], f), factors)\n lnB_future = jtu.tree_map(forward, ln_B, ln_prior, factors)\n lnB_past = jtu.tree_map(\n lambda f: backward(ln_B_marg[f], get_deps_back(qs, inv_B_deps[f])),\n factors,\n )\n else:\n lnB_future = jtu.tree_map(lambda x: 0., qs)\n lnB_past = jtu.tree_map(lambda x: 0., qs)\n \n return lnB_future, lnB_past \n\ndef run_vmp(\n A: list[Array],\n B: list[Array] | None,\n obs: list[Array],\n prior: list[Array],\n A_dependencies: list[list[int]],\n B_dependencies: list[list[int]],\n num_iter: int = 1,\n tau: float = 1.0,\n distr_obs: bool = True,\n obs_valid_mask: Array | None = None,\n transition_valid_mask: Array | None = None,\n) -> list[Array]:\n \"\"\"Run variational message passing over a sequence window.\n\n Parameters are identical to :func:`run_mmp`.\n\n Returns\n -------\n list[Array]\n Sequence posterior beliefs per hidden-state factor (same structure as\n :func:`run_mmp`).\n \"\"\"\n\n qs = update_marginals(\n get_vmp_messages,\n obs,\n A,\n B,\n prior,\n A_dependencies,\n B_dependencies,\n num_iter=num_iter,\n tau=tau,\n distr_obs=distr_obs,\n obs_valid_mask=obs_valid_mask,\n transition_valid_mask=transition_valid_mask,\n )\n return qs\n\ndef get_mmp_messages(\n ln_B: list[Array] | None,\n B: list[Array] | None,\n qs: list[Array],\n ln_prior: list[Array],\n B_deps: list[list[int]],\n transition_valid_mask: Array | None = None,\n) -> tuple[list[Array], list[Array]]:\n \n num_factors = len(qs)\n factors = list(range(num_factors))\n\n get_deps_forw = lambda x, f_idx: [x[f][:-1] for f in f_idx]\n get_deps_back = lambda x, f_idx: [x[f][1:] for f in f_idx]\n\n T = qs[0].shape[0]\n if transition_valid_mask is None:\n transition_valid_mask = jnp.ones((max(T - 1, 0),), dtype=bool)\n transition_valid_mask = transition_valid_mask.astype(bool)\n start_mask = jnp.concatenate(\n [jnp.ones((1,), dtype=bool), jnp.logical_not(transition_valid_mask)],\n axis=0,\n )\n outgoing_valid = jnp.concatenate(\n [transition_valid_mask, jnp.zeros((1,), dtype=bool)],\n axis=0,\n )\n\n def forward(b: Array, ln_prior: Array, f: int) -> Array:\n xs = get_deps_forw(qs, B_deps[f])\n dims = tuple((0, 2 + i) for i in range(len(B_deps[f])))\n msg = log_stable(factor_dot_flex(b, xs, dims, keep_dims=(0, 1) ))\n msg = jnp.where(transition_valid_mask[:, None], msg, 0.0)\n # Append the prior as the t=0 forward message so the result has length T.\n # With window masks, start_mask also resets masked boundary timesteps to the prior.\n msg = jnp.concatenate([jnp.expand_dims(ln_prior, 0), msg], axis=0)\n prior_msg = jnp.broadcast_to(jnp.expand_dims(ln_prior, 0), msg.shape)\n msg = jnp.where(start_mask[:, None], prior_msg, msg)\n # In MMP each valid transition contributes via both forward and backward terms.\n # We assign half-weight here (and half in backward below) so each edge is counted once.\n msg = msg * jnp.where(outgoing_valid[:, None], 0.5, 1.0)\n return msg\n \n def backward(Bs: list[Array], xs: list[Array]) -> Array:\n msg = 0.\n for i, b in enumerate(Bs):\n b_norm = b / jnp.clip(b.sum(-1, keepdims=True), min=MINVAL)\n # Complementary half-weight to the forward pass above.\n msg += log_stable(vmap(lambda x, y: y @ x)(b_norm, xs[i])) * .5\n\n msg = jnp.where(transition_valid_mask[:, None], msg, 0.0)\n return jnp.pad(msg, ((0, 1), (0, 0)))\n\n def marg(inv_deps: list[int], f: int) -> list[Array]:\n B_marg = []\n for i in inv_deps:\n b = B[i]\n keep_dims = (0, 1, 2 + B_deps[i].index(f))\n dims = []\n idxs = []\n for j, d in enumerate(B_deps[i]):\n if f != d:\n dims.append((0, 2 + j))\n idxs.append(d)\n xs = get_deps_forw(qs, idxs)\n B_marg.append( factor_dot_flex(b, xs, tuple(dims), keep_dims=keep_dims) )\n \n return B_marg\n\n if B is not None:\n inv_B_deps = [[i for i, d in enumerate(B_deps) if f in d] for f in factors]\n B_marg = jtu.tree_map(lambda f: marg(inv_B_deps[f], f), factors)\n lnB_future = jtu.tree_map(forward, B, ln_prior, factors) \n lnB_past = jtu.tree_map(lambda f: backward(B_marg[f], get_deps_back(qs, inv_B_deps[f])), factors)\n else: \n lnB_future = jtu.tree_map(lambda x: jnp.expand_dims(x, 0), ln_prior)\n lnB_past = jtu.tree_map(lambda x: 0., qs)\n\n return lnB_future, lnB_past\n\ndef run_mmp(\n A: list[Array],\n B: list[Array] | None,\n obs: list[Array],\n prior: list[Array],\n A_dependencies: list[list[int]],\n B_dependencies: list[list[int]],\n num_iter: int = 1,\n tau: float = 1.0,\n distr_obs: bool = True,\n obs_valid_mask: Array | None = None,\n transition_valid_mask: Array | None = None,\n) -> list[Array]:\n \"\"\"Run marginal message passing over a sequence window.\n\n Parameters\n ----------\n A : list[Array]\n Model likelihood tensors.\n B : list[Array] | None\n Transition tensors (or `None` for static-state models).\n obs : list[Array]\n Observation sequence per modality.\n prior : list[Array]\n Sequence prior over hidden states.\n A_dependencies : list[list[int]]\n Sparse observation dependencies per modality.\n B_dependencies : list[list[int]]\n Sparse transition dependencies per factor.\n num_iter : int, default=1\n Number of variational update iterations.\n tau : float, default=1.0\n Mirror-descent step size.\n distr_obs : bool, default=True\n Whether observations are already distributional.\n obs_valid_mask : Array | None, optional\n Optional validity mask for padded observation windows.\n transition_valid_mask : Array | None, optional\n Optional validity mask for transitions in padded windows.\n\n Returns\n -------\n list[Array]\n Sequence posterior beliefs per hidden-state factor.\n \"\"\"\n qs = update_marginals(\n get_mmp_messages,\n obs,\n A,\n B,\n prior,\n A_dependencies,\n B_dependencies,\n num_iter=num_iter,\n tau=tau,\n distr_obs=distr_obs,\n obs_valid_mask=obs_valid_mask,\n transition_valid_mask=transition_valid_mask,\n )\n return qs\n\ndef run_online_filtering(\n A: list[Array],\n B: list[Array],\n obs: list[Array],\n prior: list[Array],\n A_dependencies: list[list[int]],\n num_iter: int = 1,\n tau: float = 1.0,\n) -> list[Array]:\n \"\"\"Runs online filtering (HAVE TO REPLACE WITH OVF CODE)\"\"\"\n qs = update_marginals(get_mmp_messages, obs, A, B, prior, A_dependencies, num_iter=num_iter, tau=tau)\n return qs \n\n\n# Infer states hybrid & hybrid block\n\ndef run_factorized_fpi_hybrid(\n log_likelihoods: list[Array],\n prior: list[Array],\n A_dependencies: list[list[int]],\n num_iter: int,\n) -> list[Array]:\n \n log_prior = jtu.tree_map(log_stable, prior)\n log_q = jtu.tree_map(jnp.zeros_like, prior)\n\n def scan_fn(carry: list[Array], t: Array) -> tuple[list[Array], None]:\n log_q = carry\n q = jtu.tree_map(nn.softmax, log_q)\n marginal_ll = all_marginal_log_likelihood(q, log_likelihoods, A_dependencies)\n log_q = jtu.tree_map(add, marginal_ll, log_prior)\n return log_q, None\n\n res, _ = lax.scan(scan_fn, log_q, jnp.arange(num_iter))\n qs = jtu.tree_map(nn.softmax, res)\n \n return jtu.tree_map(lambda x: jnp.expand_dims(x, 0), qs)\n\n# Infer states end2end padded\n\ndef get_qs_padded(qs: list[Array], max_state_dim: int) -> list[Array]:\n qs_padded = []\n for q in qs:\n qs_padded.append(jnp.zeros((q.shape[0], max_state_dim)).at[:, 0:q.shape[1]].set(q))\n return qs_padded\n\ndef compute_qL_marginals(\n lls_padded: Array, qs_padded: list[Array], A_dependencies: list[list[int]], max_state_dim: int\n) -> list[list[Array]]:\n\n dp_dict = {}\n qL_marginals_padded = [[] for i in range(len(A_dependencies))]\n \n for i, A_dep in enumerate(A_dependencies):\n \n if len(A_dep) == 1:\n \n qL_marginals_padded[i].append(lls_padded[i])\n \n else:\n \n for j in range(len(A_dep)):\n \n axes_factors = tuple((axis, factor) for axis, factor in enumerate(A_dep) if j != axis)\n \n existing_key = None\n for sublen in range(len(axes_factors), 0, -1):\n if axes_factors[:sublen] in dp_dict:\n existing_key = axes_factors[:sublen]\n break\n \n new_key = () if existing_key is None else existing_key\n offset = 0 if existing_key is None else len(existing_key)\n curr_prod = lls_padded if existing_key is None else dp_dict[existing_key]\n \n for axis, factor in axes_factors[offset:]:\n new_key = new_key + ((axis, factor),)\n q_reshaped = qs_padded[factor].reshape(\n [1, lls_padded.shape[1]] + [max_state_dim if k == axis else 1 for k in range(lls_padded.ndim - 2)]\n )\n curr_prod = curr_prod * q_reshaped\n dp_dict[new_key] = curr_prod\n\n qL_marginals_padded[i].append(\n dp_dict[axes_factors][i].sum(\n axis=[axis + 1 for axis, _ in axes_factors]\n )\n )\n\n return qL_marginals_padded\n\ndef qL_flatten(qL_marginals_padded: list[list[Array]]) -> list[list[Array]]:\n \n qL_marginals = []\n for _qs in qL_marginals_padded:\n qL_marginals.append([])\n for _q in _qs:\n idx = (slice(0, _q.shape[0]), slice(0, _q.shape[1])) + tuple(0 for _ in range(_q.ndim - 2))\n qL_marginals[-1].append(_q[idx])\n \n return qL_marginals\n\ndef compute_qL_all(\n qL_marginals: list[list[Array]], A_dependencies: list[list[int]], num_factors: int\n) -> list[Array]:\n\n qL_all = [jnp.zeros_like(qL_marginals[0][0])] * num_factors\n \n for m, factor_list_m in enumerate(A_dependencies):\n for l, f in enumerate(factor_list_m):\n qL_all[f] += qL_marginals[m][l]\n\n return qL_all\n\ndef run_factorized_fpi_end2end_padded(\n lls_padded: Array,\n prior: list[Array],\n A_dependencies: list[list[int]],\n max_obs_dim: int,\n max_state_dim: int,\n num_iter: int,\n) -> list[Array]:\n \n log_prior = jtu.tree_map(log_stable, prior)\n log_q = jtu.tree_map(jnp.zeros_like, prior)\n\n def scan_fn(carry: list[Array], t: Array) -> tuple[list[Array], None]:\n \n log_q = carry\n q = jtu.tree_map(nn.softmax, log_q)\n \n qs_padded = get_qs_padded(q, max_state_dim)\n qL_marginals_padded = compute_qL_marginals(lls_padded, qs_padded, A_dependencies, max_state_dim)\n qL_flat = qL_flatten(qL_marginals_padded)\n qL_all = compute_qL_all(qL_flat, A_dependencies, len(q))\n \n log_q = jtu.tree_map(lambda q, lp: q[:, 0:lp.shape[1]] + lp, qL_all, log_prior)\n \n return log_q, None\n\n res, _ = lax.scan(scan_fn, log_q, jnp.arange(num_iter))\n qs = jtu.tree_map(nn.softmax, res)\n\n return jtu.tree_map(lambda x: jnp.expand_dims(x, 1), qs)\n\nclass FilterMessage(NamedTuple):\n # A: conditional transition-like matrix for the segment\n A: Array # (..., K, K)\n # log_b: log normalizer term (per left-boundary state)\n log_b: Array # (..., K)\n\n\ndef _normalize_preserve_zeros(u: Array,\n axis: int = -1,\n eps: float = 1e-15) -> Tuple[Array, Array]:\n \"\"\"\n Normalize along `axis` while preserving exact structural zeros and flooring tiny\n positive values to improve gradient stability in near-degenerate regimes.\n\n Returns normalized tensor and the (safe) normalization factor with `axis` squeezed.\n \"\"\"\n eps = jnp.asarray(eps, dtype=u.dtype)\n u_safe = jnp.where(u == 0, 0, jnp.where(u < eps, eps, u))\n c = jnp.sum(u_safe, axis=axis, keepdims=True)\n c_safe = jnp.where(c == 0, jnp.ones_like(c), c)\n return u_safe / c_safe, jnp.squeeze(c_safe, axis=axis)\n\n\ndef _log_predictive_normalizer(predicted_probs: Array,\n log_likelihoods: Array) -> Array:\n \"\"\"\n Compute log c_t = log p(x_t | x_{1:t-1}) in a stable way for each timestep.\n \"\"\"\n ll_max = jnp.max(log_likelihoods, axis=-1, keepdims=True)\n stable_weights = jnp.exp(log_likelihoods - ll_max)\n return log_stable(jnp.sum(predicted_probs * stable_weights, axis=-1)) + ll_max.squeeze(-1)\n\ndef _condition_on(A: Array,\n ll: Array,\n axis: int = -1) -> Tuple[Array, Array]:\n \"\"\"\n Condition a transition-like object A on log-likelihood ll in a numerically stable way.\n\n Works for:\n - A shape (K,) with ll shape (K,) (initial probs)\n - A shape (K,K) with ll shape (K,) (transition rows/cols)\n - and batched versions via broadcasting when ll is 1D.\n \"\"\"\n ll = jnp.asarray(ll)\n ll_max = jnp.max(ll, axis=-1)\n w = jnp.exp(ll - ll_max)\n\n if A.ndim == 1:\n A_cond, norm = _normalize_preserve_zeros(A * w, axis=0)\n return A_cond, log_stable(norm) + ll_max\n\n axis = axis if axis >= 0 else A.ndim + axis\n shape = [1] * A.ndim\n shape[axis] = w.shape[-1]\n w_b = w.reshape(shape)\n\n A_cond, norm = _normalize_preserve_zeros(A * w_b, axis=axis)\n return A_cond, log_stable(norm) + ll_max\n\n\ndef _hmm_filter_scan_row_oriented(\n initial_probs: Array,\n transition_mats: Array,\n log_likelihoods: Array,\n) -> tuple[Array, Array, Array]:\n \"\"\"\n Core row-oriented HMM filtering via associative scan.\n\n Parameters\n ----------\n initial_probs:\n Initial state distribution `p(s_0)` with shape `(K,)`.\n transition_mats:\n Transition tensors with row orientation `p(s_{t+1}=j | s_t=i)`.\n Can be `(K, K)` or `(T-1, K, K)`.\n log_likelihoods:\n Log likelihoods `log p(o_t | s_t)` with shape `(T, K)`.\n\n Returns\n -------\n marginal_loglik:\n Scalar `log p(o_{1:T})`.\n filtered_probs:\n `(T, K)` filtered beliefs `p(s_t | o_{1:t})`.\n predicted_probs:\n `(T, K)` one-step-ahead predictive prior\n `p(s_t | o_{1:t-1})` with `predicted_probs[0] = initial_probs`.\n \"\"\"\n T, K = log_likelihoods.shape\n if transition_mats.ndim == 2:\n # Use identical transition matrix for all timesteps when stationary.\n transition_mats = jnp.broadcast_to(transition_mats, (T - 1, K, K))\n\n @vmap\n def _marginalize(\n m_ij: FilterMessage, m_jk: FilterMessage\n ) -> FilterMessage:\n # Combine segment i->j with segment j->k by summing out the intermediate state.\n A_ij_cond, lognorm = _condition_on(m_ij.A, m_jk.log_b)\n A_ik = _matmul_high_precision(A_ij_cond, m_jk.A)\n log_b_ik = m_ij.log_b + lognorm\n return FilterMessage(A=A_ik, log_b=log_b_ik)\n\n A0_vec, log_b0_scalar = _condition_on(initial_probs, log_likelihoods[0])\n A0 = jnp.broadcast_to(A0_vec, (K, K))\n log_b0 = jnp.broadcast_to(log_b0_scalar, (K,))\n A1T, log_b1T = vmap(_condition_on, in_axes=(0, 0))(transition_mats, log_likelihoods[1:])\n\n partial = lax.associative_scan(\n _marginalize,\n FilterMessage(\n A=jnp.concatenate([A0[None, :, :], A1T], axis=0),\n log_b=jnp.concatenate([log_b0[None, :], log_b1T], axis=0),\n ),\n )\n\n marginal_loglik = partial.log_b[-1, 0]\n filtered_probs = partial.A[:, 0, :]\n\n if T == 1:\n predicted_probs = initial_probs[None, :]\n else:\n pred_next = vmap(_matmul_high_precision)(filtered_probs[:-1], transition_mats)\n predicted_probs = jnp.concatenate([initial_probs[None, :], pred_next], axis=0)\n\n return marginal_loglik, filtered_probs, predicted_probs\n\n\ndef hmm_filter_scan_rowstoch(\n initial_probs: Array,\n transition_mats: Array,\n log_likelihoods: Array,\n) -> tuple[Array, Array, Array]:\n \"\"\"\n Exact HMM filtering via `lax.associative_scan` for row-stochastic transitions.\n\n This variant uses the standard row-stochastic convention\n `transition_mats[t, i, j] = p(z_{t+1}=j | z_t=i)`.\n\n Parameters\n ------\n initial_probs:\n Initial state distribution `p(s_0)`.\n transition_mats:\n Row-stochastic transitions, stationary `(K, K)` or time-varying\n `(T-1, K, K)`.\n log_likelihoods:\n Sequence log likelihoods with shape `(T, K)`.\n\n Returns\n -------\n (marginal_loglik, filtered_probs, predicted_probs)\n \"\"\"\n return _hmm_filter_scan_row_oriented(initial_probs, transition_mats, log_likelihoods)\n\n\ndef _hmm_smoother_scan_row_oriented(\n initial_probs: Array,\n transition_mats: Array,\n log_likelihoods: Array,\n) -> tuple[Array, Array, Array, Array, Array, Array]:\n \"\"\"\n Core row-oriented HMM filtering + smoothing via associative scans.\n\n Computes:\n - filtered marginals using the forward scan\n - smoothed marginals with a suffix scan\n - pairwise transition posteriors `p(s_t, s_{t+1} | o_{1:T})`\n - `p(s_t | s_{t+1}, o_{1:T})` in pymdp-style conditional orientation\n \"\"\"\n T, K = log_likelihoods.shape\n marginal_loglik, filtered, predicted = _hmm_filter_scan_row_oriented(\n initial_probs, transition_mats, log_likelihoods\n )\n\n # log-normaliser c_t = p(o_t | o_{1:t-1}), used to stabilize backward factors.\n log_c = _log_predictive_normalizer(predicted, log_likelihoods)\n if T == 1:\n beta = jnp.ones((1, K))\n else:\n # Build backward matrices M_t = A_t * diag(exp(ll_{t+1} - c_{t+1}))\n # that propagate the vector beta_{t+1} -> beta_t.\n col_scale = jnp.exp(log_likelihoods[1:] - log_c[1:][:, None])\n M = transition_mats * col_scale[:, None, :]\n\n def op(x: Array, y: Array) -> Array:\n # batched matmul works; associative_scan may call this with leading batch dims\n return _matmul_high_precision(y, x)\n\n # suffix-style associative scan via reverse + reverse-back\n beta = lax.associative_scan(op, M[::-1])[::-1]\n beta = vmap(lambda P_t: _matmul_high_precision(P_t, jnp.ones((K,))))(beta)\n beta = jnp.concatenate([beta, jnp.ones((1, K))], axis=0)\n\n # p(s_t | o_{1:T}) = p(s_t | o_{1:t}) * beta_t\n smoothed = filtered * beta\n smoothed = smoothed / jnp.clip(jnp.sum(smoothed, axis=-1, keepdims=True), min=MINVAL)\n\n if T == 1:\n trans_probs = jnp.zeros((0, K, K))\n cond_probs = jnp.zeros((0, K, K))\n else:\n xi = (\n filtered[:-1, :, None] *\n transition_mats *\n col_scale[:, None, :] *\n beta[1:, None, :]\n )\n xi = xi / jnp.clip(jnp.sum(xi, axis=(1, 2), keepdims=True), min=MINVAL)\n trans_probs = xi\n cond_probs = xi.transpose(0, 2, 1) / jnp.clip(smoothed[1:, :, None], min=MINVAL)\n\n return marginal_loglik, filtered, predicted, smoothed, trans_probs, cond_probs\n\n\ndef hmm_smoother_scan_rowstoch(\n initial_probs: Array,\n transition_mats: Array,\n log_likelihoods: Array,\n) -> tuple[Array, Array, Array, Array, Array, Array]:\n \"\"\"\n Exact HMM filtering + smoothing via associative scans for row-stochastic transitions.\n\n Parameters\n ------\n initial_probs:\n Initial distribution `p(s_0)`.\n transition_mats:\n Row-stochastic transitions, stationary `(K, K)` or time-varying `(T-1, K, K)`.\n log_likelihoods:\n `(T, K)` log-likelihood matrix.\n\n Returns\n -------\n (marginal_loglik, filtered_probs, predicted_probs, smoothed_probs, trans_probs, cond_probs)\n \"\"\"\n return _hmm_smoother_scan_row_oriented(\n initial_probs, transition_mats, log_likelihoods\n )\n\n\ndef hmm_filter_scan_colstoch(\n initial_probs: Array,\n B_mats: Array,\n log_likelihoods: Array,\n) -> tuple[Array, Array, Array]:\n \"\"\"\n Exact HMM filtering via `lax.associative_scan` for column-stochastic transitions.\n\n This is the pymdp-native transition orientation:\n `B_mats[t, j, i] = p(z_{t+1}=j | z_t=i)`.\n\n Parameters\n ------\n initial_probs:\n Initial distribution `p(s_0)`.\n B_mats:\n Column-stochastic transitions, stationary `(K, K)` or time-varying `(T-1, K, K)`.\n log_likelihoods:\n `(T, K)` log-likelihood matrix.\n\n Returns\n -------\n (marginal_loglik, filtered_probs, predicted_probs)\n \"\"\"\n return _hmm_filter_scan_row_oriented(\n initial_probs,\n jnp.swapaxes(B_mats, -1, -2),\n log_likelihoods,\n )\n\n\ndef hmm_smoother_scan_colstoch(\n initial_probs: Array,\n B_mats: Array,\n log_likelihoods: Array,\n return_trans_probs: bool = False,\n) -> tuple[Any, ...]:\n \"\"\"\n Exact HMM filtering + smoothing via associative scans for column-stochastic transitions.\n\n Parameters\n ------\n initial_probs:\n Initial distribution `p(s_0)`.\n B_mats:\n Column-stochastic transitions, stationary `(K, K)` or time-varying `(T-1, K, K)`.\n In this orientation `B_mats[t, j, i] = p(s_{t+1}=j | s_t=i)`.\n log_likelihoods:\n `(T, K)` log-likelihood matrix.\n return_trans_probs:\n If `True`, includes pairwise transition posterior\n `p(s_t, s_{t+1} | o_{1:T})`.\n\n Returns\n -------\n tuple\n If `return_trans_probs=False`, returns\n `(marginal_loglik, filtered_probs, predicted_probs, smoothed_probs, cond_probs)`.\n If `True`, returns\n `(marginal_loglik, filtered_probs, predicted_probs, smoothed_probs, trans_probs, cond_probs)`.\n \"\"\"\n marginal_loglik, filtered_probs, predicted_probs = hmm_filter_scan_colstoch(\n initial_probs,\n B_mats,\n log_likelihoods,\n )\n smoothed_probs, _, cond_probs, trans_probs = hmm_smoother_from_filtered_colstoch(\n filtered_probs,\n B_mats,\n return_trans_probs=True,\n )\n\n if return_trans_probs:\n return (\n marginal_loglik,\n filtered_probs,\n predicted_probs,\n smoothed_probs,\n trans_probs,\n cond_probs,\n )\n return (\n marginal_loglik,\n filtered_probs,\n predicted_probs,\n smoothed_probs,\n cond_probs,\n )\n\n\ndef hmm_smoother_from_filtered_colstoch(\n filtered_probs: Array,\n B_mats: Array,\n return_trans_probs: bool = False,\n) -> tuple[Any, ...]:\n \"\"\"\n Exact HMM smoothing from precomputed filtering marginals for column-stochastic transitions.\n\n This routine is intended for online agent loops where filtering is computed one step at a\n time during observe-infer-act cycles, and backward smoothing is only needed at learning time.\n\n Args\n ----\n filtered_probs:\n `(T, K)` filtering marginals with `filtered_probs[t] = p(z_t | x_{1:t})`.\n B_mats:\n - `(K_next, K_curr)` stationary column-stochastic transitions, or\n - `(T-1, K_next, K_curr)` time-varying transitions.\n return_trans_probs:\n If `True`, also return pairwise posteriors in `(T-1, K_curr, K_next)` orientation.\n\n Returns\n -------\n Always returned:\n smoothed_probs: `(T, K)` with `p(z_t | x_{1:T})`.\n joint_next_curr: `(T-1, K_next, K_curr)` with\n `joint_next_curr[t, j, i] = p(z_{t+1}=j, z_t=i | x_{1:T})`.\n cond_probs: `(T-1, K_next, K_curr)` with\n `cond_probs[t, j, i] = p(z_t=i | z_{t+1}=j, x_{1:T})`.\n Additionally returned when `return_trans_probs=True`:\n trans_probs: `(T-1, K_curr, K_next)` with\n `trans_probs[t, i, j] = p(z_t=i, z_{t+1}=j | x_{1:T})`.\n \"\"\"\n T, K = filtered_probs.shape\n\n if B_mats.ndim == 2:\n B_mats = jnp.broadcast_to(B_mats, (max(T - 1, 0), K, K))\n elif B_mats.ndim == 3:\n expected_steps = max(T - 1, 0)\n if B_mats.shape[0] != expected_steps:\n raise ValueError(\n f\"B_mats has leading dimension {B_mats.shape[0]}, expected {expected_steps} for T={T}\"\n )\n else:\n raise ValueError(\"B_mats must be 2D or 3D\")\n\n if T == 1:\n smoothed = filtered_probs\n joint_next_curr = jnp.zeros((0, K, K))\n cond_probs = jnp.zeros((0, K, K))\n trans_probs = jnp.zeros((0, K, K))\n if return_trans_probs:\n return smoothed, joint_next_curr, cond_probs, trans_probs\n return smoothed, joint_next_curr, cond_probs\n\n predicted_next = vmap(_matmul_high_precision)(B_mats, filtered_probs[:-1]) # (T-1, K_next)\n\n cond_probs = (\n B_mats * filtered_probs[:-1][:, None, :]\n ) / jnp.clip(predicted_next[:, :, None], min=MINVAL) # (T-1, K_next, K_curr)\n\n # smoothed_t = cond_t^T @ smoothed_{t+1}\n M = cond_probs.transpose(0, 2, 1) # (T-1, K_curr, K_next)\n R = M[::-1]\n\n def op(x: Array, y: Array) -> Array:\n return _matmul_high_precision(y, x)\n\n P_rev = lax.associative_scan(op, R) # cumulative products from the end\n P = P_rev[::-1]\n\n q_last = filtered_probs[-1]\n smoothed_prefix = vmap(lambda P_t: _matmul_high_precision(P_t, q_last))(P) # (T-1, K)\n smoothed = jnp.concatenate([smoothed_prefix, q_last[None, :]], axis=0)\n smoothed = smoothed / jnp.clip(jnp.sum(smoothed, axis=-1, keepdims=True), min=MINVAL)\n\n joint_next_curr = cond_probs * smoothed[1:, :, None] # (T-1, K_next, K_curr)\n trans_probs = joint_next_curr.transpose(0, 2, 1) # (T-1, K_curr, K_next)\n\n if return_trans_probs:\n return smoothed, joint_next_curr, cond_probs, trans_probs\n return smoothed, joint_next_curr, cond_probs\n\ndef run_exact_single_factor_hmm_scan(\n obs: list[Array],\n A: list[Array],\n B: list[Array],\n prior: list[Array],\n actions: Array | None = None,\n distr_obs: bool = True,\n) -> tuple[Array, list[Array], list[Array], list[Array]]:\n \"\"\"\n pymdp-style single-factor wrapper around the column-stochastic scan smoother.\n\n Notes\n -----\n - `A`, `B`, and `prior` are expected as singleton lists (one hidden-state factor).\n - `B[0]` must be in pymdp-native column-stochastic orientation:\n `(K_next, K_curr[, n_actions])` (no transpose required).\n - Returns `(mll, qs, ps, qss)` with `qss[0]` equal to\n `p(z_t | z_{t+1}, x_{1:T})` in `(T-1, K_next, K_curr)` orientation.\n \"\"\"\n if len(prior) != 1 or len(B) != 1:\n raise ValueError(\"run_exact_single_factor_hmm_scan expects singleton lists for prior and B\")\n\n T = obs[0].shape[0]\n pi = prior[0] # (K,)\n B0 = B[0] # (K_next, K_curr[, n_actions]) or (T-1, K_next, K_curr)\n K = pi.shape[0]\n\n if B0.ndim == 2:\n B_seq = B0\n elif B0.ndim == 3:\n looks_time_varying = B0.shape[0] == max(T - 1, 0) and B0.shape[1] == K and B0.shape[2] == K\n if actions is not None:\n actions = jnp.asarray(actions)\n if actions.ndim == 2:\n if actions.shape[-1] == 1:\n actions = actions[:, 0]\n else:\n raise ValueError(\"single-factor scan expects actions with shape (T-1,) or (T-1, 1)\")\n if actions.ndim != 1:\n raise ValueError(\"single-factor scan expects actions with shape (T-1,) or (T-1, 1)\")\n if actions.shape[0] != max(T - 1, 0):\n raise ValueError(\n f\"actions has length {actions.shape[0]} but expected {max(T - 1, 0)} for T={T}\"\n )\n B_seq = vmap(lambda u: B0[:, :, u])(actions.astype(jnp.int32)) # (T-1, K_next, K_curr)\n elif looks_time_varying:\n B_seq = B0\n elif T <= 1:\n # No transition is needed when there is only one observation.\n B_seq = B0[:, :, 0]\n else:\n raise ValueError(\n \"actions must be provided when B has an action dimension and T > 1\"\n )\n else:\n raise ValueError(\"B[0] must be 2D or 3D\")\n\n # log_likelihoods[t] = log p(o_t | z_t) => (T, K)\n # vmap over time dimension of obs pytree\n ll = vmap(lambda obs_t: compute_log_likelihood(obs_t, A, distr_obs=distr_obs))(obs)\n\n mll, q_filt, q_pred, q_smooth, q_t_given_next = hmm_smoother_scan_colstoch(pi, B_seq, ll)\n\n # Return in pymdp-ish packaging (list per factor)\n qs = [q_smooth]\n ps = [q_pred]\n qss = [q_t_given_next] # shape (T-1, K_next, K_curr)\n\n return mll, qs, ps, qss\n\n\nif __name__ == \"__main__\":\n prior = [jnp.ones(2)/2, jnp.ones(2)/2, nn.softmax(jnp.array([0, -80., -80., -80, -80.]))]\n obs = [nn.one_hot(0, 5), nn.one_hot(5, 10)]\n A = [jnp.ones((5, 2, 2, 5))/5, jnp.ones((10, 2, 2, 5))/10]\n \n qs = jit(run_vanilla_fpi)(A, obs, prior)\n\n # test if differentiable\n\n def sum_prod(prior: list[Array]) -> Array:\n qs = jnp.concatenate(run_vanilla_fpi(A, obs, prior))\n return (qs * log_stable(qs)).sum()\n\n print(jit(grad(sum_prod))(prior))\n\n # def sum_prod(precision):\n # # prior = [jnp.ones(2)/2, jnp.ones(2)/2, nn.softmax(log_prior)]\n # prior = [jnp.ones(2)/2, jnp.ones(2)/2, nn.softmax(precision*nn.one_hot(0, 5))]\n # qs = jnp.concatenate(run_vanilla_fpi(A, obs, prior))\n # return (qs * log_stable(qs)).sum()\n\n # precis_to_test = 1.\n # print(jit(grad(sum_prod))(precis_to_test))\n\n # log_prior = jnp.array([0, -80., -80., -80, -80.])\n # print(jit(grad(sum_prod))(log_prior))\n" }, { "path": "pymdp/control.py", "content": "#!/usr/bin/env python\n# -*- coding: utf-8 -*-\n# pylint: disable=no-member\n# pylint: disable=not-an-iterable\n\"\"\"Policy construction, expected free energy, and action sampling utilities.\"\"\"\n\nimport itertools\nimport jax.numpy as jnp\nimport jax.tree_util as jtu\nfrom typing import Sequence\nfrom functools import partial\nfrom jax import lax, vmap, nn\nfrom jax import random as jr\nfrom jaxtyping import Array\n\nimport equinox as eqx\n\nfrom pymdp.maths import factor_dot, log_stable, stable_entropy, stable_xlogx, spm_wnorm\nfrom pymdp import utils\n\nclass Policies(eqx.Module):\n \"\"\" \n A class for storing an array of policies and its properties\n \n \"\"\"\n policy_arr: Array\n horizon: int = eqx.field(static=True)\n num_policies: int = eqx.field(static=True)\n\n def __init__(self, policy_arr: Array) -> None:\n self.num_policies = policy_arr.shape[0]\n self.horizon = policy_arr.shape[1]\n self.policy_arr = policy_arr\n \n def __getitem__(self, idx: int) -> Array:\n return self.policy_arr[idx]\n \n def __len__(self) -> int:\n return self.num_policies\n \ndef get_marginals(q_pi: Array, policies: Array, num_controls: Sequence[int]) -> list[Array]:\n \"\"\"\n Computes the marginal posterior(s) over actions by integrating their posterior probability under the policies that they appear within.\n\n Parameters\n ----------\n q_pi: 1D Array\n Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.\n policies: Array\n Policy matrix with shape `(num_policies, policy_len, num_factors)`.\n num_controls: Sequence[int]\n Dimensionalities of each control state factor.\n \n Returns\n ----------\n action_marginals: list[Array]\n Marginal posterior over actions for each control factor.\n \"\"\"\n num_factors = len(num_controls) \n\n action_marginals = []\n for factor_i in range(num_factors):\n actions = jnp.arange(num_controls[factor_i])[:, None]\n action_marginals.append(jnp.where(actions==policies[:, 0, factor_i], q_pi, 0).sum(-1))\n \n return action_marginals\n\ndef sample_action(\n policies: Array,\n num_controls: Sequence[int],\n q_pi: Array,\n action_selection: str = \"deterministic\",\n alpha: float = 16.0,\n rng_key: Array | None = None,\n) -> Array:\n \"\"\"\n Samples an action from posterior marginals, one action per control factor.\n\n Parameters\n ----------\n q_pi: 1D Array\n Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.\n policies: Array\n Policy matrix with shape `(num_policies, policy_len, num_factors)`.\n num_controls: Sequence[int]\n Dimensionalities of each control state factor.\n action_selection: string, default \"deterministic\"\n String indicating whether whether the selected action is chosen as the maximum of the posterior over actions,\n or whether it's sampled from the posterior marginal over actions\n alpha: float, default 16.0\n Action selection precision -- the inverse temperature of the softmax that is used to scale the \n action marginals before sampling. This is only used if `action_selection` is `\"stochastic\"`.\n rng_key: Array | None, optional\n PRNG key required when `action_selection='stochastic'`.\n\n Returns\n ----------\n selected_policy: 1D Array\n Vector containing the indices of the actions for each control factor\n \"\"\"\n\n marginal = get_marginals(q_pi, policies, num_controls)\n \n if action_selection == 'deterministic':\n selected_policy = jtu.tree_map(lambda x: jnp.argmax(x, -1), marginal)\n elif action_selection == 'stochastic':\n logits = lambda x: alpha * log_stable(x)\n selected_policy = jtu.tree_map(lambda x: jr.categorical(rng_key, logits(x)), marginal)\n else:\n raise NotImplementedError\n\n return jnp.array(selected_policy)\n\ndef sample_policy(\n policies: Array,\n q_pi: Array,\n action_selection: str = \"deterministic\",\n alpha: float = 16.0,\n rng_key: Array | None = None,\n) -> Array:\n \"\"\"Select or sample a policy, then return its first-step multi-action.\n\n Parameters\n ----------\n policies : Array\n Policy matrix with shape `(num_policies, policy_len, num_factors)`.\n q_pi : Array\n Posterior over policies for one batch element.\n action_selection : {\"deterministic\", \"stochastic\"}, default=\"deterministic\"\n Selection mode for choosing a policy.\n alpha : float, default=16.0\n Precision (inverse temperature) used for stochastic sampling.\n rng_key : Array | None, optional\n PRNG key required for `action_selection='stochastic'`.\n\n Returns\n -------\n Array\n First-step action vector for all control factors.\n \"\"\"\n\n if action_selection == \"deterministic\":\n policy_idx = jnp.argmax(q_pi)\n elif action_selection == \"stochastic\":\n log_p_policies = log_stable(q_pi) * alpha\n policy_idx = jr.categorical(rng_key, log_p_policies)\n\n selected_multiaction = policies[policy_idx, 0]\n return selected_multiaction\n\ndef construct_policies(\n num_states: Sequence[int],\n num_controls: Sequence[int] | None = None,\n policy_len: int = 1,\n control_fac_idx: Sequence[int] | None = None,\n) -> Array:\n \"\"\"\n Generate an exhaustive policy matrix for the specified planning horizon.\n\n Parameters\n ----------\n num_states: Sequence[int]\n Dimensionalities of each hidden state factor.\n num_controls: Sequence[int], default None\n Dimensionalities of each control state factor. If `None`, this is\n computed from controllable state factors.\n policy_len: int, default 1\n temporal depth (\"planning horizon\") of policies\n control_fac_idx: Sequence[int]\n Indices of controllable hidden state factors (factors `i` where `num_controls[i] > 1`).\n\n Returns\n ----------\n policies: Array\n Policy matrix with shape `(num_policies, policy_len, num_factors)`.\n \"\"\"\n\n num_factors = len(num_states)\n if control_fac_idx is None:\n if num_controls is not None:\n control_fac_idx = [f for f, n_c in enumerate(num_controls) if n_c > 1]\n else:\n control_fac_idx = list(range(num_factors))\n\n if num_controls is None:\n num_controls = [num_states[c_idx] if c_idx in control_fac_idx else 1 for c_idx in range(num_factors)]\n \n x = num_controls * policy_len\n policies = list(itertools.product(*[list(range(i)) for i in x]))\n \n for pol_i in range(len(policies)):\n policies[pol_i] = jnp.array(policies[pol_i]).reshape(policy_len, num_factors)\n\n return jnp.stack(policies)\n\n\ndef update_posterior_policies(\n policy_matrix: Array,\n qs_init: list[Array],\n A: list[Array],\n B: list[Array],\n C: list[Array],\n E: Array,\n pA: list[Array] | None,\n pB: list[Array] | None,\n A_dependencies: list[list[int]],\n B_dependencies: list[list[int]],\n gamma: float = 16.0,\n use_utility: bool = True,\n use_states_info_gain: bool = True,\n use_param_info_gain: bool = False,\n) -> tuple[Array, Array]:\n \"\"\"Compute posterior over policies and policy-wise negative expected free energy.\n\n Notes\n -----\n The returned policy score is `neg_efe = -EFE`. This same quantity is\n often denoted by `G`.\n\n Parameters\n ----------\n policy_matrix: Array\n Policy tensor with shape `(num_policies, policy_len, num_factors)`.\n qs_init: list[Array]\n Current marginal beliefs over hidden states.\n A: list[Array]\n Observation likelihood tensors.\n B: list[Array]\n Transition tensors.\n C: list[Array]\n Prior preferences over observations.\n E: Array\n Prior over policies.\n pA: list[Array] | None\n Optional posterior Dirichlet parameters for `A`. When\n `use_param_info_gain=True`, provide `pA`, `pB`, or both.\n pB: list[Array] | None\n Optional posterior Dirichlet parameters for `B`. When\n `use_param_info_gain=True`, provide `pA`, `pB`, or both.\n A_dependencies: list[list[int]]\n Observation dependencies between modalities and hidden-state factors.\n B_dependencies: list[list[int]]\n Transition dependencies between hidden-state factors.\n gamma: float, default=16.0\n Policy precision parameter.\n use_utility: bool, default=True\n Whether to include expected utility in EFE.\n use_states_info_gain: bool, default=True\n Whether to include state epistemic value.\n use_param_info_gain: bool, default=False\n Whether to include parameter epistemic value.\n\n Returns\n -------\n tuple[Array, Array]\n `(q_pi, neg_efe_all_policies)` where `q_pi` is the posterior over policies.\n \"\"\"\n if use_param_info_gain and pA is None and pB is None:\n raise ValueError(\n \"use_param_info_gain=True requires at least one of pA or pB.\"\n )\n\n # policy --> n_levels_factor_f x 1\n # factor --> n_levels_factor_f x n_policies\n ## vmap across policies\n compute_neg_efe_fixed_states = partial(\n compute_neg_efe_policy,\n qs_init,\n A,\n B,\n C,\n pA,\n pB,\n A_dependencies,\n B_dependencies,\n use_utility=use_utility,\n use_states_info_gain=use_states_info_gain,\n use_param_info_gain=use_param_info_gain,\n )\n\n # only in the case of policy-dependent qs_inits\n # in_axes_list = (1,) * n_factors\n # all_neg_efe_of_policies = vmap(compute_neg_efe_policy, in_axes=(in_axes_list, 0))(qs_init_pi, policy_matrix)\n\n # policies needs to be an NDarray of shape (n_policies, n_timepoints, n_control_factors)\n neg_efe_all_policies = vmap(compute_neg_efe_fixed_states)(policy_matrix)\n\n return nn.softmax(gamma * neg_efe_all_policies + log_stable(E)), neg_efe_all_policies\n\ndef compute_expected_state(\n qs_prior: list[Array],\n B: list[Array],\n u_t: Array | Sequence[int],\n B_dependencies: list[list[int]] | None = None,\n) -> list[Array]:\n \"\"\"\n Compute posterior over next state, given belief about previous state, transition model and action...\n\n Parameters\n ----------\n qs_prior: list[Array]\n Marginal beliefs over hidden states at time `t`.\n B: list[Array]\n Transition model tensors.\n u_t: Array | Sequence[int]\n Action indices for each control factor.\n B_dependencies: list[list[int]], optional\n Optional dependencies used to marginalize transition tensors. If `None`,\n defaults to factor-local transitions.\n\n Returns\n -------\n list[Array]\n Marginal beliefs over next-time hidden states.\n \"\"\"\n #Note: this algorithm is only correct if each factor depends only on itself. For any interactions, \n # we will have empirical priors with codependent factors. \n assert len(u_t) == len(B)\n if B_dependencies is None:\n B_dependencies = utils.resolve_b_dependencies(len(B))\n qs_next = []\n for B_f, u_f, deps in zip(B, u_t, B_dependencies):\n relevant_factors = [qs_prior[idx] for idx in deps]\n qs_next_f = factor_dot(B_f[...,u_f], relevant_factors, keep_dims=(0,))\n qs_next.append(qs_next_f)\n \n # P(s'|s, u) = \\sum_{s, u} P(s'|s) P(s|u) P(u|pi)P(pi) because u pi\n return qs_next\n\ndef compute_expected_state_and_Bs(\n qs_prior: list[Array], B: list[Array], u_t: Array | Sequence[int]\n) -> tuple[list[Array], list[Array]]:\n \"\"\"Compute one-step predictive states and selected transition matrices.\n\n Parameters\n ----------\n qs_prior: list[Array]\n Marginal beliefs over hidden states at time `t`.\n B: list[Array]\n Transition model tensors for each hidden-state factor.\n u_t: Array | Sequence[int]\n Action indices for each control factor at time `t`.\n\n Returns\n -------\n tuple[list[Array], list[Array]]\n `(qs_next, Bs)` where `qs_next` are next-state marginals and `Bs` are\n the action-conditioned transition slices used for each factor.\n \"\"\"\n assert len(u_t) == len(B) \n qs_next = []\n Bs = []\n for qs_f, B_f, u_f in zip(qs_prior, B, u_t):\n qs_next.append( B_f[..., u_f].dot(qs_f) )\n Bs.append(B_f[..., u_f])\n \n return qs_next, Bs\n\ndef compute_expected_obs(\n qs: list[Array], A: list[Array], A_dependencies: list[list[int]]\n) -> list[Array]:\n \"\"\"\n New version of expected observation (computation of Q(o|pi)) that takes into account sparse dependencies between observation\n modalities and hidden state factors\n\n Parameters\n ----------\n qs: list[Array]\n Beliefs over hidden states.\n A: list[Array]\n Observation likelihood models.\n A_dependencies: list[list[int]]\n Observation dependencies between modalities and state factors.\n\n Returns\n -------\n list[Array]\n Predictive beliefs over observations for each modality.\n \"\"\"\n \n def compute_expected_obs_modality(A_m: Array, m: int) -> Array:\n deps = A_dependencies[m]\n relevant_factors = [qs[idx] for idx in deps]\n return factor_dot(A_m, relevant_factors, keep_dims=(0,))\n\n return jtu.tree_map(compute_expected_obs_modality, A, list(range(len(A))))\n\ndef compute_info_gain(\n qs: list[Array], qo: list[Array], A: list[Array], A_dependencies: list[list[int]]\n) -> Array:\n \"\"\"Compute expected state-information gain term of expected free energy.\n\n Parameters\n ----------\n qs: list[Array]\n Predicted hidden-state beliefs.\n qo: list[Array]\n Predicted observation beliefs.\n A: list[Array]\n Observation likelihood tensors.\n A_dependencies: list[list[int]]\n Observation dependencies between modalities and hidden-state factors.\n\n Returns\n -------\n Array\n Scalar epistemic value from expected information gain.\n \"\"\"\n\n def compute_info_gain_for_modality(qo_m: Array, A_m: Array, m: int) -> Array:\n H_qo = stable_entropy(qo_m)\n H_A_m = - stable_xlogx(A_m).sum(0)\n deps = A_dependencies[m]\n relevant_factors = [qs[idx] for idx in deps]\n qs_H_A_m = factor_dot(H_A_m, relevant_factors)\n return H_qo - qs_H_A_m\n \n info_gains_per_modality = jtu.tree_map(compute_info_gain_for_modality, qo, A, list(range(len(A))))\n \n return jtu.tree_reduce(lambda x,y: x+y, info_gains_per_modality)\n\ndef compute_expected_utility(qo: list[Array], C: list[Array], t: int = 0) -> Array:\n \"\"\"Compute expected utility from predictive observations and preferences.\n\n Parameters\n ----------\n qo: list[Array]\n Predicted observations for each modality.\n C: list[Array]\n Prior preferences per modality. Each modality can be static `(num_obs,)`\n or time-indexed `(policy_len, num_obs)`.\n t: int, default=0\n Planning timestep used when `C[m]` is time-indexed.\n\n Returns\n -------\n Array\n Scalar expected utility contribution.\n \"\"\"\n\n util = 0.\n for o_m, C_m in zip(qo, C):\n if C_m.ndim > 1:\n util += (o_m * C_m[t]).sum()\n else:\n util += (o_m * C_m).sum()\n \n return util\n\ndef calc_negative_pA_info_gain(\n pA: list[Array], qo: list[Array], qs: list[Array], A_dependencies: list[list[int]]\n) -> Array:\n \"\"\"\n Compute the negative expected Dirichlet information gain about `pA`.\n\n Notes\n -----\n This helper returns the negative of the parameter epistemic-value term.\n Subtract its return value when adding parameter information gain to\n `neg_efe`.\n\n Parameters\n ----------\n pA: list[Array]\n Dirichlet parameters over observation model (same shape as `A`).\n qo: list[Array]\n Predictive posterior beliefs over observations; stores the beliefs about\n observations expected under the policy at some arbitrary time `t`.\n qs: list[Array]\n Predictive posterior beliefs over hidden states, stores the beliefs about\n hidden states expected under the policy at some arbitrary time `t`.\n\n Returns\n -------\n neg_infogain_pA: Array\n Negative expected information gain (scalar JAX array) for the pair of\n predictive distributions `qo` and `qs`.\n \"\"\"\n\n def infogain_per_modality(pa_m: Array, qo_m: Array, m: int) -> Array:\n wa_m = spm_wnorm(pa_m) * (pa_m > 0.)\n relevant_factors = [qs[idx] for idx in A_dependencies[m]]\n fd = factor_dot(wa_m, relevant_factors, keep_dims=(0,))[..., None]\n return qo_m.dot(fd)\n\n pA_neg_infogain_per_modality = jtu.tree_map(\n infogain_per_modality, pA, qo, list(range(len(qo)))\n )\n \n neg_infogain_pA = jtu.tree_reduce(lambda x, y: x + y, pA_neg_infogain_per_modality)\n return neg_infogain_pA.squeeze(-1)\n\ndef calc_negative_pB_info_gain(\n pB: list[Array],\n qs_t: list[Array],\n qs_t_minus_1: list[Array],\n B_dependencies: list[list[int]],\n u_t_minus_1: Array | Sequence[int],\n) -> Array:\n \"\"\"\n Compute the negative expected Dirichlet information gain about `pB`.\n\n Notes\n -----\n This helper returns the negative of the parameter epistemic-value term.\n Subtract its return value when adding parameter information gain to\n `neg_efe`.\n\n Parameters\n ----------\n pB: list[Array]\n Dirichlet parameters over transition model (same shape as `B`).\n qs_t: list[Array]\n Predictive posterior beliefs over hidden states expected under the\n policy at time `t`.\n qs_t_minus_1: list[Array]\n Posterior over hidden states at time `t-1` (before receiving\n observations).\n B_dependencies: list[list[int]]\n For each state factor, indices of the state factors that its\n transition model depends on.\n u_t_minus_1: Array | Sequence[int]\n Actions in time step t-1 for each factor.\n\n Returns\n -------\n neg_infogain_pB: Array\n Negative expected information gain (scalar JAX array) under the\n policy in question.\n \"\"\"\n \n wB = lambda pb: spm_wnorm(pb) * (pb > 0.)\n fd = lambda x, i: factor_dot(\n x,\n [qs_t_minus_1[idx] for idx in B_dependencies[i]],\n keep_dims=(0,),\n )[..., None]\n \n pB_neg_infogain_per_factor = jtu.tree_map(lambda pb, qs, f: qs.dot(fd(wB(pb[..., u_t_minus_1[f]]), f)), pB, qs_t, list(range(len(qs_t))))\n neg_infogain_pB = jtu.tree_reduce(lambda x, y: x + y, pB_neg_infogain_per_factor)[0]\n return neg_infogain_pB\n\ndef compute_neg_efe_policy(\n qs_init: list[Array],\n A: list[Array],\n B: list[Array],\n C: list[Array],\n pA: list[Array] | None,\n pB: list[Array] | None,\n A_dependencies: list[list[int]],\n B_dependencies: list[list[int]],\n policy_i: Array,\n use_utility: bool = True,\n use_states_info_gain: bool = True,\n use_param_info_gain: bool = False,\n) -> Array:\n \"\"\"Compute policy-wise negative expected free energy for one policy.\n\n Notes\n -----\n This function computes `neg_efe = -EFE` for a single policy. This policy\n score (`neg_efe`) is commonly denoted `G`.\n\n Parameters\n ----------\n qs_init: list[Array]\n Initial hidden-state marginals at current timestep.\n A: list[Array]\n Observation likelihood tensors.\n B: list[Array]\n Transition tensors.\n C: list[Array]\n Prior preferences over observations.\n pA: list[Array] | None\n Optional posterior Dirichlet parameters for `A`. When\n `use_param_info_gain=True`, provide `pA`, `pB`, or both.\n pB: list[Array] | None\n Optional posterior Dirichlet parameters for `B`. When\n `use_param_info_gain=True`, provide `pA`, `pB`, or both.\n A_dependencies: list[list[int]]\n Observation dependencies between modalities and hidden-state factors.\n B_dependencies: list[list[int]]\n Transition dependencies between hidden-state factors.\n policy_i: Array\n Single policy trajectory with shape `(policy_len, num_factors)`.\n use_utility: bool, default=True\n Include expected utility term.\n use_states_info_gain: bool, default=True\n Include state-information-gain term.\n use_param_info_gain: bool, default=False\n Include parameter-information-gain term.\n\n Returns\n -------\n Array\n Scalar negative expected free energy for `policy_i`.\n \"\"\"\n if use_param_info_gain and pA is None and pB is None:\n raise ValueError(\n \"use_param_info_gain=True requires at least one of pA or pB.\"\n )\n\n def scan_body(carry: tuple[list[Array], Array], t: Array) -> tuple[tuple[list[Array], Array], None]:\n\n qs, neg_efe = carry\n\n qs_next = compute_expected_state(qs, B, policy_i[t], B_dependencies)\n\n qo = compute_expected_obs(qs_next, A, A_dependencies)\n\n info_gain = compute_info_gain(qs_next, qo, A, A_dependencies) if use_states_info_gain else 0.\n\n utility = compute_expected_utility(qo, C, t) if use_utility else 0.\n\n neg_param_info_gain = 0.\n if pA is not None:\n neg_param_info_gain += calc_negative_pA_info_gain(pA, qo, qs_next, A_dependencies) if use_param_info_gain else 0.\n if pB is not None:\n neg_param_info_gain += calc_negative_pB_info_gain(pB, qs_next, qs, B_dependencies, policy_i[t]) if use_param_info_gain else 0.\n\n neg_efe += info_gain + utility - neg_param_info_gain\n\n return (qs_next, neg_efe), None\n\n qs = qs_init\n neg_efe = 0.\n final_state, _ = lax.scan(scan_body, (qs, neg_efe), jnp.arange(policy_i.shape[0]))\n qs_final, neg_efe = final_state\n return neg_efe\n\ndef compute_neg_efe_policy_inductive(\n qs_init: list[Array],\n A: list[Array],\n B: list[Array],\n C: list[Array],\n pA: list[Array] | None,\n pB: list[Array] | None,\n A_dependencies: list[list[int]],\n B_dependencies: list[list[int]],\n I: list[Array],\n policy_i: Array,\n inductive_epsilon: float = 1e-3,\n use_utility: bool = True,\n use_states_info_gain: bool = True,\n use_param_info_gain: bool = False,\n use_inductive: bool = False,\n) -> Array:\n \"\"\"\n Compute policy-wise negative expected free energy with inductive planning.\n\n Notes\n -----\n This function computes `neg_efe = -EFE` for a single policy with optional\n inductive-value terms. This score is commonly denoted `G`, so here\n `G = neg_efe = -EFE`.\n\n Parameters\n ----------\n qs_init: list[Array]\n Initial hidden-state marginals at current timestep.\n A: list[Array]\n Observation likelihood tensors.\n B: list[Array]\n Transition tensors.\n C: list[Array]\n Prior preferences over observations.\n pA: list[Array] | None\n Optional posterior Dirichlet parameters for `A`. When\n `use_param_info_gain=True`, provide `pA`, `pB`, or both.\n pB: list[Array] | None\n Optional posterior Dirichlet parameters for `B`. When\n `use_param_info_gain=True`, provide `pA`, `pB`, or both.\n A_dependencies: list[list[int]]\n Observation dependencies between modalities and hidden-state factors.\n B_dependencies: list[list[int]]\n Transition dependencies between hidden-state factors.\n I: list[Array]\n Inductive reachability matrices.\n policy_i: Array\n Single policy trajectory with shape `(policy_len, num_factors)`.\n inductive_epsilon: float, default=1e-3\n Scale of the inductive-value contribution.\n use_utility: bool, default=True\n Include expected utility term.\n use_states_info_gain: bool, default=True\n Include state-information-gain term.\n use_param_info_gain: bool, default=False\n Include parameter-information-gain term.\n use_inductive: bool, default=False\n Include inductive-value term.\n\n Returns\n -------\n Array\n Scalar negative expected free energy for `policy_i`.\n \"\"\"\n if use_param_info_gain and pA is None and pB is None:\n raise ValueError(\n \"use_param_info_gain=True requires at least one of pA or pB.\"\n )\n\n def scan_body(carry: tuple[list[Array], Array], t: Array) -> tuple[tuple[list[Array], Array], None]:\n\n qs, neg_efe = carry\n\n qs_next = compute_expected_state(qs, B, policy_i[t], B_dependencies)\n\n qo = compute_expected_obs(qs_next, A, A_dependencies)\n\n info_gain = compute_info_gain(qs_next, qo, A, A_dependencies) if use_states_info_gain else 0.\n\n utility = compute_expected_utility(qo, C, t) if use_utility else 0.\n\n # Keep inductive admissibility anchored to the starting-state belief\n # across the rollout to preserve current policy-scoring semantics.\n inductive_value = calc_inductive_value_t(qs_init, qs_next, I, epsilon=inductive_epsilon) if use_inductive else 0.\n\n neg_param_info_gain = 0.\n if pA is not None:\n neg_param_info_gain += calc_negative_pA_info_gain(pA, qo, qs_next, A_dependencies) if use_param_info_gain else 0.\n if pB is not None:\n neg_param_info_gain += calc_negative_pB_info_gain(pB, qs_next, qs, B_dependencies, policy_i[t]) if use_param_info_gain else 0.\n\n neg_efe += info_gain + utility - neg_param_info_gain + inductive_value\n\n return (qs_next, neg_efe), None\n\n qs = qs_init\n neg_efe = 0.\n final_state, _ = lax.scan(scan_body, (qs, neg_efe), jnp.arange(policy_i.shape[0]))\n _, neg_efe = final_state\n return neg_efe\n\ndef update_posterior_policies_inductive(\n policy_matrix: Array,\n qs_init: list[Array],\n A: list[Array],\n B: list[Array],\n C: list[Array],\n E: Array,\n pA: list[Array] | None,\n pB: list[Array] | None,\n A_dependencies: list[list[int]],\n B_dependencies: list[list[int]],\n I: list[Array],\n gamma: float = 16.0,\n inductive_epsilon: float = 1e-3,\n use_utility: bool = True,\n use_states_info_gain: bool = True,\n use_param_info_gain: bool = False,\n use_inductive: bool = True,\n) -> tuple[Array, Array]:\n \"\"\"\n Compute policy posterior and negative expected free energy with optional\n inductive terms.\n\n Notes\n -----\n The returned policy score is `neg_efe = -EFE`. This same quantity is\n often denoted by `G`.\n\n Parameters\n ----------\n policy_matrix: Array\n Policy tensor with shape `(num_policies, policy_len, num_factors)`.\n qs_init: list[Array]\n Current marginal state beliefs.\n A: list[Array]\n Observation likelihood models.\n B: list[Array]\n Transition models.\n C: list[Array]\n Prior preference vectors.\n E: Array\n Policy prior over the policy space.\n pA: list[Array] | None\n Optional posterior Dirichlet parameters for `A`. When\n `use_param_info_gain=True`, provide `pA`, `pB`, or both.\n pB: list[Array] | None\n Optional posterior Dirichlet parameters for `B`. When\n `use_param_info_gain=True`, provide `pA`, `pB`, or both.\n A_dependencies: list[list[int]]\n Observation dependencies between modalities and state factors.\n B_dependencies: list[list[int]]\n Transition dependencies between hidden-state factors and control factors.\n I: list[Array]\n Inductive planning matrices.\n gamma: float = 16.0\n Policy precision for softmax policy posterior.\n inductive_epsilon: float = 1e-3\n Inductive value scale factor.\n use_utility: bool = True\n Include utility term in expected free energy.\n use_states_info_gain: bool = True\n Include epistemic state-information gain term.\n use_param_info_gain: bool = False\n Include epistemic parameter-information gain term.\n use_inductive: bool = True\n Include inductive value term.\n\n Returns\n -------\n q_pi: Array\n Posterior over policies.\n neg_efe_all_policies: Array\n Policy-wise negative expected free energies.\n \"\"\"\n if use_param_info_gain and pA is None and pB is None:\n raise ValueError(\n \"use_param_info_gain=True requires at least one of pA or pB.\"\n )\n\n # policy --> n_levels_factor_f x 1\n # factor --> n_levels_factor_f x n_policies\n ## vmap across policies\n compute_neg_efe_fixed_states = partial(\n compute_neg_efe_policy_inductive,\n qs_init,\n A,\n B,\n C,\n pA,\n pB,\n A_dependencies,\n B_dependencies,\n I,\n inductive_epsilon=inductive_epsilon,\n use_utility=use_utility,\n use_states_info_gain=use_states_info_gain,\n use_param_info_gain=use_param_info_gain,\n use_inductive=use_inductive,\n )\n\n # only in the case of policy-dependent qs_inits\n # in_axes_list = (1,) * n_factors\n # all_neg_efe_of_policies = vmap(compute_neg_efe_policy, in_axes=(in_axes_list, 0))(qs_init_pi, policy_matrix)\n\n # policies needs to be an NDarray of shape (n_policies, n_timepoints, n_control_factors)\n neg_efe_all_policies = vmap(compute_neg_efe_fixed_states)(policy_matrix)\n\n return nn.softmax(gamma * neg_efe_all_policies + log_stable(E)), neg_efe_all_policies\n\ndef generate_I_matrix(H: list[Array], B: list[Array], threshold: float, depth: int) -> list[Array]:\n \"\"\" \n Generate inductive reachability matrices using backward state reachability.\n\n These matrices store whether state `j` (columns) can still reach the\n intended state set after `i` backward steps (rows).\n Parameters\n ---------- \n H: list[Array]\n Constraints over desired states (1 if you want to reach that state, 0 otherwise)\n B: list[Array]\n Dynamics likelihood mapping or transition model, mapping from hidden states at `t` to hidden states at `t+1`, given some control state `u`.\n Each element `B[f]` stores a 3-D tensor for hidden state factor `f`, whose entries `B[f][s, v, u]` store the probability\n of hidden state level `s` at the current time, given hidden state level `v` and action `u` at the previous time.\n threshold: float\n The threshold for pruning transitions that are below a certain probability\n depth: int\n The temporal depth of the backward induction\n\n Returns\n ----------\n I: list[Array]\n For each state factor, contains a 2D indicator array whose element\n `i, j` is `1` when state `j` can still reach the intended state set\n after `i` backward steps, and `0` otherwise.\n \"\"\"\n if depth < 1:\n raise ValueError(\"`depth` must be >= 1\")\n \n num_factors = len(H)\n I = []\n for f in range(num_factors):\n # Compute backward reachability separately for each hidden-state factor.\n\n # If there exists an action that allows transitioning from\n # previous_state to next_state with probability above threshold,\n # set reachable_next_prev[next_state, previous_state] to 1.\n reachable_next_prev = jnp.where(B[f] > threshold, 1.0, 0.0).sum(axis=-1)\n reachable_next_prev = jnp.where(reachable_next_prev > 0.0, 1.0, 0.0)\n predecessor_reachable = jnp.swapaxes(reachable_next_prev, 0, 1)\n\n def step_fn(carry: Array, _: Array) -> tuple[Array, Array]:\n I_prev = carry\n # Predecessor states are allowed if they can reach any currently\n # allowed successor state.\n I_next = jnp.dot(predecessor_reachable, I_prev)\n I_next = jnp.where(I_next > 0.0, 1.0, 0.0)\n return I_next, I_next\n \n _, I_f = lax.scan(step_fn, H[f], jnp.arange(depth-1))\n I_f = jnp.concatenate([H[f][None,...], I_f], axis=0)\n\n I.append(I_f)\n \n return I\n\ndef calc_inductive_value_t(\n qs: list[Array], qs_next: list[Array], I: list[Array], epsilon: float = 1e-3\n) -> Array:\n \"\"\"\n Computes the inductive value of a state at a particular time (translation of @tverbele's `numpy` implementation of inductive planning, formerly\n called `calc_inductive_cost`).\n\n Parameters\n ----------\n qs: list[Array]\n Marginal posterior beliefs over hidden states at a given timepoint.\n qs_next: list[Array]\n Predictive posterior beliefs over hidden states expected under the policy.\n I: list[Array]\n For each state factor, contains a 2D array whose element i,j yields the probability\n of reaching the goal state backwards from state j after i steps.\n epsilon: float\n Value that tunes the strength of the inductive value (how much it contributes to the expected free energy of policies)\n\n Returns\n -------\n inductive_val: float\n Value (negative inductive cost) of visiting this state using backwards induction under the policy in question\n \"\"\"\n \n # initialise inductive value\n inductive_val = 0.\n\n log_eps = log_stable(epsilon)\n for f in range(len(qs)):\n # we also assume precise beliefs here?!\n idx = jnp.argmax(qs[f])\n # m = arg max_n p_n < sup p\n\n # i.e. find first entry at which I_idx equals 1, and then m is the index before that\n m = jnp.maximum(jnp.argmax(I[f][:, idx])-1, 0)\n I_m = (1. - I[f][m, :]) * log_eps\n path_available = jnp.clip(I[f][:, idx].sum(0), min=0, max=1) # if there are any 1's at all in that column of I, then this == 1, otherwise 0\n inductive_val += path_available * I_m.dot(qs_next[f]) # scaling by path_available will nullify the addition of inductive value in the case we find no path to goal (i.e. when no goal specified)\n\n return inductive_val\n\n# if __name__ == '__main__':\n\n# from jax import random as jr\n# key = jr.PRNGKey(1)\n# num_obs = [3, 4]\n\n# A = [jr.uniform(key, shape = (no, 2, 2)) for no in num_obs]\n# B = [jr.uniform(key, shape = (2, 2, 2)), jr.uniform(key, shape = (2, 2, 2))]\n# C = [log_stable(jnp.array([0.8, 0.1, 0.1])), log_stable(jnp.ones(4)/4)]\n# policy_1 = jnp.array([[0, 1],\n# [1, 1]])\n# policy_2 = jnp.array([[1, 0],\n# [0, 0]])\n# policy_matrix = jnp.stack([policy_1, policy_2]) # 2 x 2 x 2 tensor\n \n# qs_init = [jnp.ones(2)/2, jnp.ones(2)/2]\n# neg_efe_all_policies = jit(update_posterior_policies)(policy_matrix, qs_init, A, B, C)\n# print(neg_efe_all_policies)\n" }, { "path": "pymdp/distribution.py", "content": "import numpy as np\nfrom pymdp.utils import norm_dist\nfrom typing import Any, Iterator, Optional\n\n\nclass Distribution:\n\n def __init__(self, event: dict, batch: dict = {}, data: np.ndarray | None = None) -> None:\n self.event = event\n self.batch = batch\n\n self.event_indices = {\n key: {v: i for i, v in enumerate(values)}\n for key, values in event.items()\n }\n self.batch_indices = {\n key: {v: i for i, v in enumerate(values)}\n for key, values in batch.items()\n }\n\n if data is not None:\n self._data = data\n else:\n shape = []\n for v in event.values():\n shape.append(len(v))\n for v in batch.values():\n shape.append(len(v))\n self._data = np.zeros(shape)\n\n @property\n def data(self) -> np.ndarray:\n return self._data\n\n @data.setter\n def data(self, value: np.ndarray) -> None:\n if hasattr(self, '_data') and self._data is not None:\n if self._data.shape != value.shape:\n raise ValueError(f\"When setting the tensor directly, the new shape {value.shape} must match the existing tensor shape {self._data.shape}\")\n self._data = value\n\n def get(self, batch: dict | None = None, event: dict | None = None) -> np.ndarray:\n event_slices = self._get_slices(event, self.event_indices, self.event)\n batch_slices = self._get_slices(batch, self.batch_indices, self.batch)\n\n slices = event_slices + batch_slices\n return self._data[tuple(slices)]\n\n def set(\n self, batch: dict | None = None, event: dict | None = None, values: np.ndarray | float | int | None = None\n ) -> None:\n event_slices = self._get_slices(event, self.event_indices, self.event)\n batch_slices = self._get_slices(batch, self.batch_indices, self.batch)\n\n slices = event_slices + batch_slices\n self._data[tuple(slices)] = values\n\n def _get_slices(self, keys: dict | None, indices: dict, full_indices: dict) -> list[Any]:\n slices = []\n if keys is None:\n return [slice(None)] * len(full_indices)\n for key in full_indices:\n if key in keys:\n if isinstance(keys[key], list):\n slices.append(\n [self._get_index(v, indices[key]) for v in keys[key]]\n )\n else:\n slices.append(self._get_index(keys[key], indices[key]))\n else:\n slices.append(slice(None))\n return slices\n\n def _get_index(self, key: Any, index_map: dict) -> int:\n if isinstance(key, int):\n return key\n else:\n return index_map[key]\n\n def _get_index_from_axis(self, axis: int, element: Any) -> int | slice:\n if isinstance(element, slice):\n return slice(None)\n if axis < len(self.event):\n key = list(self.event.keys())[axis]\n index_map = self.event_indices[key]\n else:\n key = list(self.batch.keys())[axis - len(self.event)]\n index_map = self.batch_indices[key]\n return self._get_index(element, index_map)\n\n def __getitem__(self, indices: Any) -> np.ndarray:\n if not isinstance(indices, tuple):\n indices = (indices,)\n index_list = [\n self._get_index_from_axis(i, idx) for i, idx in enumerate(indices)\n ]\n return self._data[tuple(index_list)]\n\n def __setitem__(self, indices: Any, value: Any) -> None:\n if not isinstance(indices, tuple):\n indices = (indices,)\n index_list = [\n self._get_index_from_axis(i, idx) for i, idx in enumerate(indices)\n ]\n self._data[tuple(index_list)] = value\n\n def normalize(self) -> None:\n self.data = norm_dist(self.data)\n\n def __repr__(self) -> str:\n return f\"Distribution({self.event}, {self.batch})\\n {self.data}\"\n\n\nclass DistributionIndexer(dict):\n \"\"\"\n Helper class to allow for indexing of distributions by their event keys.\n Acts as a list otherwise ...\n \"\"\"\n\n def __init__(self, distributions: list[Distribution]) -> None:\n super().__init__()\n self.distributions = distributions\n for d in distributions:\n for key in d.event:\n self[key] = d\n\n def __getitem__(self, key: str | int) -> Distribution:\n if isinstance(key, int):\n return self.distributions[key]\n else:\n if key not in self.keys():\n raise KeyError(\n f\"Key {key} not found in \" + str([k for k in self.keys()])\n )\n return super().__getitem__(key)\n\n def __iter__(self) -> Iterator[Distribution]:\n return iter(self.distributions)\n\n\nclass Model(dict):\n\n def __init__(\n self,\n likelihoods: list[Distribution],\n transitions: list[Distribution],\n preferred_observations: list[Distribution],\n priors: list[Distribution],\n preferred_states: list[Distribution],\n B_action_dependencies: Optional[list[list[int]]]=None,\n num_controls: Optional[list[int]]=None,\n ) -> None:\n super().__init__()\n super().__setitem__(\"A\", likelihoods)\n super().__setitem__(\"B\", transitions)\n super().__setitem__(\"C\", preferred_observations)\n super().__setitem__(\"D\", priors)\n super().__setitem__(\"H\", preferred_states)\n super().__setitem__(\"B_action_dependencies\", B_action_dependencies)\n super().__setitem__(\"num_controls\", num_controls)\n\n def __getattr__(self, key: str) -> Any:\n if key in [\"A\", \"B\", \"C\", \"D\", \"H\"]:\n return DistributionIndexer(self[key])\n elif key == \"B_action_dependencies\":\n return self[\"B_action_dependencies\"]\n elif key == \"num_controls\":\n return self[\"num_controls\"]\n raise AttributeError(\"Model only supports attributes A,B,C,D,H, B_action_dependencies, and num_controls\")\n\n\ndef compile_model(config: dict[str, Any]) -> Model:\n \"\"\"Compile a model from a config.\n\n Takes a model description dictionary and builds the corresponding\n Likelihood and Transition tensors. The tensors are filled with only\n zeros and need to be filled in later by the caller of this function.\n ---\n The config should consist of three top-level keys:\n * observations\n * controls\n * states\n where each entry consists of another dictionary with the name of the\n modality as key and the modality description.\n\n The modality description should consist out of either a `size` or `elements`\n field indicating the named elements or the size of the integer array.\n In the case of an observation the `depends_on` field needs to be present to\n indicate what state factor links to this observation. In the case of states\n the `depends_on` and `controlled_by` fields are needed.\n ---\n example config:\n { \"observations\": {\n \"observation_1\": {\"size\": 10, \"depends_on\": [\"factor_1\"]},\n \"observation_2\": {\n \"elements\": [\"A\", \"B\"],\n \"depends_on\": [\"factor_1\"],\n },\n },\n \"controls\": {\n \"control_1\": {\"size\": 2},\n \"control_2\": {\"elements\": [\"X\", \"Y\"]},\n },\n \"states\": {\n \"factor_1\": {\n \"elements\": [\"II\", \"JJ\", \"KK\"],\n \"depends_on\": [\"factor_1\", \"factor_2\"],\n \"controlled_by\": [\"control_1\", \"control_2\"],\n },\n \"factor_2\": {\n \"elements\": [\"foo\", \"bar\"],\n \"depends_on\": [\"factor_2\"],\n \"controlled_by\": [\"control_2\"],\n },\n }}\n \"\"\"\n # these are needed to get the ordering of the dimensions correct for pymdp\n state_dependencies = dict()\n control_dependencies = dict()\n likelihood_dependencies = dict()\n transition_events = dict()\n likelihood_events = dict()\n labels = dict()\n shape = dict()\n for mod in config:\n for k, v in config[mod].items():\n for keyword in v:\n match keyword:\n case \"elements\":\n shape[k] = len(v[keyword])\n labels[k] = [name for name in v[keyword]]\n case \"size\":\n shape[k] = v[keyword]\n labels[k] = list(range(v[keyword]))\n case \"depends_on\":\n if mod == \"states\":\n state_dependencies[k] = [\n name for name in v[keyword]\n ]\n if k in v[keyword]:\n transition_events[k] = labels[k]\n else:\n likelihood_dependencies[k] = [\n name for name in v[keyword]\n ]\n likelihood_events[k] = labels[k]\n case \"controlled_by\":\n control_dependencies[k] = [name for name in v[keyword]]\n\n transitions = []\n for event, description in transition_events.items():\n arr_shape = [len(description)]\n batch_descr = dict()\n event_descr = {event: description}\n for dep in state_dependencies[event]:\n arr_shape.append(shape[dep])\n batch_descr[dep] = labels[dep]\n for dep in control_dependencies[event]:\n arr_shape.append(shape[dep])\n batch_descr[dep] = labels[dep]\n arr = np.zeros(arr_shape)\n transitions.append(Distribution(event_descr, batch_descr, arr))\n\n priors = []\n for event, description in transition_events.items():\n arr_shape = [len(description)]\n arr = np.ones(arr_shape) / len(description)\n event_descr = {event: description}\n priors.append(Distribution(event_descr, data=arr))\n\n likelihoods = []\n for event, description in likelihood_events.items():\n arr_shape = [len(description)]\n batch_descr = dict()\n event_descr = {event: description}\n for dep in likelihood_dependencies[event]:\n arr_shape.append(shape[dep])\n batch_descr[dep] = labels[dep]\n arr = np.zeros(arr_shape)\n likelihoods.append(Distribution(event_descr, batch_descr, arr))\n\n preferred_observations = []\n for event, description in likelihood_events.items():\n arr_shape = [len(description)]\n arr = np.zeros(arr_shape)\n event_descr = {event: description}\n preferred_observations.append(Distribution(event_descr, data=arr))\n\n preferred_states = []\n for event, description in transition_events.items():\n arr_shape = [len(description)]\n arr = np.ones(arr_shape) / len(description)\n event_descr = {event: description}\n preferred_states.append(Distribution(event_descr, data=arr))\n\n B_action_dependencies = [\n [list(config[\"controls\"].keys()).index(i) for i in s[\"controlled_by\"]] \n for s in config[\"states\"].values()\n ]\n\n num_controls = []\n for c in config[\"controls\"].values():\n if \"elements\" in c:\n num_controls.append(len(c[\"elements\"]))\n elif \"size\" in c:\n num_controls.append(int(c[\"size\"]))\n else:\n raise ValueError(f\"Control {c} has no elements or size\")\n\n return Model(\n likelihoods, transitions, preferred_observations, priors, preferred_states, B_action_dependencies, num_controls\n )\n\n\ndef get_dependencies(\n likelihoods: list[Distribution], transitions: list[Distribution]\n) -> tuple[list[list[int]], list[list[int]]]:\n likelihood_dependencies = dict()\n transition_dependencies = dict()\n states = [list(trans.event.keys())[0] for trans in transitions]\n for like in likelihoods:\n likelihood_dependencies[list(like.event.keys())[0]] = [\n states.index(name) for name in like.batch.keys()\n ]\n for trans in transitions:\n transition_dependencies[list(trans.event.keys())[0]] = [\n states.index(name) for name in trans.batch.keys() if name in states\n ]\n return list(likelihood_dependencies.values()), list(\n transition_dependencies.values()\n )\n\n\nif __name__ == \"__main__\":\n controls = [\"up\", \"down\"]\n locations = [\"A\", \"B\", \"C\", \"D\"]\n\n data = np.zeros((len(locations), len(locations), len(controls)))\n transition = Distribution(\n {\"location\": locations},\n {\"location\": locations, \"control\": controls},\n data,\n )\n\n assert transition[\"A\", \"B\", \"up\"] == 0.0\n assert transition[:, \"B\", \"up\"].shape == (4,)\n assert transition[\"A\", \"B\", :].shape == (2,)\n assert transition[:, \"B\", :].shape == (4, 2)\n assert transition[:, :, :].shape == (4, 4, 2)\n assert transition[0, \"B\", 0] == 0.0\n assert transition[:, \"B\", 0].shape == (4,)\n\n transition[\"A\", \"B\", \"up\"] = 0.5\n assert transition[\"A\", \"B\", \"up\"] == 0.5\n transition[:, \"B\", \"up\"] = np.ones(4)\n assert np.all(transition[:, \"B\", \"up\"] == 1.0)\n\n assert transition.get({\"location\": \"A\"}, {\"location\": \"B\"}).shape == (2,)\n assert (\n transition.get({\"location\": \"A\", \"control\": \"up\"}, {\"location\": \"B\"})\n == 0.0\n )\n assert transition.get({\"control\": \"up\"}).shape == (4, 4)\n\n transition.set({\"location\": \"A\", \"control\": \"up\"}, {\"location\": \"B\"}, 0.5)\n assert (\n transition.get({\"location\": \"A\", \"control\": \"up\"}, {\"location\": \"B\"})\n == 0.5\n )\n transition.set({\"location\": 0, \"control\": \"up\"}, {\"location\": \"B\"}, 0.7)\n assert (\n transition.get({\"location\": \"A\", \"control\": \"up\"}, {\"location\": \"B\"})\n == 0.7\n )\n transition.set({\"location\": \"A\"}, {\"location\": \"B\"}, np.ones(2))\n assert np.all(transition.get({\"location\": \"A\"}, {\"location\": \"B\"}) == 1.0)\n\n model_example = {\n \"observations\": {\n \"observation_1\": {\"size\": 10, \"depends_on\": [\"factor_1\"]},\n \"observation_2\": {\n \"elements\": [\"A\", \"B\"],\n \"depends_on\": [\"factor_2\"],\n },\n },\n \"controls\": {\n \"control_1\": {\"size\": 2},\n \"control_2\": {\"elements\": [\"X\", \"Y\"]},\n },\n \"states\": {\n \"factor_1\": {\n \"elements\": [\"II\", \"JJ\", \"KK\"],\n \"depends_on\": [\"factor_1\", \"factor_2\"],\n \"controlled_by\": [\"control_1\", \"control_2\"],\n },\n \"factor_2\": {\n \"elements\": [\"foo\", \"bar\"],\n \"depends_on\": [\"factor_2\"],\n \"controlled_by\": [\"control_2\"],\n },\n },\n }\n model = compile_model(model_example)\n like = model.A\n trans = model.B\n assert len(trans) == 2\n assert len(like) == 2\n assert trans[0].data.shape == (3, 3, 2, 2, 2)\n assert trans[1].data.shape == (2, 2, 2)\n assert like[0].data.shape == (10, 3)\n assert like[1].data.shape == (2, 2)\n assert like[\"observation_1\"][:, \"II\"] is not None\n assert like[\"observation_2\"][1, :] is not None\n A_deps, B_deps = get_dependencies(like, trans)\n print(A_deps, B_deps)\n\n model_description = {\n \"observations\": {\n \"o1\": {\"elements\": [\"A\", \"B\", \"C\", \"D\"], \"depends_on\": [\"s1\"]},\n },\n \"controls\": {\"c1\": {\"elements\": [\"up\", \"down\"]}},\n \"states\": {\n \"s1\": {\n \"elements\": [\"A\", \"B\", \"C\", \"D\"],\n \"depends_on\": [\"s1\"],\n \"controlled_by\": [\"c1\"],\n },\n },\n }\n\n model = compile_model(model_description)\n" }, { "path": "pymdp/envs/__init__.py", "content": "from .tmaze import TMaze, SimplifiedTMaze\nfrom .rollout import rollout\nfrom .env import Env, PymdpEnv, make\nfrom .graph_worlds import GraphEnv\nfrom .grid_world import GridWorld\nfrom .cue_chaining import CueChainingEnv\n" }, { "path": "pymdp/envs/cue_chaining.py", "content": "\"\"\"Cue-chaining grid world implemented as a JAX-compatible ``PymdpEnv``.\n\nThis module ports the legacy cue-chaining demo environment to the modern\nJAX-first environment API. The environment encodes a two-stage epistemic chain:\n\n1. Visiting ``cue1_location`` reveals which second-level cue location is active.\n2. Visiting that active second-level cue location reveals the reward condition.\n3. Visiting one of the reward locations yields reward or punishment depending on\n the latent reward condition.\n\"\"\"\n\nfrom __future__ import annotations\n\nfrom typing import Sequence\n\nimport jax.numpy as jnp\n\nfrom .env import PymdpEnv\n\n\nclass CueChainingEnv(PymdpEnv):\n \"\"\"Grid-world cue-chaining task using factorized categorical dynamics.\n\n Hidden state factors\n --------------------\n - factor 0 (location): flattened grid position\n - factor 1 (cue-2 state): which second-level cue location is informative\n - factor 2 (reward condition): which reward location contains reward\n\n Observation modalities\n ----------------------\n - modality 0 (location): identity observation over location\n - modality 1 (cue-1): null everywhere except at ``cue1_location``, where it\n reveals the active cue-2 state\n - modality 2 (cue-2): null everywhere except at the active cue-2 location,\n where it reveals reward condition\n - modality 3 (reward): null away from reward locations; at reward locations\n yields reward or punishment based on reward condition\n \"\"\"\n\n ACTION_LABELS = (\"UP\", \"DOWN\", \"LEFT\", \"RIGHT\", \"STAY\")\n\n def __init__(\n self,\n grid_shape: tuple[int, int] = (5, 7),\n start_location: tuple[int, int] = (0, 0),\n cue1_location: tuple[int, int] = (2, 0),\n cue2_locations: Sequence[tuple[int, int]] = ((0, 2), (1, 3), (3, 3), (4, 2)),\n reward_locations: Sequence[tuple[int, int]] = ((1, 5), (3, 5)),\n cue2_state: int | None = None,\n reward_condition: int | None = None,\n cue2_names: Sequence[str] | None = None,\n reward_condition_names: Sequence[str] | None = None,\n categorical_obs: bool = False,\n ) -> None:\n \"\"\"Initialize the cue-chaining environment.\n\n Parameters\n ----------\n grid_shape : tuple[int, int], optional\n Number of rows and columns in the grid.\n start_location : tuple[int, int], optional\n Initial agent location.\n cue1_location : tuple[int, int], optional\n Location of the first cue.\n cue2_locations : sequence[tuple[int, int]], optional\n Candidate locations of the second cue. The latent ``cue2_state``\n selects which one is informative in an episode.\n reward_locations : sequence[tuple[int, int]], optional\n Candidate reward locations. Exactly two are supported, matching the\n ``Cheese``/``Shock`` reward observations.\n cue2_state : int | None, optional\n Fixed initial state for factor 1. If ``None``, use a uniform prior.\n reward_condition : int | None, optional\n Fixed initial state for factor 2. If ``None``, use a uniform prior.\n cue2_names : sequence[str] | None, optional\n Labels for cue-2 states. Defaults to ``(\"L1\", \"L2\", ...)``.\n reward_condition_names : sequence[str] | None, optional\n Labels for reward conditions. Defaults to ``(\"TOP\", \"BOTTOM\")``.\n categorical_obs : bool, default=False\n If ``True``, ``reset()`` and ``step()`` emit one-hot categorical\n observation vectors with shape ``(1, num_obs_m)`` for each\n modality. If ``False``, they emit discrete observation indices with\n shape ``(1,)``.\n \"\"\"\n rows, cols = grid_shape\n if rows <= 0 or cols <= 0:\n raise ValueError(\"`grid_shape` must contain strictly positive integers.\")\n if len(cue2_locations) == 0:\n raise ValueError(\"`cue2_locations` must contain at least one location.\")\n if len(reward_locations) != 2:\n raise ValueError(\"`reward_locations` must contain exactly two locations.\")\n\n self.grid_shape = tuple(grid_shape)\n self.start_location = tuple(start_location)\n self.cue1_location = tuple(cue1_location)\n self.cue2_locations = tuple(tuple(c) for c in cue2_locations)\n self.reward_locations = tuple(tuple(r) for r in reward_locations)\n\n for coord in (self.start_location, self.cue1_location):\n self._validate_coord(coord)\n for coord in self.cue2_locations:\n self._validate_coord(coord)\n for coord in self.reward_locations:\n self._validate_coord(coord)\n\n self.num_location_states = rows * cols\n self.num_cue2_states = len(self.cue2_locations)\n self.num_reward_states = len(self.reward_locations)\n\n if cue2_state is not None and not (0 <= cue2_state < self.num_cue2_states):\n raise ValueError(\"`cue2_state` out of bounds for provided `cue2_locations`.\")\n if reward_condition is not None and not (0 <= reward_condition < self.num_reward_states):\n raise ValueError(\"`reward_condition` out of bounds for provided `reward_locations`.\")\n\n if cue2_names is None:\n cue2_names = tuple(f\"L{i + 1}\" for i in range(self.num_cue2_states))\n if len(cue2_names) != self.num_cue2_states:\n raise ValueError(\"`cue2_names` length must match `cue2_locations`.\")\n\n if reward_condition_names is None:\n reward_condition_names = (\"TOP\", \"BOTTOM\")\n if len(reward_condition_names) != self.num_reward_states:\n raise ValueError(\n \"`reward_condition_names` length must match `reward_locations`.\"\n )\n\n self.cue2_names = tuple(cue2_names)\n self.reward_condition_names = tuple(reward_condition_names)\n\n self.location_obs_names = tuple(\n f\"({row}, {col})\" for row in range(rows) for col in range(cols)\n )\n self.cue1_obs_names = (\"Null\",) + self.cue2_names\n self.cue2_obs_names = (\"Null\",) + tuple(\n f\"reward_on_{name.lower()}\" for name in self.reward_condition_names\n )\n self.reward_obs_names = (\"Null\", \"Cheese\", \"Shock\")\n\n self.start_index = self.coords_to_index(self.start_location)\n self.cue1_index = self.coords_to_index(self.cue1_location)\n self.cue2_indices = tuple(self.coords_to_index(coord) for coord in self.cue2_locations)\n self.reward_indices = tuple(\n self.coords_to_index(coord) for coord in self.reward_locations\n )\n\n A, A_dependencies = self._generate_A()\n B, B_dependencies = self._generate_B()\n D = self._generate_D(cue2_state=cue2_state, reward_condition=reward_condition)\n\n super().__init__(\n A=A,\n B=B,\n D=D,\n A_dependencies=A_dependencies,\n B_dependencies=B_dependencies,\n categorical_obs=categorical_obs,\n )\n\n def coords_to_index(self, coord: tuple[int, int]) -> int:\n \"\"\"Convert ``(row, col)`` coordinates to a flattened location index.\"\"\"\n self._validate_coord(coord)\n row, col = coord\n return int(row * self.grid_shape[1] + col)\n\n def index_to_coords(self, index: int) -> tuple[int, int]:\n \"\"\"Convert a flattened location index to ``(row, col)`` coordinates.\"\"\"\n if not (0 <= index < self.num_location_states):\n raise ValueError(\"`index` out of bounds for location state space.\")\n return (index // self.grid_shape[1], index % self.grid_shape[1])\n\n def _validate_coord(self, coord: tuple[int, int]) -> None:\n row, col = coord\n rows, cols = self.grid_shape\n if not (0 <= row < rows and 0 <= col < cols):\n raise ValueError(f\"Coordinate {coord} is outside grid bounds {self.grid_shape}.\")\n\n def _generate_A(self) -> tuple[list[jnp.ndarray], list[list[int]]]:\n num_loc = self.num_location_states\n num_cue2 = self.num_cue2_states\n num_reward = self.num_reward_states\n\n # m0: location observation\n A_loc = jnp.eye(num_loc, dtype=jnp.float32)\n\n # m1: cue-1 observation (null + cue2 labels)\n A_cue1 = jnp.zeros((1 + num_cue2, num_loc, num_cue2), dtype=jnp.float32)\n A_cue1 = A_cue1.at[0, :, :].set(1.0)\n for cue_state in range(num_cue2):\n A_cue1 = A_cue1.at[0, self.cue1_index, cue_state].set(0.0)\n A_cue1 = A_cue1.at[1 + cue_state, self.cue1_index, cue_state].set(1.0)\n\n # m2: cue-2 observation (null + reward condition labels)\n A_cue2 = jnp.zeros((1 + num_reward, num_loc, num_cue2, num_reward), dtype=jnp.float32)\n A_cue2 = A_cue2.at[0, :, :, :].set(1.0)\n for cue_state, cue_loc_idx in enumerate(self.cue2_indices):\n A_cue2 = A_cue2.at[0, cue_loc_idx, cue_state, :].set(0.0)\n for reward_state in range(num_reward):\n A_cue2 = A_cue2.at[1 + reward_state, cue_loc_idx, cue_state, reward_state].set(1.0)\n\n # m3: reward observation (null, cheese, shock)\n A_reward = jnp.zeros((3, num_loc, num_reward), dtype=jnp.float32)\n A_reward = A_reward.at[0, :, :].set(1.0)\n for reward_loc_state, reward_loc_idx in enumerate(self.reward_indices):\n A_reward = A_reward.at[0, reward_loc_idx, :].set(0.0)\n for reward_state in range(num_reward):\n obs_idx = 1 if reward_loc_state == reward_state else 2\n A_reward = A_reward.at[obs_idx, reward_loc_idx, reward_state].set(1.0)\n\n A = [A_loc, A_cue1, A_cue2, A_reward]\n A_dependencies = [[0], [0, 1], [0, 1, 2], [0, 2]]\n return A, A_dependencies\n\n def _generate_B(self) -> tuple[list[jnp.ndarray], list[list[int]]]:\n rows, cols = self.grid_shape\n num_loc = self.num_location_states\n num_actions = len(self.ACTION_LABELS)\n\n B_loc = jnp.zeros((num_loc, num_loc, num_actions), dtype=jnp.float32)\n\n for curr_idx in range(num_loc):\n row, col = self.index_to_coords(curr_idx)\n\n # UP\n up_idx = self.coords_to_index((max(row - 1, 0), col))\n B_loc = B_loc.at[up_idx, curr_idx, 0].set(1.0)\n\n # DOWN\n down_idx = self.coords_to_index((min(row + 1, rows - 1), col))\n B_loc = B_loc.at[down_idx, curr_idx, 1].set(1.0)\n\n # LEFT\n left_idx = self.coords_to_index((row, max(col - 1, 0)))\n B_loc = B_loc.at[left_idx, curr_idx, 2].set(1.0)\n\n # RIGHT\n right_idx = self.coords_to_index((row, min(col + 1, cols - 1)))\n B_loc = B_loc.at[right_idx, curr_idx, 3].set(1.0)\n\n # STAY\n B_loc = B_loc.at[curr_idx, curr_idx, 4].set(1.0)\n\n B_cue2 = jnp.eye(self.num_cue2_states, dtype=jnp.float32).reshape(\n self.num_cue2_states, self.num_cue2_states, 1\n )\n B_reward = jnp.eye(self.num_reward_states, dtype=jnp.float32).reshape(\n self.num_reward_states, self.num_reward_states, 1\n )\n\n B = [B_loc, B_cue2, B_reward]\n B_dependencies = [[0], [1], [2]]\n return B, B_dependencies\n\n def _generate_D(\n self,\n cue2_state: int | None,\n reward_condition: int | None,\n ) -> list[jnp.ndarray]:\n D_location = jnp.zeros((self.num_location_states,), dtype=jnp.float32)\n D_location = D_location.at[self.start_index].set(1.0)\n\n if cue2_state is None:\n D_cue2 = jnp.ones((self.num_cue2_states,), dtype=jnp.float32) / self.num_cue2_states\n else:\n D_cue2 = jnp.zeros((self.num_cue2_states,), dtype=jnp.float32)\n D_cue2 = D_cue2.at[cue2_state].set(1.0)\n\n if reward_condition is None:\n D_reward = (\n jnp.ones((self.num_reward_states,), dtype=jnp.float32) / self.num_reward_states\n )\n else:\n D_reward = jnp.zeros((self.num_reward_states,), dtype=jnp.float32)\n D_reward = D_reward.at[reward_condition].set(1.0)\n\n return [D_location, D_cue2, D_reward]\n" }, { "path": "pymdp/envs/env.py", "content": "\"\"\"Environment interfaces and POMDP-backed environment utilities.\n\nThis module provides:\n- `Env`: an abstract JAX-compatible environment interface used by `rollout()`,\n- `PymdpEnv`: a concrete environment driven by categorical `A`, `B`, and `D`,\n- `make(...)`: a convenience constructor for `PymdpEnv` and optional params.\n\"\"\"\n\nfrom abc import ABC, abstractmethod\nfrom functools import partial\nfrom typing import Any, Sequence\n\nimport jax.numpy as jnp\nfrom jax import jit, nn, random as jr, tree_util as jtu, vmap\nfrom jaxtyping import Array\n\nfrom pymdp.distribution import Distribution, get_dependencies\n\n\ndef _float_to_int_index(x: Array) -> Array:\n \"\"\"Cast index arrays to int32 for safe advanced indexing.\n\n Parameters\n ----------\n x : Array\n Index leaf, potentially represented in floating type.\n\n Returns\n -------\n Array\n Integer index array (`int32`) with the same structure as `x`.\n \"\"\"\n return jnp.asarray(x, jnp.int32)\n\n\ndef select_probs(\n positions: Sequence[Array],\n matrix: Array,\n dependency_list: Sequence[int],\n actions: Array | None = None,\n) -> Array:\n \"\"\"Select conditional probabilities from a factorized tensor.\n\n Parameters\n ----------\n positions : Sequence[Array]\n Current hidden-state indices for all factors.\n matrix : Array\n Likelihood or transition tensor to index.\n dependency_list : Sequence[int]\n Indices of factors used to index `matrix` lagging dimensions.\n actions : Array | None, optional\n Optional action index (or action indices) used to select the final\n action axis in transition tensors.\n\n Returns\n -------\n Array\n Selected conditional probability vector(s).\n \"\"\"\n index_args = tuple(_float_to_int_index(positions[i]) for i in dependency_list)\n if actions is not None:\n index_args += (_float_to_int_index(actions),)\n return matrix[(..., *index_args)]\n\n\ndef cat_sample(key: Array, p: Array) -> Array:\n \"\"\"Sample from one or more categorical distributions.\n\n Parameters\n ----------\n key : Array\n JAX PRNG key.\n p : Array\n Probability vector or batch of probability vectors on the last axis.\n\n Returns\n -------\n Array\n Sampled category index/indices as floating values.\n \"\"\"\n a = jnp.arange(p.shape[-1], dtype=jnp.float32)\n if p.ndim > 1:\n choice = lambda key, p: jr.choice(key, a, p=p)\n keys = jr.split(key, len(p))\n return vmap(choice)(keys, p)\n\n return jr.choice(key, a, p=p)\n\n\ndef make(\n A: Sequence[Array] | Sequence[Distribution],\n B: Sequence[Array] | Sequence[Distribution],\n D: Sequence[Array] | Sequence[Distribution],\n A_dependencies: list[list[int]] | None = None,\n B_dependencies: list[list[int]] | None = None,\n make_env_params: bool = False,\n **kwargs: Any,\n) -> tuple[\"PymdpEnv\", dict[str, list[Array]] | None]:\n \"\"\"Construct a `PymdpEnv` (and optionally environment parameters).\n\n Parameters\n ----------\n A : sequence[Array] | sequence[Distribution]\n Observation likelihood tensors, one per observation modality.\n B : sequence[Array] | sequence[Distribution]\n Transition tensors, one per hidden-state factor.\n D : sequence[Array] | sequence[Distribution]\n Initial-state priors, one per hidden-state factor.\n A_dependencies : list[list[int]] | None, optional\n Explicit modality-to-state dependencies. If `None`, dependencies are\n inferred when possible.\n B_dependencies : list[list[int]] | None, optional\n Explicit state-transition dependencies. If `None`, dependencies are\n inferred when possible.\n make_env_params : bool, default=False\n If `True`, also return `env_params={\"A\": ..., \"B\": ..., \"D\": ...}`\n with `Distribution` entries converted to dense arrays.\n **kwargs : Any\n Additional keyword arguments forwarded to `PymdpEnv`.\n\n Returns\n -------\n tuple[PymdpEnv, dict[str, list[Array]] | None]\n Constructed environment and optional unbatched environment parameters.\n To broadcast parameters to a larger batch, call\n `env.generate_env_params(batch_size=...)`.\n \"\"\"\n env = PymdpEnv(\n A=A,\n B=B,\n D=D,\n A_dependencies=A_dependencies,\n B_dependencies=B_dependencies,\n **kwargs,\n )\n if not make_env_params:\n return env, None\n\n def _to_arrays(params: Sequence[Array] | Sequence[Distribution] | None) -> list[Array] | None:\n if params is None:\n return None\n return [jnp.array(p.data) if isinstance(p, Distribution) else p for p in params]\n\n env_params = {\"A\": _to_arrays(A), \"B\": _to_arrays(B), \"D\": _to_arrays(D)}\n\n return env, env_params\n\n\nclass Env(ABC):\n \"\"\"Abstract JAX-compatible environment interface used by `rollout()`.\"\"\"\n\n @abstractmethod\n def reset(\n self,\n key: Array,\n state: list[Array] | None = None,\n env_params: dict[str, list[Array]] | None = None,\n ) -> tuple[list[Array], list[Array]]:\n \"\"\"Reset environment state and return initial observation/state.\n\n Parameters\n ----------\n key : Array\n JAX PRNG key.\n state : list[Array] | None, optional\n Optional explicit initial hidden state.\n env_params : dict[str, list[Array]] | None, optional\n Optional runtime override for environment parameters.\n\n Returns\n -------\n tuple[list[Array], list[Array]]\n Initial observations and hidden state.\n \"\"\"\n raise NotImplementedError\n\n @abstractmethod\n def step(\n self,\n key: Array,\n state: list[Array],\n action: Array | None,\n env_params: dict[str, list[Array]] | None = None,\n ) -> tuple[list[Array], list[Array]]:\n \"\"\"Advance one environment step and return new observation/state.\n\n Parameters\n ----------\n key : Array\n JAX PRNG key.\n state : list[Array]\n Current hidden state.\n action : Array | None\n Action sampled by the agent. `None` can be used for no-op updates.\n env_params : dict[str, list[Array]] | None, optional\n Optional runtime override for environment parameters.\n\n Returns\n -------\n tuple[list[Array], list[Array]]\n Next observations and hidden state.\n \"\"\"\n raise NotImplementedError\n\n def generate_env_params(\n self, key: Array | None = None, batch_size: int | None = None\n ) -> dict[str, list[Array]] | None:\n \"\"\"Generate optional environment parameter pytrees.\n\n Parameters\n ----------\n key : Array | None, optional\n Optional JAX PRNG key (unused by default implementation).\n batch_size : int | None, optional\n Optional batch size for parameter generation.\n\n Returns\n -------\n dict[str, list[Array]] | None\n Environment parameters or `None` if not implemented.\n \"\"\"\n return None\n\n\nclass PymdpEnv(Env):\n \"\"\"Environment whose dynamics are defined by categorical `A`, `B`, and `D`.\n\n `PymdpEnv` is useful when the environment is isomorphic to a discrete POMDP\n generative process:\n - `A[m]`: observation likelihoods per modality,\n - `B[f]`: transitions per hidden-state factor,\n - `D[f]`: initial-state priors per hidden-state factor.\n \"\"\"\n\n def __init__(\n self,\n A: Sequence[Array] | Sequence[Distribution] | None = None,\n B: Sequence[Array] | Sequence[Distribution] | None = None,\n D: Sequence[Array] | Sequence[Distribution] | None = None,\n A_dependencies: list[list[int]] | None = None,\n B_dependencies: list[list[int]] | None = None,\n categorical_obs: bool = False,\n **kwargs: Any,\n ) -> None:\n \"\"\"Initialize `PymdpEnv`.\n\n Parameters\n ----------\n A : sequence[Array] | sequence[Distribution] | None, optional\n Observation likelihood tensors.\n B : sequence[Array] | sequence[Distribution] | None, optional\n Transition tensors.\n D : sequence[Array] | sequence[Distribution] | None, optional\n Initial-state priors.\n A_dependencies : list[list[int]] | None, optional\n Modality-to-state dependencies for `A`.\n B_dependencies : list[list[int]] | None, optional\n State-to-state dependencies for `B`.\n categorical_obs : bool, default=False\n If `True`, emit one-hot categorical observation vectors with shape\n `(1, num_obs)` per modality. Otherwise emit discrete indices with\n shape `(1,)`.\n **kwargs : Any\n Accepted for forward compatibility.\n \"\"\"\n del kwargs\n self.categorical_obs = categorical_obs\n\n if A_dependencies is not None:\n self.A_dependencies = A_dependencies\n elif A is not None and B is not None:\n if isinstance(A[0], Distribution) and isinstance(B[0], Distribution):\n self.A_dependencies, _ = get_dependencies(A, B)\n else:\n self.A_dependencies = [list(range(len(B))) for _ in range(len(A))]\n else:\n raise ValueError(\"Need to provide A and B or A_dependencies\")\n\n if B_dependencies is not None:\n self.B_dependencies = B_dependencies\n elif A is not None and B is not None:\n if isinstance(A[0], Distribution) and isinstance(B[0], Distribution):\n _, self.B_dependencies = get_dependencies(A, B)\n else:\n self.B_dependencies = [[f] for f in range(len(B))]\n else:\n raise ValueError(\"Need to provide A and B or B_dependencies\")\n\n if A is not None:\n self.A = [jnp.array(a.data) if isinstance(a, Distribution) else a for a in A]\n else:\n self.A = None\n\n if B is not None:\n self.B = [jnp.array(b.data) if isinstance(b, Distribution) else b for b in B]\n else:\n self.B = None\n\n if D is not None:\n self.D = [jnp.array(d.data) if isinstance(d, Distribution) else d for d in D]\n else:\n self.D = None\n\n def generate_env_params(\n self, key: Array | None = None, batch_size: int | None = None\n ) -> dict[str, list[Array]]:\n \"\"\"Return default environment params, optionally broadcast to batch.\n\n Parameters\n ----------\n key : Array | None, optional\n Optional JAX PRNG key (unused).\n batch_size : int | None, optional\n If provided, broadcast each parameter leaf with leading shape\n `(batch_size, ...)`.\n\n Returns\n -------\n dict[str, list[Array]]\n Dictionary with keys `\"A\"`, `\"B\"`, and `\"D\"`.\n \"\"\"\n del key\n\n env_params = {\"A\": self.A, \"B\": self.B, \"D\": self.D}\n if batch_size is None:\n return env_params\n\n expand_to_batch = lambda x: jnp.broadcast_to(jnp.asarray(x), (batch_size,) + x.shape)\n return jtu.tree_map(expand_to_batch, {\"A\": self.A, \"B\": self.B, \"D\": self.D})\n\n @partial(jit, static_argnums=(0,))\n def reset(\n self,\n key: Array,\n state: list[Array] | None = None,\n env_params: dict[str, list[Array]] | None = None,\n ) -> tuple[list[Array], list[Array]]:\n \"\"\"Reset state and emit an initial observation sample.\n\n If `state` is omitted, states are sampled from `D`.\n \"\"\"\n if state is None:\n probs = env_params[\"D\"] if env_params is not None else self.D\n keys = list(jr.split(key, len(probs) + 1))\n key = keys[0]\n state = jtu.tree_map(cat_sample, keys[1:], probs)\n obs = self._sample_obs(key, state, env_params)\n return obs, state\n\n @partial(jit, static_argnums=(0,))\n def step(\n self,\n key: Array,\n state: list[Array],\n action: Array | None,\n env_params: dict[str, list[Array]] | None = None,\n ) -> tuple[list[Array], list[Array]]:\n \"\"\"Advance the process by one timestep.\n\n If `action` is provided, next hidden states are sampled from `B`.\n Observations are then sampled from `A` conditioned on the new state.\n \"\"\"\n key_state, key_obs = jr.split(key)\n if action is not None:\n action = list(action)\n _select_probs = partial(select_probs, state)\n B = env_params[\"B\"] if env_params is not None else self.B\n state_probs = jtu.tree_map(_select_probs, B, self.B_dependencies, action)\n\n keys = list(jr.split(key_state, len(state_probs)))\n new_state = jtu.tree_map(cat_sample, keys, state_probs)\n else:\n new_state = state\n\n new_obs = self._sample_obs(key_obs, new_state, env_params)\n\n return new_obs, new_state\n\n def _sample_obs(\n self, key: Array, state: list[Array], env_params: dict[str, list[Array]] | None\n ) -> list[Array]:\n \"\"\"Sample all observation modalities conditioned on hidden state.\"\"\"\n _select_probs = partial(select_probs, state)\n A = env_params[\"A\"] if env_params is not None else self.A\n obs_probs = jtu.tree_map(_select_probs, A, self.A_dependencies)\n\n keys = list(jr.split(key, len(obs_probs)))\n obs_idx = jtu.tree_map(cat_sample, keys, obs_probs)\n\n if self.categorical_obs:\n new_obs = [\n jnp.expand_dims(\n nn.one_hot(jnp.asarray(obs_m, dtype=jnp.int32), probs_m.shape[-1]),\n axis=-2,\n )\n for obs_m, probs_m in zip(obs_idx, obs_probs)\n ]\n return new_obs\n\n new_obs = jtu.tree_map(lambda x: jnp.expand_dims(x, -1), obs_idx)\n return new_obs\n" }, { "path": "pymdp/envs/generalized_tmaze.py", "content": "from .env import PymdpEnv\nfrom typing import Any\nimport numpy as np\nimport math\nimport jax.numpy as jnp\n\nimport matplotlib.pyplot as plt\nfrom pymdp.utils import fig2img\n\nfrom jax import random as jr\nfrom jaxtyping import PRNGKeyArray\nfrom matplotlib.lines import Line2D\n\n\ndef get_maze_matrix(small: bool = False) -> np.ndarray:\n\n \"\"\"\n We create a matrix representation of the T-maze environment\n \n Matrix values:\n 0: Grid cells the agent can move through\n 1: Initial position of the agent\n 2: Walls of the grid cells\n 3, 6, 9: Cue locations (multiples of 3, where 3 is cue for reward set 1, 6 for set 2, etc.)\n 4+: Potential reward locations:\n 4-5: Reward set 1 locations\n 7-8: Reward set 2 locations\n 10-11: Reward set 3 locations\n \n Args:\n small: If True, creates a 3x3 maze with 2 reward sets\n If False, creates a 5x5 maze with 3 reward sets\n \"\"\"\n\n if small:\n M = np.zeros((3, 3)) # 3x3 grid\n\n # Set the reward locations for sets 1 and 2\n M[0,0] = 4 # First location of reward set 1\n M[1,0] = 5 # Second location of reward set 1\n M[1,2] = 7 # First location of reward set 2\n M[0,2] = 8 # Second location of reward set 2\n\n # Set the cue locations\n M[2,0] = 3 # Cue for reward set 1 (3 = 3*1)\n M[2,2] = 6 # Cue for reward set 2 (6 = 3*2)\n\n # Set the initial position\n M[2,1] = 1\n else:\n M = np.zeros((5, 5)) # 5x5 grid\n\n # Set the reward locations for sets 1, 2, and 3\n M[0,0] = 4 # First location of reward set 1\n M[1,0] = 5 # Second location of reward set 1\n M[1,4] = 7 # First location of reward set 2\n M[0,4] = 8 # Second location of reward set 2\n M[4,1] = 10 # First location of reward set 3\n M[4,3] = 11 # Second location of reward set 3\n\n # Set the cue locations\n M[2,1] = 3 # Cue for reward set 1 (3 = 3*1)\n M[2,3] = 6 # Cue for reward set 2 (6 = 3*2)\n M[3,2] = 9 # Cue for reward set 3 (9 = 3*3)\n\n # Set the initial position\n M[2,2] = 1\n\n return M\n\ndef parse_maze(maze: np.ndarray, rng_key: PRNGKeyArray) -> dict[str, Any]:\n \"\"\"\n Parses the maze matrix into a format needed for the environment and its visualization.\n \n Parameters\n ----------\n maze : array\n A matrix representation of the environment where values represent:\n 0: Grid cells the agent can move through\n 1: Initial position of the agent\n 2: Walls of the grid cells \n 3, 6, 9: Cue locations (multiples of 3, where 3 is cue for reward set 1, 6 for set 2, etc.)\n 4+: Potential reward locations:\n 4-5: Reward set 1 locations\n 7-8: Reward set 2 locations\n 10-11: Reward set 3 locations\n \n rng_key : PRNGKeyArray\n Random key for determining which location in each set will be reward vs punishment\n \n Returns\n ----------\n env_info : dict\n Dictionary containing:\n - maze: The original maze matrix\n - actions: Possible movements [(up), (down), (left), (right)]\n - num_cues: Number of cue-reward sets\n - cue_positions: Coordinates of each cue\n - reward_indices: Flattened indices of true reward locations\n - no_reward_indices: Flattened indices of punishment locations\n - initial_position: Starting coordinates of agent\n - reward_1_positions: Coordinates of first potential reward location in each set\n - reward_2_positions: Coordinates of second potential reward location in each set\n - reward_locations: Binary array indicating which position (1 or 2) contains reward for each set\n \"\"\"\n rows, cols = maze.shape\n\n # Calculate number of cue-reward sets based on highest value in maze\n # (max value - 2) // 3 gives us number of sets because:\n # Set 1: cue=3, rewards=4,5\n # Set 2: cue=6, rewards=7,8\n # Set 3: cue=9, rewards=10,11\n num_cues = int((jnp.max(maze) - 2) // 3)\n\n \n # Store coordinates for each set's cue and potential reward locations\n cue_positions = []\n reward_1_positions = []\n reward_2_positions = []\n for i in range(num_cues):\n # For set i:\n # Cue value = 3 + 3i (3,6,9)\n cue_positions.append(tuple(jnp.argwhere(maze == 3 + 3 * i)[0]))\n # First reward location value = 4 + 3i (4,7,10)\n reward_1_positions.append(tuple(jnp.argwhere(maze == 4 + 3 * i)[0]))\n # Second reward location value = 5 + 3i (5,8,11)\n reward_2_positions.append(tuple(jnp.argwhere(maze == 5 + 3 * i)[0]))\n\n # Get agent's starting position (value = 1 in maze)\n initial_position = tuple(jnp.argwhere(maze == 1)[0])\n\n # Define possible movements in (row, col) format\n actions = [(-1, 0), (1, 0), (0, -1), (0, 1)]\n\n # Randomly assign which location in each set will be reward vs punishment\n # reward_locations[i] = 0 means first location is reward, 1 means second location is reward\n # Using uniform random numbers\n key, subkey = jr.split(rng_key)\n reward_locations = (jr.uniform(subkey, shape=(num_cues,)) > 0.5).astype(jnp.int32)\n # reward_locations = jr.choice(rng_key, 2, shape=(num_cues,))\n reward_indices = []\n no_reward_indices = []\n\n # Convert 2D coordinates to flattened indices for each set\n for i in range(num_cues):\n if reward_locations[i] == 0:\n # First location (4,7,10) is reward\n reward_indices += [jnp.ravel_multi_index(jnp.array(reward_1_positions[i]), maze.shape).item()]\n # Second location (5,8,11) is punishment\n no_reward_indices += [jnp.ravel_multi_index(jnp.array(reward_2_positions[i]), maze.shape).item()]\n else:\n # Second location is reward\n reward_indices += [jnp.ravel_multi_index(jnp.array(reward_2_positions[i]), maze.shape).item()]\n # First location is punishment\n no_reward_indices += [jnp.ravel_multi_index(jnp.array(reward_1_positions[i]), maze.shape).item()]\n\n return {\n \"maze\": maze,\n \"actions\": actions,\n \"num_cues\": num_cues,\n \"cue_positions\": cue_positions,\n \"reward_indices\": reward_indices,\n \"no_reward_indices\": no_reward_indices,\n \"initial_position\": initial_position,\n \"reward_1_positions\": reward_1_positions,\n \"reward_2_positions\": reward_2_positions,\n \"reward_locations\": reward_locations,\n }\n\n\ndef generate_A(maze_info: dict[str, Any]) -> tuple[list[jnp.ndarray], list[list[int]]]:\n \"\"\"\n Parameters\n ----------\n maze_info:\n info dict returned from `parse_maze` which contains the information\n about the reward locations, initial positions, etc.\n Returns\n ----------\n A matrix:\n The likelihood mapping for the generalized T-maze. Maps the observations\n of (position, *cue_i, *reward_i) to states (position, reward)\n A dependencies:\n The state dependencies that generate observation for modality i\n \"\"\"\n # Positional observation likelihood\n maze = maze_info[\"maze\"]\n rows, cols = maze.shape\n num_cues = maze_info[\"num_cues\"]\n cue_positions = maze_info[\"cue_positions\"]\n reward_1_positions = maze_info[\"reward_1_positions\"]\n reward_2_positions = maze_info[\"reward_2_positions\"]\n\n num_states = rows * cols\n position_likelihood = jnp.zeros((num_states, num_states))\n for i in range(num_states):\n # Agent can be certain about its position regardless of reward state\n position_likelihood = position_likelihood.at[i, i].set(1)\n\n cue_likelihoods = []\n for i in range(num_cues):\n # Cue observation likelihood, cue_position = (11, 5)\n # obs (nothing, left location, right location)\n # state: (current position, reward i position)\n cue_likelihood = jnp.zeros((3, num_states, 2))\n cue_likelihood = cue_likelihood.at[0, :, :].set(1) # Default: no info about reward\n\n cue_state_idx = jnp.ravel_multi_index(jnp.array(cue_positions[i]), maze.shape)\n reward_1_state_idx = jnp.ravel_multi_index(jnp.array(reward_1_positions[i]), maze.shape)\n reward_2_state_idx = jnp.ravel_multi_index(jnp.array(reward_2_positions[i]), maze.shape)\n\n cue_likelihood = cue_likelihood.at[:, cue_state_idx, 0].set(jnp.array([0, 1, 0])) # Reward in r1\n cue_likelihood = cue_likelihood.at[:, cue_state_idx, 1].set(jnp.array([0, 0, 1])) # Reward in r2\n cue_likelihoods.append(cue_likelihood)\n\n # Reward observation likelihood, r1 = (4, 7), r2 = (8, 7)\n reward_likelihoods = []\n\n for i in range(num_cues):\n # observation (nothing, no reward, reward)\n reward_likelihood = jnp.zeros((3, num_states, 2))\n reward_likelihood = reward_likelihood.at[0, :, :].set(1) # Default: no reward\n\n reward_1_state_idx = jnp.ravel_multi_index(jnp.array(reward_1_positions[i]), maze.shape)\n reward_2_state_idx = jnp.ravel_multi_index(jnp.array(reward_2_positions[i]), maze.shape)\n\n # Reward in (8,4) if reward state is 0\n reward_likelihood = reward_likelihood.at[:, reward_1_state_idx, 0].set(jnp.array([0, 1, 0]))\n # Reward in (8,8) if reward state is 0\n reward_likelihood = reward_likelihood.at[:, reward_2_state_idx, 0].set(jnp.array([0, 0, 1]))\n # Reward in (8,4) if reward state is 0\n reward_likelihood = reward_likelihood.at[:, reward_1_state_idx, 1].set(jnp.array([0, 0, 1]))\n # Reward in (8,8) if reward state is 0\n reward_likelihood = reward_likelihood.at[:, reward_2_state_idx, 1].set(jnp.array([0, 1, 0]))\n reward_likelihoods.append(reward_likelihood)\n\n combined_likelihood = []\n combined_likelihood.append(position_likelihood)\n for cue_likelihood in cue_likelihoods:\n combined_likelihood.append(cue_likelihood)\n for reward_likelihood in reward_likelihoods:\n combined_likelihood.append(reward_likelihood)\n\n likelihood_dependencies = (\n [[0]]\n + [[0, 1 + i] for i in range(num_cues)]\n + [[0, 1 + i] for i in range(num_cues)]\n )\n\n return combined_likelihood, likelihood_dependencies\n\n\ndef generate_B(maze_info: dict[str, Any]) -> tuple[list[jnp.ndarray], list[list[int]]]:\n \"\"\"\n Parameters\n ----------\n maze_info:\n info dict returned from `parse_maze` which contains the information\n about the reward locations, initial positions, etc.\n Returns\n ----------\n B matrix:\n The transition matrix for the generalized T-maze. The position state\n is transitioned according to the maze layout, for the other states\n the transition matrix is the identity.\n B dependencies:\n The state dependencies that generate transition for state i\n \"\"\"\n\n maze = maze_info[\"maze\"]\n actions = maze_info[\"actions\"]\n num_cues = maze_info[\"num_cues\"]\n\n rows, cols = maze.shape\n num_states = rows * cols\n num_actions = len(actions)\n\n P = jnp.zeros((num_states, num_actions), dtype=int)\n\n for s in range(num_states):\n row, col = divmod(s, cols)\n\n for a in range(num_actions):\n ns_row, ns_col = row + actions[a][0], col + actions[a][1]\n\n if (\n ns_row < 0\n or ns_row >= rows\n or ns_col < 0\n or ns_col >= cols\n or maze[ns_row, ns_col] == 2\n ):\n P = P.at[s, a].set(s)\n else:\n P = P.at[s, a].set(jnp.ravel_multi_index(jnp.array((ns_row, ns_col)), maze.shape))\n\n B = jnp.zeros((num_states, num_states, num_actions))\n for s in range(num_states):\n for a in range(num_actions):\n ns = P[s, a]\n B = B.at[ns, s, a].set(1)\n # add do nothing action \n B = jnp.concatenate([B, jnp.eye(num_states)[..., None]], -1)\n\n assert jnp.all(jnp.logical_or(B == 0, B == 1))\n assert jnp.allclose(B.sum(axis=0), 1)\n\n reward_transitions = []\n for i in range(num_cues):\n reward_transition = jnp.eye(2).reshape(2, 2, 1)\n reward_transitions.append(reward_transition)\n\n combined_transition = []\n combined_transition.append(B)\n for reward_transition in reward_transitions:\n combined_transition.append(reward_transition)\n\n transition_dependencies = [[0]] + [[i + 1] for i in range(num_cues)]\n\n return combined_transition, transition_dependencies\n\n\ndef generate_D(maze_info: dict[str, Any]) -> list[jnp.ndarray]:\n \"\"\"\n Parameters\n ----------\n maze_info:\n info dict returned from `parse_maze` which contains the information\n about the reward locations, initial positions, etc.\n Returns\n ----------\n D vector:\n The initial state for the environment, i.e. each state is a one hot\n based on the environment initial conditions.\n \"\"\"\n maze = maze_info[\"maze\"]\n rows, cols = maze.shape\n num_cues = maze_info[\"num_cues\"]\n reward_locations = maze_info[\"reward_locations\"]\n initial_position = maze_info[\"initial_position\"]\n\n D = [None for _ in range(1 + num_cues)]\n\n D[0] = jnp.zeros(cols * rows)\n # Position of the agent when starting the environment\n D[0] = D[0].at[jnp.ravel_multi_index(jnp.array(initial_position), maze.shape)].set(1)\n\n # Cue state i.e. where is the reward\n for i in range(num_cues):\n r1 = reward_locations[i]\n D[1 + i] = jnp.zeros(2)\n D[1 + i] = D[1 + i].at[r1].set(1)\n\n return D\nclass GeneralizedTMazeEnv(PymdpEnv):\n \"\"\"\n Extended version of the T-Maze in which there are multiple cues and reward pairs\n similar to the original T-maze.\n \"\"\"\n\n def __init__(self, env_info: dict[str, Any], categorical_obs: bool = False) -> None:\n \"\"\"Initialize the generalized T-maze environment.\n\n Parameters\n ----------\n env_info : dict[str, Any]\n Environment specification used to construct the maze dynamics.\n categorical_obs : bool, default=False\n If ``True``, ``reset()`` and ``step()`` emit one-hot categorical\n observation vectors with shape ``(1, num_obs_m)`` for each\n modality. If ``False``, they emit discrete observation indices with\n shape ``(1,)``.\n \"\"\"\n A, A_dependencies = generate_A(env_info)\n B, B_dependencies = generate_B(env_info)\n D = generate_D(env_info)\n super().__init__(\n A,\n B,\n D,\n A_dependencies,\n B_dependencies,\n categorical_obs=categorical_obs,\n )\n self.env_info = env_info\n\n def render(self, states: list[jnp.ndarray], mode: str = \"human\") -> jnp.ndarray | None:\n \"\"\"\n Renders the environment\n Parameters\n ----------\n states:\n The environment states to render\n mode: str, optional\n The mode to render with (\"human\" or \"rgb_array\")\n Returns\n ----------\n if mode == \"human\":\n returns None, renders the environment using matplotlib inside the function\n elif mode == \"rgb_array\":\n A (H, W, 3) jax.numpy array that can act as input to functions like plt.imshow, with values between 0 and 255\n \"\"\"\n\n if (states[0].ndim == 0):\n states = [jnp.expand_dims(s,0) for s in states] # add batch dimension\n\n batch_size = states[0].shape[0]\n\n plt.clf() # Clear the current figure\n\n maze = self.env_info[\"maze\"].copy()\n num_cues = self.env_info[\"num_cues\"]\n cue_positions = self.env_info[\"cue_positions\"]\n reward_1_positions = self.env_info[\"reward_1_positions\"]\n reward_2_positions = self.env_info[\"reward_2_positions\"]\n\n # Set all states not in [1] to be 0 (accessible state)\n mask = np.isin(maze, [2], invert=True)\n maze[mask] = 0\n\n # create n x n subplots for the batch_size\n n = math.ceil(math.sqrt(batch_size))\n\n # create the subplots\n fig, axes = plt.subplots(n, n, figsize=(8,8),squeeze=False)\n axes_flat = axes.ravel()\n\n cmap = plt.get_cmap(\"tab10\")\n\n for (i, ax) in enumerate(axes_flat[:batch_size]):\n \n current_position = states[0][i]\n current_position = jnp.unravel_index(current_position, maze.shape) # (row, col)\n\n ax.imshow(maze, cmap=\"gray_r\", origin=\"lower\")\n\n # cues\n ax.scatter(\n [ci[1] for ci in cue_positions],\n [ci[0] for ci in cue_positions],\n color=[cmap(i) for i in range(len(cue_positions))],\n s=200,\n alpha=0.5,\n )\n ax.scatter(\n [ci[1] for ci in cue_positions],\n [ci[0] for ci in cue_positions],\n color=\"black\",\n s=50,\n label=\"Cue\",\n marker=\"x\",\n )\n\n # reward candidates\n ax.scatter(\n [ri[1] for ri in reward_1_positions],\n [ri[0] for ri in reward_1_positions],\n color=[cmap(i) for i in range(len(cue_positions))],\n s=200,\n alpha=0.5,\n )\n\n ax.scatter(\n [ri[1] for ri in reward_2_positions],\n [ri[0] for ri in reward_2_positions],\n color=[cmap(i) for i in range(len(cue_positions))],\n s=200,\n alpha=0.5,\n )\n\n for j, (r1, r2) in enumerate(zip(reward_1_positions, reward_2_positions)):\n if j == self.env_info[\"num_cues\"] - 1: # Only for the true reward set\n if self.env_info[\"reward_locations\"][j] == 0:\n # First location is reward\n ax.scatter(r1[1], r1[0], color='red', s=100, marker='o', zorder=4, label = \"Reward\") # Red dot\n ax.scatter(r2[1], r2[0], color='blue', s=100, marker='o', zorder=4, label = \"Punishment\") # Blue dot\n else:\n # Second location is reward\n ax.scatter(r2[1], r2[0], color='red', s=100, marker='o', zorder=4, label = \"Reward\") # Red dot\n ax.scatter(r1[1], r1[0], color='blue', s=100, marker='o', zorder=4, label = \"Punishment\") # Blue dot\n\n\n ax.scatter(\n current_position[1],\n current_position[0],\n c=\"tab:green\",\n marker=\"s\",\n s=100,\n label=\"Agent\",\n )\n\n # hide unused axes\n for k in range(batch_size, n * n):\n axes_flat[k].axis(\"off\")\n\n plt.suptitle(\"Generalized T-Maze Environment\")\n\n base_ax = axes_flat[next(i for i in range(len(axes_flat)) if axes_flat[i].has_data())] # get \n handles, labels = base_ax.get_legend_handles_labels()\n for i in range(num_cues):\n if i == num_cues - 1:\n label = \"True Reward Set\"\n else:\n label = f\"Distractor Set {i + 1}\"\n patch = Line2D(\n [0],\n [0],\n marker=\"o\",\n markersize=10,\n markerfacecolor=cmap(i),\n markeredgecolor=cmap(i),\n label=label,\n alpha=0.5,\n linestyle=\"\",\n )\n handles.append(patch)\n\n plt.legend(\n handles=handles, loc=\"upper left\", bbox_to_anchor=(1, 1), fancybox=True\n )\n plt.tight_layout()\n\n if mode == \"human\":\n plt.show()\n elif mode == \"rgb_array\":\n img = fig2img(fig)\n plt.close(fig) \n return img\n \n" }, { "path": "pymdp/envs/graph_worlds.py", "content": "import networkx as nx\nfrom jax import numpy as jnp, random as jr, tree_util as jtu\nfrom typing import Any, Optional, List, Tuple\nfrom jaxtyping import PRNGKeyArray\nfrom .env import PymdpEnv\nimport warnings\n\ndef generate_connected_clusters(\n cluster_size: int = 2, connections: int = 2\n) -> tuple[nx.Graph, dict[str, list[str]]]:\n edges = []\n connecting_node = 0\n while connecting_node < connections * cluster_size:\n edges += [(connecting_node, a) for a in range(connecting_node + 1, connecting_node + cluster_size + 1)]\n connecting_node = len(edges)\n graph = nx.Graph()\n graph.add_edges_from(edges)\n return graph, {\n \"locations\": [\n (f\"hallway {i}\" if len(list(graph.neighbors(loc))) > 1 else f\"room {i}\")\n for i, loc in enumerate(graph.nodes)\n ]\n }\n\nclass GraphEnv(PymdpEnv):\n \"\"\"\n A simple environment where an agent can move around a graph and search an object.\n The agent observes its own location, as well as whether the object is at its location.\n \"\"\"\n\n def __init__(\n self,\n graph: nx.Graph,\n object_location: Optional[int] = None,\n agent_location: Optional[int] = None,\n key: Optional[PRNGKeyArray] = None,\n categorical_obs: bool = False,\n ) -> None:\n \"\"\"Initialize the graph environment.\n\n Parameters\n ----------\n graph : nx.Graph\n Connectivity graph for agent movement.\n object_location : int | None, optional\n Fixed initial object location. If ``None``, sampled randomly.\n agent_location : int | None, optional\n Fixed initial agent location. If ``None``, sampled randomly.\n key : PRNGKeyArray | None, optional\n Random key used when initial locations are sampled.\n categorical_obs : bool, default=False\n If ``True``, ``reset()`` and ``step()`` emit one-hot categorical\n observation vectors with shape ``(1, num_obs_m)`` for each\n modality. If ``False``, they emit discrete observation indices with\n shape ``(1,)``.\n \"\"\"\n\n A, A_dependencies = self.generate_A(graph)\n B, B_dependencies = self.generate_B(graph)\n\n if object_location is None:\n key = jr.PRNGKey(0) if key is None else key\n _, _key = jr.split(key)\n object_location = jr.randint(_key, shape=(), minval=0, maxval=len(graph.nodes) + 1) # +1 for \"not here\"\n if agent_location is None:\n key = jr.PRNGKey(1) if key is None else key\n _, _key = jr.split(key)\n agent_location = jr.randint(_key, shape=(), minval=0, maxval=len(graph.nodes))\n\n D = self.generate_D(graph, object_location, agent_location)\n\n super().__init__(\n A=A,\n B=B,\n D=D,\n A_dependencies=A_dependencies,\n B_dependencies=B_dependencies,\n categorical_obs=categorical_obs,\n )\n\n def generate_A(self, graph: nx.Graph) -> tuple[list[jnp.ndarray], list[list[int]]]:\n A = []\n A_dependencies = []\n\n num_locations = len(graph.nodes)\n num_object_locations = num_locations + 1 # +1 for \"not here\"\n p = 1.0 # probability of seeing object if it is at the same location as the agent\n\n # agent location modality\n A.append(jnp.eye(num_locations))\n A_dependencies.append([0])\n\n # object visibility modality\n A.append(jnp.zeros((2, num_locations, num_object_locations)))\n\n for agent_loc in range(num_locations):\n for object_loc in range(num_locations):\n if agent_loc == object_loc:\n # object seen\n A[1] = A[1].at[0, agent_loc, object_loc].set(1 - p)\n A[1] = A[1].at[1, agent_loc, object_loc].set(p)\n else:\n A[1] = A[1].at[0, agent_loc, object_loc].set(p)\n A[1] = A[1].at[1, agent_loc, object_loc].set(1.0 - p)\n\n # object not here, we can't see it anywhere\n A[1] = A[1].at[0, :, -1].set(1.0)\n A[1] = A[1].at[1, :, -1].set(0.0)\n\n A_dependencies.append([0, 1])\n return A, A_dependencies\n\n def generate_B(self, graph: nx.Graph) -> tuple[list[jnp.ndarray], list[list[int]]]:\n B = []\n B_dependencies = []\n\n num_locations = len(graph.nodes)\n num_object_locations = num_locations + 1\n\n # agent location transitions, based on graph connectivity\n B.append(jnp.zeros((num_locations, num_locations, num_locations)))\n for action in range(num_locations):\n for from_loc in range(num_locations):\n for to_loc in range(num_locations):\n if action == to_loc:\n # we transition if connected in graph\n if graph.has_edge(from_loc, to_loc):\n B[0] = B[0].at[to_loc, from_loc, action].set(1.0)\n else:\n B[0] = B[0].at[from_loc, from_loc, action].set(1.0)\n\n B_dependencies.append([0])\n\n # objects don't move\n B.append(jnp.zeros((num_object_locations, num_object_locations, 1)))\n B[1] = B[1].at[:, :, 0].set(jnp.eye(num_object_locations))\n B_dependencies.append([1])\n\n return B, B_dependencies\n \n def generate_D(\n self, graph: nx.Graph, object_location: int, agent_location: int\n ) -> list[jnp.ndarray]:\n\n num_locations = len(graph.nodes)\n num_object_locations = num_locations + 1\n\n states = [num_locations, num_object_locations]\n D = [jnp.zeros(s) for s in states]\n\n # set the start locations\n D[0] = D[0].at[agent_location].set(1.0)\n D[1] = D[1].at[object_location].set(1.0)\n\n return D\n \n def generate_env_params(\n self,\n graph: nx.Graph,\n key: Optional[PRNGKeyArray] = None,\n object_locations: Optional[List[int]] = None,\n agent_locations: Optional[List[int]] = None,\n batch_size: Optional[int] = None,\n ) -> dict[str, Any]:\n \"\"\"\n Override of `generate_env_params` from `Env` class that returns batched environmental parameters, with\n the option to randomize initial object and agent locations (lists of integers) which, if provided, should be of length `batch_size`\n and are used to set the initial locations in the D vector for each batch element.\n \n If batch size is provided but object_locations and agent_locations are not, then random locations will be sampled for each batch element.\n args:\n graph: networkx Graph object representing the environment\n key: JAX random key (used to sample random initial locations if object_locations and agent_locations are not provided)\n object_locations: list of integers specifying initial object locations for each batch element\n agent_locations: list of integers specifying initial agent locations for each batch element\n batch_size: integer specifying the number of batch elements. If None but object_locations and agent_locations are provided, batch_size is inferred from their length.\n returns:\n env_params: dictionary containing batched environmental parameters\n \"\"\"\n if batch_size is None:\n if object_locations is not None and agent_locations is not None:\n batch_size = len(object_locations)\n else:\n warnings.warn(\"Neither `batch_size` nor `object_locations` nor `agent_locations` are provided, so just returning the unbatched env params\")\n return super().generate_env_params(key=key, batch_size=batch_size)\n\n num_locations = len(graph.nodes)\n num_object_locations = num_locations + 1\n\n if object_locations is None or agent_locations is None:\n if key is None:\n raise ValueError(\"A random key must be provided to sample random initial locations.\")\n keys = jr.split(key, 2)\n if object_locations is None:\n object_locations = jr.randint(keys[0], shape=(batch_size,), minval=0, maxval=num_object_locations)\n if agent_locations is None:\n agent_locations = jr.randint(keys[1], shape=(batch_size,), minval=0, maxval=num_locations)\n\n D = [jnp.zeros((batch_size, s)) for s in [num_locations, num_object_locations]]\n\n D[0] = D[0].at[jnp.arange(batch_size), agent_locations].set(1.0)\n D[1] = D[1].at[jnp.arange(batch_size), object_locations].set(1.0)\n\n expand_to_batch = lambda x: jnp.broadcast_to(jnp.asarray(x), (batch_size,) + x.shape)\n\n env_params ={**jtu.tree_map(expand_to_batch, {\"A\": self.A, \"B\": self.B}), **{\"D\": D}}\n \n return env_params\n" }, { "path": "pymdp/envs/grid_world.py", "content": "from __future__ import annotations\n\nfrom typing import Iterable, Optional, Tuple\n\nimport jax.numpy as jnp\nimport numpy as np\nimport jax.tree_util as jtu\n\nfrom .env import PymdpEnv\n\n\nclass GridWorld(PymdpEnv):\n \"\"\"\n Classic 2D grid world as a JAX-compatible PymdpEnv.\n\n Hidden state factors\n --------------------\n - factor 0 (location): a single discrete factor with `rows * cols` states (linear index row*cols + col)\n\n Observations\n ------------\n - modality 0 (location observation): identity over location (the agent observes its true grid index)\n\n Controls / Actions\n ------------------\n - One control factor with 4 or 5 discrete actions:\n 0: UP\n 1: RIGHT\n 2: DOWN\n 3: LEFT\n 4: STAY (optional; controlled by include_stay=True)\n\n Parameters\n ----------\n shape : tuple[int, int]\n Grid shape as (rows, cols).\n walls : Optional[Iterable[Tuple[int, int]]]\n Iterable of (row, col) coordinates that are *blocked* and cannot be entered.\n Invalid attempts to enter a wall result in staying put.\n initial_position : Optional[Tuple[int, int] | int]\n If provided, sets the initial position deterministically (one-hot D).\n Accepts (row, col) or linear index (0..rows*cols-1).\n If None, D is uniform over all *free* cells.\n include_stay : bool\n If True (default), include a \"STAY\" action as the 5th action.\n success_prob : float\n Probability (in [0, 1]) that a movement action succeeds and moves to its intended neighbor.\n The remaining probability (1 - success_prob) results in staying in place.\n Invalid moves (out-of-bounds or into walls) always result in staying put with probability 1.\n categorical_obs : bool\n If ``True``, ``reset()`` and ``step()`` emit one-hot categorical\n observation vectors with shape ``(1, num_obs)``. If ``False``, they\n emit discrete observation indices with shape ``(1,)``.\n\n Notes\n -----\n - Shapes follow the JAX Env API:\n A[0].shape == (num_obs, num_states)\n B[0].shape == (num_states, num_states, num_actions)\n D[0].shape == (num_states,)\n A_dependencies == [[0]]\n B_dependencies == [[0]]\n - Works directly with `pymdp.envs.rollout.rollout` and the JAX `Agent`.\n \"\"\"\n\n # Action ids\n UP = 0\n RIGHT = 1\n DOWN = 2\n LEFT = 3\n STAY = 4 # only present if include_stay=True\n\n def __init__(\n self,\n shape: Tuple[int, int] = (3, 3),\n walls: Optional[Iterable[Tuple[int, int]]] = None,\n initial_position: Optional[Tuple[int, int] | int] = None,\n include_stay: bool = True,\n success_prob: float = 1.0,\n categorical_obs: bool = False,\n ) -> None:\n rows, cols = shape\n assert rows >= 1 and cols >= 1, \"Grid shape must be positive.\"\n assert 0.0 <= success_prob <= 1.0, \"`success_prob` must be in [0, 1].\"\n\n # Precompute data we need\n walls_flat = _flatten_walls(shape, walls)\n n_states = rows * cols\n\n # --- Build A (likelihood), B (transitions), D (initial state) ---\n A, A_dependencies = _generate_A(n_states)\n B, B_dependencies = _generate_B(shape, walls_flat, include_stay, success_prob)\n D = _generate_D(shape, walls_flat, initial_position)\n\n # Wrap in single-element lists to align with the `PymdpEnv` API\n super().__init__(\n A=[A],\n B=[B],\n D=[D],\n A_dependencies=A_dependencies,\n B_dependencies=B_dependencies,\n categorical_obs=categorical_obs,\n )\n\n # ---------------------------------------------------------------------\n # Optional convenience accessors (not required by the API)\n # ---------------------------------------------------------------------\n @staticmethod\n def coords_to_index(shape: Tuple[int, int], coord: Tuple[int, int]) -> int:\n \"\"\"Convert (row, col) -> linear index in 0..rows*cols-1.\"\"\"\n return int(jnp.ravel_multi_index(jnp.array(coord), jnp.array(shape)))\n\n @staticmethod\n def index_to_coords(shape: Tuple[int, int], idx: int) -> Tuple[int, int]:\n \"\"\"Convert linear index -> (row, col).\"\"\"\n return tuple(map(int, jnp.unravel_index(jnp.array(idx), jnp.array(shape))))\n\n\n# =============================================================================\n# Helpers to build A, B, D\n# =============================================================================\n\ndef _flatten_walls(shape: Tuple[int, int], walls: Optional[Iterable[Tuple[int, int]]]) -> set[int]:\n \"\"\"Return a set of flattened indices that are blocked.\"\"\"\n if walls is None:\n return set()\n rows, cols = shape\n walls_flat = set()\n for (r, c) in walls:\n if 0 <= r < rows and 0 <= c < cols:\n walls_flat.add(int(jnp.ravel_multi_index(jnp.array((r, c)), jnp.array(shape))))\n return walls_flat\n\n\ndef _generate_A(n_states: int) -> tuple[jnp.ndarray, list[list[int]]]:\n \"\"\"\n Identity observation over location.\n Returns:\n A: (num_obs, num_states) where num_obs == n_states\n A_dependencies: [[0]] (depends only on location state factor)\n \"\"\"\n A = jnp.eye(n_states) # observe exact location\n A_dependencies = [[0]]\n return A, A_dependencies\n\n\ndef _neighbors(shape: Tuple[int, int], s: int) -> Tuple[int, int, int, int]:\n \"\"\"Return potential neighbor indices for UP, RIGHT, DOWN, LEFT (no validity checks).\"\"\"\n rows, cols = shape\n r, c = divmod(s, cols)\n up = r - 1, c\n right = r, c + 1\n down = r + 1, c\n left = r, c - 1\n # Convert to flattened, but keep invalid ones negative for now (we’ll validate after)\n to_idx = lambda rc: (\n int(jnp.ravel_multi_index(jnp.array(rc), jnp.array(shape))) if (0 <= rc[0] < rows and 0 <= rc[1] < cols) else -1\n )\n return tuple(map(to_idx, (up, right, down, left)))\n\n\ndef _generate_B(\n shape: Tuple[int, int],\n walls_flat: set[int],\n include_stay: bool,\n success_prob: float,\n) -> tuple[jnp.ndarray, list[list[int]]]:\n \"\"\"\n Build transition tensor B with shape (num_states, num_states, num_actions):\n B[next_state, current_state, action]\n - Movement actions that target invalid cells or walls result in staying in place.\n - If success_prob < 1, the remainder (1 - success_prob) stays in place.\n \"\"\"\n rows, cols = shape\n n_states = rows * cols\n n_actions = 4 + int(include_stay)\n\n # Initialize\n B = np.zeros((n_states, n_states, n_actions), dtype=float)\n\n for s in range(n_states):\n # If current state is a wall (shouldn't happen if D avoids it), just reflect self\n stay_state = s\n up_idx, right_idx, down_idx, left_idx = _neighbors(shape, s)\n\n # Resolve invalid or walled neighbors to \"stay\"\n nb = [up_idx, right_idx, down_idx, left_idx]\n nb = [ni if (ni >= 0 and ni not in walls_flat) else stay_state for ni in nb]\n\n # Four movement actions: UP, RIGHT, DOWN, LEFT\n for a, target in enumerate(nb):\n if target == stay_state:\n # invalid move -> always stay\n B[stay_state, s, a] = 1.0\n else:\n if success_prob >= 1.0:\n B[target, s, a] = 1.0\n else:\n # move succeeds with prob p; otherwise stay\n B[target, s, a] = success_prob\n B[stay_state, s, a] = 1.0 - success_prob\n\n # Optional STAY action\n if include_stay:\n B[stay_state, s, 4] = 1.0\n\n # Sanity: columns over next_state must be normalized per (s, a)\n # (they already are by construction above)\n B = jnp.array(B)\n B_dependencies = [[0]] # depends only on its own factor (location)\n return B, B_dependencies\n\n\ndef _generate_D(\n shape: Tuple[int, int],\n walls_flat: set[int],\n initial_position: Optional[Tuple[int, int] | int],\n) -> jnp.ndarray:\n \"\"\"\n Initial state distribution over location.\n - If initial_position is given (r,c) or linear index -> one-hot at that state.\n - Else -> uniform over free cells (not walls).\n \"\"\"\n rows, cols = shape\n n_states = rows * cols\n if initial_position is None:\n # Uniform over free cells\n mask = jnp.ones(n_states, dtype=float)\n if walls_flat:\n idx = jnp.array(sorted(list(walls_flat)))\n mask = mask.at[idx].set(0.0)\n mass = mask.sum()\n # Handle the (rare) degenerate case of all walls (avoid div by zero)\n D = jnp.where(mass > 0, mask / jnp.clip(mass, 1e-16), jnp.ones(n_states) / n_states)\n else:\n if isinstance(initial_position, tuple):\n start_idx = int(jnp.ravel_multi_index(jnp.array(initial_position), jnp.array(shape)))\n else:\n start_idx = int(initial_position)\n assert start_idx not in walls_flat, \"initial_position cannot be a wall.\"\n D = jnp.zeros(n_states)\n D = D.at[start_idx].set(1.0)\n return D\n" }, { "path": "pymdp/envs/rollout.py", "content": "\"\"\"Utilities for running active-inference loops against environment dynamics.\n\nThe two primary public entry points are:\n- :func:`infer_and_plan` for one-step inference/planning/action selection\n- :func:`rollout` for multi-step scanned execution with optional online learning\n\"\"\"\n\nimport warnings\nfrom functools import partial\nfrom typing import Any, Callable\n\nfrom jax import lax, vmap\nimport jax.numpy as jnp\nimport jax.random as jr\nimport jax.tree_util as jtu\nfrom jaxtyping import Array\n\nfrom pymdp import control\nfrom pymdp.agent import Agent\nfrom pymdp.envs.env import Env\nfrom pymdp.inference import SEQUENCE_METHODS, SMOOTHING_METHODS\n\n\nMAX_WINDOWED_HISTORY_WITHOUT_HORIZON = 32\n\n\ndef _append_to_window(window: Array, value: Array) -> Array:\n if window.shape[1] == 0:\n return window\n\n if value.ndim == window.ndim - 1:\n value = jnp.expand_dims(value, axis=1)\n\n value = value[:, -1:, ...]\n return jnp.concatenate([window[:, 1:, ...], value], axis=1)\n\n\ndef _resolve_history_len(agent: Agent, num_timesteps: int, use_windowing: bool) -> int:\n if not use_windowing:\n return 1\n\n if agent.inference_horizon is not None:\n return agent.inference_horizon\n\n uncapped_history_len = num_timesteps + 1\n if uncapped_history_len > MAX_WINDOWED_HISTORY_WITHOUT_HORIZON:\n warnings.warn(\n \"No `inference_horizon` provided for a windowed inference mode; \"\n f\"capping rollout history to {MAX_WINDOWED_HISTORY_WITHOUT_HORIZON} steps \"\n \"to keep fixed-size rollout buffers bounded. \"\n \"Set `inference_horizon` explicitly to override this cap.\",\n UserWarning,\n stacklevel=2,\n )\n return min(uncapped_history_len, MAX_WINDOWED_HISTORY_WITHOUT_HORIZON)\n\n\ndef default_policy_search(agent: Agent, qs: list[Array], rng_key: Array) -> tuple[Array, dict[str, Array]]:\n qpi, neg_efe = agent.infer_policies(\n qs\n ) # infer_policies returns posterior over policies and neg_efe (= -EFE, SPM G)\n return qpi, {\"neg_efe\": neg_efe}\n\n\ndef _resolve_empirical_prior(\n agent: Agent,\n qs_prev: list[Array],\n action_prev: Array | None,\n empirical_prior: list[Array] | None,\n) -> list[Array]:\n if empirical_prior is not None:\n return empirical_prior\n\n if action_prev is None:\n return agent.D\n\n return lax.cond(\n jnp.any(action_prev < 0),\n lambda _: agent.D, # no valid previous action available\n lambda _: agent.update_empirical_prior(action_prev, qs_prev),\n operand=None,\n )\n\n\ndef update_parameters_online(\n agent: Agent,\n qs_prev: list[Array],\n qs: list[Array],\n observation: list[Array] | Array,\n action_prev: Array,\n *,\n learning_observations: list[Array] | Array | None = None,\n learning_actions: Array | None = None,\n learning_beliefs: list[Array] | None = None,\n) -> Agent:\n # `qs_prev` must remain available here: we need it to construct temporal\n # belief pairs for transition learning and smoothing windows.\n if agent.inference_algo in SEQUENCE_METHODS:\n observations_for_learning = (\n observation if learning_observations is None else learning_observations\n )\n if agent.learn_B:\n if learning_actions is None:\n actions_for_learning = jnp.expand_dims(action_prev, 1)\n beliefs_B = jtu.tree_map(\n lambda x, y: jnp.concatenate([x, y], axis=1), qs_prev, qs\n )\n else:\n actions_for_learning = learning_actions\n beliefs_B = qs\n else:\n actions_for_learning = action_prev\n beliefs_B = None\n\n return agent.infer_parameters(\n qs,\n observations_for_learning,\n actions_for_learning,\n beliefs_B=beliefs_B,\n )\n\n if (agent.inference_algo in SMOOTHING_METHODS) and (learning_beliefs is not None):\n observations_for_learning = (\n observation if learning_observations is None else learning_observations\n )\n beliefs_for_learning = jtu.tree_map(\n _append_to_window,\n learning_beliefs,\n qs,\n )\n\n if agent.learn_B:\n actions_for_learning = (\n learning_actions\n if learning_actions is not None\n else jnp.expand_dims(action_prev, 1)\n )\n beliefs_B = beliefs_for_learning\n else:\n actions_for_learning = (\n learning_actions\n if learning_actions is not None\n else action_prev\n )\n beliefs_B = None\n\n return agent.infer_parameters(\n beliefs_for_learning,\n observations_for_learning,\n actions_for_learning,\n beliefs_B=beliefs_B,\n )\n\n if agent.learn_B:\n # Stack beliefs so B-learning can build t->t+1 transitions.\n beliefs_B = jtu.tree_map(lambda x, y: jnp.concatenate([x, y], axis=1), qs_prev, qs)\n action_B = jnp.expand_dims(action_prev, 1)\n else:\n beliefs_B = None\n action_B = action_prev\n\n return agent.infer_parameters(\n qs,\n observation,\n action_B if agent.learn_B else action_prev,\n beliefs_B=beliefs_B,\n )\n\n\ndef _compute_sequence_empirical_prior_next(\n updated_agent: Agent,\n qs_window: list[Array],\n action_hist: Array,\n empirical_prior: list[Array],\n valid_steps: Array,\n history_len: int,\n) -> list[Array]:\n def _shift_empirical_prior(_: Any) -> list[Array]:\n qs_window_start = jtu.tree_map(lambda x: x[:, 0, ...], qs_window)\n action_window_start = action_hist[:, 0, :]\n propagate = partial(\n control.compute_expected_state,\n B_dependencies=updated_agent.B_dependencies,\n )\n return vmap(propagate)(qs_window_start, updated_agent.B, action_window_start)\n\n return lax.cond(\n (valid_steps == history_len) & (history_len > 1),\n _shift_empirical_prior,\n lambda _: empirical_prior,\n operand=None,\n )\n\n\ndef _run_sequence_fixed_window_step(\n agent: Agent,\n qs_prev: list[Array],\n observation_hist: list[Array],\n action_hist: Array,\n action_prev: Array,\n empirical_prior: list[Array],\n valid_steps: Array,\n history_len: int,\n rng_key: Array,\n policy_search: Callable[[Agent, list[Array], Array], tuple[Array, dict[str, Array]]],\n) -> tuple[Agent, Array, list[Array], dict[str, Any], list[Array], list[Array], list[Array]]:\n updated_agent, action_next, qs, xtra = infer_and_plan(\n agent,\n qs_prev,\n observation=observation_hist,\n action_prev=action_prev,\n rng_key=rng_key,\n policy_search=policy_search,\n past_actions=action_hist,\n empirical_prior=empirical_prior,\n learning_observations=observation_hist,\n learning_actions=action_hist,\n valid_steps=valid_steps,\n )\n qs_carry = qs\n qs_latest = jtu.tree_map(lambda x: x[:, -1, ...], qs)\n empirical_prior_next = _compute_sequence_empirical_prior_next(\n updated_agent,\n qs,\n action_hist,\n empirical_prior,\n valid_steps,\n history_len,\n )\n return updated_agent, action_next, qs, xtra, qs_carry, qs_latest, empirical_prior_next\n\n\ndef _run_smoothing_fixed_window_step(\n agent: Agent,\n qs_prev: list[Array],\n observation: list[Array] | Array,\n observation_hist: list[Array],\n action_hist: Array,\n action_prev: Array,\n rng_key: Array,\n policy_search: Callable[[Agent, list[Array], Array], tuple[Array, dict[str, Array]]],\n) -> tuple[Agent, Array, list[Array], dict[str, Any], list[Array], list[Array]]:\n updated_agent, action_next, qs, xtra = infer_and_plan(\n agent,\n qs_prev,\n observation,\n action_prev,\n rng_key,\n policy_search=policy_search,\n learning_observations=observation_hist,\n learning_actions=action_hist,\n learning_beliefs=qs_prev,\n )\n qs_carry = jtu.tree_map(_append_to_window, qs_prev, qs)\n qs_latest = jtu.tree_map(lambda x: x[:, -1, ...], qs)\n return updated_agent, action_next, qs, xtra, qs_carry, qs_latest\n\n\ndef _run_non_window_step(\n agent: Agent,\n qs_prev: list[Array],\n observation: list[Array] | Array,\n action_prev: Array,\n rng_key: Array,\n policy_search: Callable[[Agent, list[Array], Array], tuple[Array, dict[str, Array]]],\n) -> tuple[Agent, Array, list[Array], dict[str, Any], list[Array], list[Array]]:\n updated_agent, action_next, qs, xtra = infer_and_plan(\n agent,\n qs_prev,\n observation,\n action_prev,\n rng_key,\n policy_search=policy_search,\n )\n qs_latest = jtu.tree_map(lambda x: x[:, -1, ...], qs)\n qs_carry = jtu.tree_map(lambda x: x[:, -1:, ...], qs)\n return updated_agent, action_next, qs, xtra, qs_carry, qs_latest\n\n\ndef _update_window_buffers(\n observation_hist: list[Array],\n action_hist: Array,\n valid_steps: Array,\n observation_next: list[Array],\n action_next: Array,\n history_len: int,\n) -> tuple[list[Array], Array, Array]:\n observation_hist_next = jtu.tree_map(_append_to_window, observation_hist, observation_next)\n action_hist_next = _append_to_window(action_hist, action_next)\n valid_steps_next = jnp.minimum(valid_steps + 1, history_len)\n return observation_hist_next, action_hist_next, valid_steps_next\n\n\ndef _init_observation_history(obs: Array, history_len: int, categorical_obs: bool) -> Array:\n if obs.ndim == 1:\n obs = jnp.expand_dims(obs, axis=1)\n history_shape = (obs.shape[0], history_len) + obs.shape[2:]\n if categorical_obs and obs.shape[-1] > 0:\n # Padded categorical timesteps should contribute no evidence.\n hist = jnp.zeros(history_shape, dtype=obs.dtype)\n else:\n hist = jnp.full(history_shape, -1, dtype=obs.dtype)\n start_idx = (0, history_len - 1) + (0,) * (hist.ndim - 2)\n return lax.dynamic_update_slice(hist, obs[:, :1, ...], start_idx)\n\n\ndef _init_windowed_carry(\n agent: Agent,\n observation_0: list[Array],\n env_state: Any,\n rng_key: Array,\n history_len: int,\n action_history_len: int,\n is_sequence_method: bool,\n) -> dict[str, Any]:\n action_0 = -jnp.ones((agent.batch_size, agent.policies.policy_arr.shape[-1]), dtype=jnp.int32)\n\n # Initialize windowed beliefs with D across all slots. Left padded slots are\n # intentionally prior-filled (not neutral-padded): sequence inference/learning\n # uses `valid_steps` and action-validity masks to ignore them until they become\n # part of the valid suffix, and the rolling window then overwrites them over time.\n qs_0 = jtu.tree_map(\n lambda x: jnp.broadcast_to(\n jnp.expand_dims(x, axis=1),\n (x.shape[0], history_len, x.shape[-1]),\n ),\n agent.D,\n )\n\n observation_hist_0 = jtu.tree_map(\n lambda obs: _init_observation_history(obs, history_len, agent.categorical_obs),\n observation_0,\n )\n action_hist_0 = -jnp.ones(\n (agent.batch_size, action_history_len, agent.policies.policy_arr.shape[-1]),\n dtype=jnp.int32,\n )\n\n carry = {\n \"qs\": qs_0,\n \"action\": action_0,\n \"observation\": observation_0,\n \"observation_hist\": observation_hist_0,\n \"action_hist\": action_hist_0,\n \"valid_steps\": jnp.array(1, dtype=jnp.int32),\n \"env_state\": env_state,\n \"agent\": agent,\n \"rng_key\": rng_key,\n }\n if is_sequence_method:\n carry[\"empirical_prior\"] = agent.D\n return carry\n\n\ndef _init_non_windowed_carry(\n agent: Agent, observation_0: list[Array], env_state: Any, rng_key: Array\n) -> dict[str, Any]:\n action_0 = -jnp.ones((agent.batch_size, agent.policies.policy_arr.shape[-1]), dtype=jnp.int32)\n qs_0 = jtu.tree_map(lambda x: jnp.expand_dims(x, -2), agent.D)\n return {\n \"qs\": qs_0,\n \"action\": action_0,\n \"observation\": observation_0,\n \"env_state\": env_state,\n \"agent\": agent,\n \"rng_key\": rng_key,\n }\n\n\ndef infer_and_plan(\n agent: Agent,\n qs_prev: list[Array],\n observation: list[Array] | list[int],\n action_prev: Array | None = None,\n rng_key: Array | None = None,\n policy_search: Callable[[Agent, list[Array], Array], tuple[Array, dict[str, Array]]] | None = None,\n past_actions: Array | None = None,\n empirical_prior: list[Array] | None = None,\n learning_observations: list[Array] | Array | None = None,\n learning_actions: Array | None = None,\n learning_beliefs: list[Array] | None = None,\n valid_steps: int | Array | None = None,\n) -> tuple[Agent, Array, list[Array], dict[str, Any]]:\n \"\"\"Run one active-inference step (state update, policy inference, action sample).\n\n Parameters\n ----------\n agent : Agent\n Active inference agent instance.\n qs_prev : list[Array]\n Previous posterior beliefs over hidden states.\n observation : list[Array] | list[int]\n Current environment observation.\n action_prev : Array | None, optional\n Previous action. If `None`, `agent.D` is used as empirical prior.\n rng_key : Array\n PRNG key used by policy search and action sampling.\n policy_search : callable | None, optional\n Optional custom policy-search function. Defaults to expected-free-energy\n policy inference.\n past_actions : Array | None, optional\n Optional action history for sequence inference methods.\n empirical_prior : list[Array] | None, optional\n Optional override for the empirical prior.\n learning_observations : optional\n Optional learning observation buffer; defaults to current observation.\n learning_actions : optional\n Optional learning action buffer.\n learning_beliefs : optional\n Optional learning belief buffer for smoothing-based updates.\n valid_steps : int | Array | None, optional\n Number of valid timesteps in padded fixed windows.\n\n Returns\n -------\n tuple\n `(updated_agent, action, qs, info)` where `info` contains policy\n posterior and additional policy-search diagnostics.\n \"\"\"\n if policy_search is None:\n policy_search = default_policy_search\n\n empirical_prior = _resolve_empirical_prior(\n agent, qs_prev, action_prev, empirical_prior\n )\n\n # infer states\n qs = agent.infer_states(\n observations=observation,\n empirical_prior=empirical_prior,\n past_actions=past_actions,\n valid_steps=valid_steps,\n )\n\n # get posterior over policies\n rng_key, key = jr.split(rng_key)\n qpi, xtra = policy_search(\n agent, qs, key\n ) # compute policy posterior using EFE - uses C to consider preferred observations\n\n # for learning A and/or B\n if (\n (action_prev is not None)\n and (agent.learning_mode == \"online\")\n and (agent.learn_A or agent.learn_B)\n ):\n agent = update_parameters_online(\n agent,\n qs_prev,\n qs,\n observation,\n action_prev,\n learning_observations=learning_observations,\n learning_actions=learning_actions,\n learning_beliefs=learning_beliefs,\n )\n\n # sample action from policy distribution\n keys = jr.split(rng_key, agent.batch_size + 1)\n rng_key = keys[0]\n action = agent.sample_action(qpi, rng_key=keys[1:])\n\n info = {\"empirical_prior\": empirical_prior, \"qpi\": qpi}\n info.update(xtra) # add extra information from policy search\n return agent, action, qs, info\n\n\ndef rollout(\n agent: Agent,\n env: Env,\n num_timesteps: int,\n rng_key: Array,\n initial_carry: dict[str, Any] | None = None,\n policy_search: Callable[[Agent, list[Array], Array], tuple[Array, dict[str, Array]]] | None = None,\n env_params: Any = None,\n) -> tuple[dict[str, Any], dict[str, Any]]:\n \"\"\"Roll out an active-inference agent/environment loop for `num_timesteps`.\n\n Parameters\n ----------\n agent : Agent\n Active inference agent.\n env : Env\n Environment implementing `reset` and `step`.\n num_timesteps : int\n Number of timesteps to simulate.\n rng_key : Array\n Root PRNG key; internally split per-step and per-batch.\n initial_carry : dict | None, optional\n Optional carry overrides for warm-starting from existing state.\n policy_search : callable | None, optional\n Optional custom policy-search routine.\n env_params : pytree | None, optional\n Optional batched environment parameters.\n\n Returns\n ----------\n last : dict\n Final carry state after the final timestep.\n info : dict\n Time-indexed rollout traces (actions, observations, beliefs, etc.).\n \"\"\"\n\n # get the batch_size of the agent\n batch_size = agent.batch_size\n is_sequence_method = agent.inference_algo in SEQUENCE_METHODS\n use_smoothing_online_windows = (\n (agent.inference_algo in SMOOTHING_METHODS)\n and (agent.learning_mode == \"online\")\n and (agent.learn_A or agent.learn_B)\n )\n use_windowing = is_sequence_method or use_smoothing_online_windows\n history_len = _resolve_history_len(agent, num_timesteps, use_windowing)\n action_history_len = max(history_len - 1, 0)\n\n # default policy search just uses standard active inference policy selection\n if policy_search is None:\n policy_search = default_policy_search\n\n def step_fn(carry: dict[str, Any], t: Array) -> tuple[dict[str, Any], dict[str, Any]]:\n # Carry current action/observation/beliefs/state and RNG through scan.\n # We keep `qs_prev` explicitly because smoothing and transition learning\n # require temporal belief context beyond the empirical prior alone.\n action = carry[\"action\"]\n observation = carry[\"observation\"]\n qs_prev = carry[\"qs\"]\n env_state = carry[\"env_state\"]\n agent = carry[\"agent\"]\n rng_key = carry[\"rng_key\"]\n\n keys = jr.split(rng_key, batch_size + 2)\n rng_key = keys[0] # carry first key\n\n use_fixed_window = is_sequence_method or use_smoothing_online_windows\n if use_fixed_window:\n observation_hist = carry[\"observation_hist\"]\n action_hist = carry[\"action_hist\"]\n valid_steps = carry[\"valid_steps\"]\n\n if is_sequence_method:\n empirical_prior = carry[\"empirical_prior\"]\n (\n updated_agent,\n action_next,\n qs,\n xtra,\n qs_carry,\n qs_latest,\n empirical_prior_next,\n ) = _run_sequence_fixed_window_step(\n agent,\n qs_prev,\n observation_hist,\n action_hist,\n action,\n empirical_prior,\n valid_steps,\n history_len,\n keys[1],\n policy_search,\n )\n else:\n updated_agent, action_next, qs, xtra, qs_carry, qs_latest = _run_smoothing_fixed_window_step(\n agent,\n qs_prev,\n observation,\n observation_hist,\n action_hist,\n action,\n keys[1],\n policy_search,\n )\n empirical_prior_next = None\n else:\n # infer next action and beliefs using the agent's inference and planning methods\n updated_agent, action_next, qs, xtra, qs_carry, qs_latest = _run_non_window_step(\n agent,\n qs_prev,\n observation,\n action,\n keys[1],\n policy_search,\n )\n\n observation_next, env_state_next = vmap(env.step)(\n keys[2:], env_state, action_next, env_params=env_params\n )\n if updated_agent.learn_A:\n xtra[\"A\"] = updated_agent.A\n xtra[\"pA\"] = updated_agent.pA\n if updated_agent.learn_B:\n xtra[\"B\"] = updated_agent.B\n xtra[\"pB\"] = updated_agent.pB\n\n if use_fixed_window:\n observation_hist = carry[\"observation_hist\"]\n action_hist = carry[\"action_hist\"]\n valid_steps = carry[\"valid_steps\"]\n (\n observation_hist_next,\n action_hist_next,\n valid_steps_next,\n ) = _update_window_buffers(\n observation_hist,\n action_hist,\n valid_steps,\n observation_next,\n action_next,\n history_len,\n )\n\n carry = {\n \"action\": action_next,\n \"observation\": observation_next,\n \"observation_hist\": observation_hist_next,\n \"action_hist\": action_hist_next,\n \"valid_steps\": valid_steps_next,\n \"qs\": qs_carry,\n \"env_state\": env_state_next,\n \"agent\": updated_agent,\n \"rng_key\": rng_key,\n }\n if is_sequence_method:\n carry[\"empirical_prior\"] = empirical_prior_next\n else:\n carry = {\n \"action\": action_next,\n \"observation\": observation_next,\n \"qs\": qs_carry,\n \"env_state\": env_state_next,\n \"agent\": updated_agent,\n \"rng_key\": rng_key,\n }\n\n info = {\n \"qs\": qs_latest,\n \"env_state\": env_state,\n \"observation\": observation,\n \"action\": action_next,\n }\n info.update(xtra) # add extra information from inference and planning\n\n return carry, info\n\n # initialise first observation from environment\n keys = jr.split(rng_key, batch_size + 1)\n rng_key = keys[0]\n observation_0, env_state = vmap(env.reset)(keys[1:], env_params=env_params)\n\n if is_sequence_method or use_smoothing_online_windows:\n built_carry = _init_windowed_carry(\n agent,\n observation_0,\n env_state,\n rng_key,\n history_len,\n action_history_len,\n is_sequence_method,\n )\n else:\n built_carry = _init_non_windowed_carry(\n agent,\n observation_0,\n env_state,\n rng_key,\n )\n\n if initial_carry is not None:\n built_carry = {**built_carry, **initial_carry}\n\n initial_carry = built_carry\n \n # run the active inference loop for num_timesteps using lax.scan\n last, info = lax.scan(step_fn, initial_carry, jnp.arange(num_timesteps + 1))\n\n info = jtu.tree_map(\n lambda x: x.transpose((1, 0) + tuple(range(2, x.ndim))), info\n ) # transpose to have timesteps as first dimension\n\n if agent.learning_mode == \"offline\":\n def _format_offline_observations(x: Array) -> Array:\n # Handle env wrappers that emit either (B, T, 1, O) or (B, T, O)\n # for categorical observations, and either (B, T, 1) or (B, T) for\n # discrete observations.\n if agent.categorical_obs:\n if x.ndim >= 4 and x.shape[2] == 1:\n return x[:, :, 0, ...]\n return x\n if x.ndim >= 3 and x.shape[-1] == 1:\n return x[..., 0]\n return x\n\n observations_for_learning = jtu.tree_map(_format_offline_observations, info[\"observation\"])\n last[\"agent\"] = last[\"agent\"].infer_parameters(\n info[\"qs\"],\n observations_for_learning,\n info[\"action\"],\n )\n\n return last, info\n" }, { "path": "pymdp/envs/tmaze.py", "content": "import os\nimport math\nfrom typing import Optional\nimport jax.numpy as jnp\nimport matplotlib.pyplot as plt\nimport matplotlib.patches as patches\nfrom matplotlib.offsetbox import OffsetImage, AnnotationBbox\nimport scipy.ndimage as ndimage\nfrom pymdp.utils import fig2img\nfrom equinox import field\nfrom .env import PymdpEnv\n\n\n# load assets\nassets_dir = os.path.join(os.path.dirname(os.path.realpath(__file__)), \"assets\")\nmouse_img = plt.imread(os.path.join(assets_dir, \"mouse.png\"))\nright_mouse_img = jnp.clip(ndimage.rotate(mouse_img, 90, reshape=True), 0.0, 1.0)\nleft_mouse_img = jnp.clip(ndimage.rotate(mouse_img, -90, reshape=True), 0.0, 1.0)\nup_mouse_img = jnp.clip(ndimage.rotate(mouse_img, 180, reshape=True), 0.0, 1.0)\ncheese_img = plt.imread(os.path.join(assets_dir, \"cheese.png\"))\nshock_img = plt.imread(os.path.join(assets_dir, \"shock.png\"))\n\n\nclass BaseTMaze(PymdpEnv):\n \"\"\"\n Shared T-Maze implementation with configurable layout and observation structure.\n Description: A T-shaped maze where an agent must navigate to find a reward, with:\n - 4 (or 5) locations: centre, left arm, right arm, cue position (bottom), and optionally a middle location\n - 2 reward conditions: reward in left or right arm\n - 2 possible cues at the bottom arm that indicate which arm contains the reward\n \"\"\"\n\n reward_probability: float = field(static=True)\n punishment_probability: float = field(static=True)\n cue_validity: float = field(static=True)\n reward_condition: float = field(static=True)\n dependent_outcomes: bool = field(static=True)\n cue_mode: str = field(static=True)\n connectivity: str = field(static=True)\n has_middle: bool = field(static=True)\n num_locations: int = field(static=True)\n location_obs_size: int = field(static=True)\n\n def __init__(\n self,\n reward_probability: float = 1.0,\n punishment_probability: float = 1.0,\n cue_validity: float = 0.95,\n reward_condition: Optional[int] = None,\n dependent_outcomes: bool = False,\n categorical_obs: bool = False,\n *,\n num_locations: int,\n cue_mode: str,\n connectivity: str,\n has_middle: bool,\n location_obs_size: Optional[int] = None,\n ) -> None:\n \"\"\"\n Initialize a configurable T-Maze environment.\n\n Parameters\n ----------\n reward_probability : float, optional\n Probability of receiving reward when choosing the correct arm.\n punishment_probability : float, optional\n Probability of receiving punishment when choosing the incorrect arm.\n cue_validity : float, optional\n Probability that the cue correctly indicates the reward location.\n reward_condition : int | None, optional\n If specified, fixes reward to left (0) or right (1) arm, otherwise random.\n dependent_outcomes : bool, optional\n If ``True``, punishment occurs as a function of reward probability.\n If ``False``, punishment occurs with the fixed\n ``punishment_probability``.\n categorical_obs : bool, default=False\n If ``True``, ``reset()`` and ``step()`` emit one-hot categorical\n observation vectors with shape ``(1, num_obs_m)`` for each modality.\n If ``False``, they emit discrete observation indices with shape\n ``(1,)``.\n num_locations : int\n Number of locations in the maze (4 or 5).\n cue_mode : str\n ``\"separate\"`` for a separate cue modality or ``\"embedded\"`` for\n cue information embedded in the location modality.\n connectivity : str\n ``\"fully_connected\"`` or ``\"adjacent\"`` transition structure.\n has_middle : bool\n If ``True``, includes a middle location between arms.\n location_obs_size : int | None, optional\n Size of the location observation modality. Required for embedded cue\n mode when overriding the default.\n \"\"\"\n self.reward_probability = reward_probability\n self.punishment_probability = punishment_probability\n self.cue_validity = cue_validity\n self.reward_condition = reward_condition\n self.dependent_outcomes = dependent_outcomes\n self.cue_mode = cue_mode\n self.connectivity = connectivity\n self.has_middle = has_middle\n self.num_locations = num_locations\n\n self._location_indices = {\"centre\": 0, \"left\": 1, \"right\": 2, \"cue\": 3}\n if self.has_middle:\n self._location_indices[\"middle\"] = 4\n\n if self.cue_mode == \"embedded\":\n self._loc_obs_cued_left = self._location_indices[\"cue\"]\n self._loc_obs_cued_right = self._location_indices[\"cue\"] + 1\n if location_obs_size is None:\n location_obs_size = self._loc_obs_cued_right + 1\n else:\n if location_obs_size is None:\n location_obs_size = self.num_locations\n self.location_obs_size = location_obs_size\n\n if self.cue_mode == \"embedded\":\n self._loc_obs_to_location = list(range(self._location_indices[\"cue\"] + 1))\n self._loc_obs_to_location.append(self._location_indices[\"cue\"])\n self._cue_obs_from_loc_obs = [0] * self.location_obs_size\n self._cue_obs_from_loc_obs[self._loc_obs_cued_left] = 1\n self._cue_obs_from_loc_obs[self._loc_obs_cued_right] = 2\n else:\n self._loc_obs_to_location = list(range(self.location_obs_size))\n self._cue_obs_from_loc_obs = None\n\n A, A_dependencies = self.generate_A()\n B, B_dependencies = self.generate_B()\n D = self.generate_D()\n\n super().__init__(\n A=A,\n B=B,\n D=D,\n A_dependencies=A_dependencies,\n B_dependencies=B_dependencies,\n categorical_obs=categorical_obs,\n )\n\n def _set_reward_outcome(self, A_reward: jnp.ndarray, loc: int, reward_condition: int) -> jnp.ndarray:\n if loc == (reward_condition + 1):\n A_reward = A_reward.at[1, loc, reward_condition].set(self.reward_probability)\n if self.dependent_outcomes:\n A_reward = A_reward.at[2, loc, reward_condition].set(1 - self.reward_probability)\n else:\n A_reward = A_reward.at[0, loc, reward_condition].set(1 - self.reward_probability)\n else:\n if self.dependent_outcomes:\n A_reward = A_reward.at[2, loc, reward_condition].set(self.reward_probability)\n A_reward = A_reward.at[1, loc, reward_condition].set(1 - self.reward_probability)\n else:\n A_reward = A_reward.at[2, loc, reward_condition].set(self.punishment_probability)\n A_reward = A_reward.at[0, loc, reward_condition].set(1 - self.punishment_probability)\n return A_reward\n\n def generate_A(self) -> tuple[list[jnp.ndarray], list[list[int]]]:\n if self.cue_mode == \"separate\":\n return self._generate_A_separate()\n if self.cue_mode == \"embedded\":\n return self._generate_A_embedded()\n raise ValueError(f\"Unsupported cue_mode: {self.cue_mode}\")\n\n def _generate_A_separate(self) -> tuple[list[jnp.ndarray], list[list[int]]]:\n \"\"\"\n Generate observation likelihood tensors.\n \n Returns three observation matrices:\n A[0]: Location observations (5x5 identity matrix)\n - Maps true location to observed location\n - [centre, left, right, cue, middle] x [centre, left, right, cue, middle]\n A[1]: Reward observations (3x5 x2 matrix)\n - [no outcome, reward, punishment] x [5 locations] x [2 reward conditions]\n A[2]: Cue observations (3x5x2 matrix)\n - [no cue, cued left arm, cued right arm] x [5 locations] x [2 reward conditions]\n \"\"\"\n A = []\n A.append(jnp.eye(self.num_locations))\n A.append(jnp.zeros([3, self.num_locations, 2]))\n A.append(jnp.zeros([3, self.num_locations, 2]))\n\n A_dependencies = [[0], [0, 1], [0, 1]]\n middle_idx = self._location_indices.get(\"middle\")\n\n for loc in range(self.num_locations):\n for reward_condition in range(2):\n if loc == self._location_indices[\"centre\"]:\n A[1] = A[1].at[0, loc, reward_condition].set(1.0)\n A[2] = A[2].at[0, loc, reward_condition].set(1.0)\n elif loc == self._location_indices[\"cue\"]:\n A[1] = A[1].at[0, loc, reward_condition].set(1.0)\n A[2] = A[2].at[reward_condition + 1, loc, reward_condition].set(self.cue_validity)\n wrong_cue = (1 - reward_condition) + 1\n A[2] = A[2].at[wrong_cue, loc, reward_condition].set(1 - self.cue_validity)\n elif middle_idx is not None and loc == middle_idx:\n A[1] = A[1].at[0, loc, reward_condition].set(1.0)\n A[2] = A[2].at[0, loc, reward_condition].set(1.0)\n else:\n A[1] = self._set_reward_outcome(A[1], loc, reward_condition)\n A[2] = A[2].at[0, loc, reward_condition].set(1.0)\n\n return A, A_dependencies\n\n def _generate_A_embedded(self) -> tuple[list[jnp.ndarray], list[list[int]]]:\n \"\"\"\n Generate observation likelihood tensors.\n \n Returns two observation matrices:\n A[0]: Location observations with embedded cues (location_obs_size x5x2 matrix)\n - Maps true location to observed location with embedded cue information\n - [centre, left, right, cued left, cued right] x [centre, left, right, cue, middle] x [2 reward conditions]\n A[1]: Reward observations (3x5x2 matrix)\n - [no outcome, reward, punishment] x [5 locations] x [2 reward conditions]\n \"\"\"\n A = []\n A.append(jnp.zeros([self.location_obs_size, self.num_locations, 2]))\n A.append(jnp.zeros([3, self.num_locations, 2]))\n\n A_dependencies = [[0, 1], [0, 1]]\n\n for loc in range(self.num_locations):\n for reward_condition in range(2):\n if loc == self._location_indices[\"centre\"]:\n A[0] = A[0].at[0, loc, reward_condition].set(1.0)\n A[1] = A[1].at[0, loc, reward_condition].set(1.0)\n elif loc == self._location_indices[\"cue\"]:\n if reward_condition == 0:\n A[0] = A[0].at[self._loc_obs_cued_left, loc, reward_condition].set(self.cue_validity)\n A[0] = A[0].at[self._loc_obs_cued_right, loc, reward_condition].set(1 - self.cue_validity)\n else:\n A[0] = A[0].at[self._loc_obs_cued_right, loc, reward_condition].set(self.cue_validity)\n A[0] = A[0].at[self._loc_obs_cued_left, loc, reward_condition].set(1 - self.cue_validity)\n A[1] = A[1].at[0, loc, reward_condition].set(1.0)\n else:\n A[0] = A[0].at[loc, loc, reward_condition].set(1.0)\n A[1] = self._set_reward_outcome(A[1], loc, reward_condition)\n\n return A, A_dependencies\n\n def _valid_connections(self) -> list[tuple[int, int]]:\n centre = self._location_indices[\"centre\"]\n left = self._location_indices[\"left\"]\n right = self._location_indices[\"right\"]\n cue = self._location_indices[\"cue\"]\n\n if self.has_middle:\n middle = self._location_indices[\"middle\"]\n return [\n (centre, cue),\n (cue, centre),\n (centre, middle),\n (middle, centre),\n (middle, left),\n (left, middle),\n (middle, right),\n (right, middle),\n ]\n return [\n (centre, cue),\n (cue, centre),\n (centre, left),\n (left, centre),\n (centre, right),\n (right, centre),\n ]\n\n def generate_B(self) -> tuple[list[jnp.ndarray], list[list[int]]]:\n \"\"\"\n Generate transition model matrices.\n \n Returns two transition matrices:\n B[0]: Location transitions (num_locations x num_locations x num_locations)\n - Agent can move between either\n all locations in the T-Maze (fully-connected) or adjacent locations, including a middle location between the two arms, in the T-Maze (adjacent)\n B[1]: Reward condition transitions (2x2x1)\n - Reward location stays fixed\n \"\"\"\n B = []\n B_loc = jnp.zeros((self.num_locations, self.num_locations, self.num_locations))\n\n if self.connectivity == \"fully_connected\":\n for action in range(self.num_locations):\n B_loc = B_loc.at[action, :, action].set(1.0)\n elif self.connectivity == \"adjacent\":\n valid_connections = set(self._valid_connections())\n for _from in range(self.num_locations):\n for action in range(self.num_locations):\n _to = action\n if (_from, _to) in valid_connections:\n B_loc = B_loc.at[_to, _from, action].set(1.0)\n else:\n B_loc = B_loc.at[_from, _from, action].set(1.0)\n else:\n raise ValueError(f\"Unsupported connectivity: {self.connectivity}\")\n\n B.append(B_loc)\n B_reward = jnp.eye(2).reshape(2, 2, 1)\n B.append(B_reward)\n B_dependencies = [[0], [1]]\n return B, B_dependencies\n\n def generate_D(self) -> list[jnp.ndarray]:\n \"\"\"\n Generate initial state distribution.\n \n Returns two initial state vectors:\n D[0]: Initial location (5,)\n - Agent always starts in centre (index 0)\n D[1]: Initial reward condition (2,)\n - Either random (50/50) or fixed based on reward_condition\n \n Args:\n reward_condition: If specified, fixes reward to left (0) or right (1) arm, otherwise random\n \"\"\"\n D = []\n D_loc = jnp.zeros([self.num_locations])\n D_loc = D_loc.at[self._location_indices[\"centre\"]].set(1.0)\n D.append(D_loc)\n\n if self.reward_condition is None:\n D_reward = jnp.ones(2) * 0.5\n else:\n D_reward = jnp.zeros(2)\n D_reward = D_reward.at[self.reward_condition].set(1.0)\n D.append(D_reward)\n return D\n\n def render(\n self, observations: list[jnp.ndarray], mode: str = \"human\", title: Optional[str] = None\n ) -> jnp.ndarray | None:\n batch_size = observations[0].shape[0]\n\n plt.clf()\n\n def _decode_obs(modality: int, batch_idx: int) -> int:\n obs_value = observations[modality][batch_idx, 0]\n if obs_value.size > 1:\n return int(jnp.argmax(obs_value))\n return int(jnp.squeeze(obs_value))\n\n # create n x n subplots for the batch_size\n n = math.ceil(math.sqrt(batch_size))\n fig, axes = plt.subplots(n, n, figsize=(6, 6))\n if title:\n fig.suptitle(title, fontsize=9)\n\n # loop through the batch_size and plot on each subplot\n for i in range(batch_size):\n row = i // n\n col = i % n\n if batch_size == 1:\n ax = axes\n else:\n ax = axes[row, col]\n\n grid_dims = [3, 3]\n X, Y = jnp.meshgrid(jnp.arange(grid_dims[1] + 1), jnp.arange(grid_dims[0] + 1))\n ax.pcolormesh(\n X, Y, jnp.ones(grid_dims), edgecolors=\"none\", vmin=0, vmax=30, linewidth=5, cmap=\"coolwarm\", snap=True\n )\n ax.invert_yaxis()\n ax.axis(\"off\")\n ax.set_aspect(\"equal\")\n\n ax.add_patch(\n patches.Rectangle(\n (0, 1),\n 1.0,\n 2.0,\n linewidth=0,\n facecolor=[1.0, 1.0, 1.0],\n )\n )\n\n ax.add_patch(\n patches.Rectangle(\n (2, 1),\n 1.0,\n 2.0,\n linewidth=0,\n facecolor=[1.0, 1.0, 1.0],\n )\n )\n\n ax.add_patch(\n patches.Rectangle(\n (0, 0),\n 1.0,\n 1.0,\n linewidth=0,\n facecolor=\"tab:orange\",\n )\n )\n\n ax.add_patch(\n patches.Rectangle(\n (2, 0),\n 1.0,\n 1.0,\n linewidth=0,\n facecolor=\"tab:purple\",\n )\n )\n\n loc_obs = _decode_obs(0, i)\n reward_obs = _decode_obs(1, i)\n if self.cue_mode == \"embedded\":\n cue_obs = self._cue_obs_from_loc_obs[loc_obs]\n loc = self._loc_obs_to_location[loc_obs]\n else:\n cue_obs = _decode_obs(2, i)\n loc = loc_obs\n\n if cue_obs == 0:\n cue_color = \"tab:gray\"\n edge_color = \"tab:gray\"\n elif cue_obs == 1:\n cue_color = \"tab:orange\"\n edge_color = \"tab:gray\"\n else:\n cue_color = \"tab:purple\"\n edge_color = \"tab:gray\"\n\n ax.add_patch(\n patches.Circle(\n (1.5, 2.5),\n 0.3,\n linewidth=8,\n edgecolor=edge_color,\n facecolor=cue_color,\n )\n )\n\n coords = None\n if loc == 1:\n coords = (0.5, 0.5)\n elif loc == 2:\n coords = (2.5, 0.5)\n\n if coords is not None:\n if reward_obs == 1:\n cheese_im = OffsetImage(cheese_img, zoom=0.025 / n)\n ab_cheese = AnnotationBbox(cheese_im, coords, xycoords=\"data\", frameon=False)\n an_cheese = ax.add_artist(ab_cheese)\n an_cheese.set_zorder(2)\n elif reward_obs == 2:\n shock_im = OffsetImage(shock_img, zoom=0.1 / n)\n ab_shock = AnnotationBbox(shock_im, coords, xycoords=\"data\", frameon=False)\n ab_shock = ax.add_artist(ab_shock)\n ab_shock.set_zorder(2)\n\n if loc == 0:\n up_mouse_im = OffsetImage(up_mouse_img, zoom=0.04 / n)\n ab_mouse = AnnotationBbox(up_mouse_im, (1.5, 1.5), xycoords=\"data\", frameon=False)\n ab_mouse = ax.add_artist(ab_mouse)\n ab_mouse.set_zorder(3)\n elif loc == 1:\n left_mouse_im = OffsetImage(left_mouse_img, zoom=0.04 / n)\n ab_mouse = AnnotationBbox(left_mouse_im, (0.75, 0.5), xycoords=\"data\", frameon=False)\n ab_mouse = ax.add_artist(ab_mouse)\n ab_mouse.set_zorder(3)\n elif loc == 2:\n right_mouse_im = OffsetImage(right_mouse_img, zoom=0.04 / n)\n ab_mouse = AnnotationBbox(right_mouse_im, (2.25, 0.5), xycoords=\"data\", frameon=False)\n ab_mouse = ax.add_artist(ab_mouse)\n ab_mouse.set_zorder(3)\n elif loc == 3:\n down_mouse_im = OffsetImage(mouse_img, zoom=0.04 / n)\n ab_mouse = AnnotationBbox(down_mouse_im, (1.5, 2.25), xycoords=\"data\", frameon=False)\n ab_mouse = ax.add_artist(ab_mouse)\n ab_mouse.set_zorder(3)\n elif loc == 4:\n middle_mouse_im = OffsetImage(up_mouse_img, zoom=0.04 / n)\n ab_mouse = AnnotationBbox(middle_mouse_im, (1.5, 0.5), xycoords=\"data\", frameon=False)\n ab_mouse = ax.add_artist(ab_mouse)\n ab_mouse.set_zorder(3)\n\n for i in range(batch_size, n * n):\n fig.delaxes(axes.flatten()[i])\n\n if title:\n fig.tight_layout(rect=[0, 0, 1, 0.93])\n else:\n plt.tight_layout()\n\n if mode == \"human\":\n plt.show()\n elif mode == \"rgb_array\":\n img = fig2img(fig)\n plt.close(fig)\n return img\n\n\nclass TMaze(BaseTMaze):\n \"\"\"\n Classic T-Maze with a middle connector, adjacent transitions, and a separate cue modality.\n \"\"\"\n\n def __init__(\n self,\n reward_probability: float = 1.0,\n punishment_probability: float = 1.0,\n cue_validity: float = 0.95,\n reward_condition: Optional[int] = None,\n dependent_outcomes: bool = False,\n categorical_obs: bool = False,\n ) -> None:\n super().__init__(\n reward_probability=reward_probability,\n punishment_probability=punishment_probability,\n cue_validity=cue_validity,\n reward_condition=reward_condition,\n dependent_outcomes=dependent_outcomes,\n categorical_obs=categorical_obs,\n num_locations=5,\n cue_mode=\"separate\",\n connectivity=\"adjacent\",\n has_middle=True,\n )\n\n\nclass SimplifiedTMaze(BaseTMaze):\n \"\"\"\n Fully connected T-Maze with embedded cues and no middle connector.\n \"\"\"\n\n def __init__(\n self,\n reward_condition: Optional[int] = None,\n cue_validity: float = 0.95,\n reward_probability: float = 1.0,\n dependent_outcomes: bool = False,\n punishment_probability: float = 1.0,\n categorical_obs: bool = False,\n ) -> None:\n super().__init__(\n reward_probability=reward_probability,\n punishment_probability=punishment_probability,\n cue_validity=cue_validity,\n reward_condition=reward_condition,\n dependent_outcomes=dependent_outcomes,\n categorical_obs=categorical_obs,\n num_locations=4,\n cue_mode=\"embedded\",\n connectivity=\"fully_connected\",\n has_middle=False,\n location_obs_size=5,\n )\n" }, { "path": "pymdp/inference.py", "content": "#!/usr/bin/env python\n# -*- coding: utf-8 -*-\n# pylint: disable=no-member\n\"\"\"State inference and smoothing utilities for modern JAX-based pymdp agents.\n\nThis module provides:\n- one-step posterior updates (`fpi`, `exact`, `ovf`),\n- sequence-based inference (`mmp`, `vmp`),\n- backward smoothing utilities for transition/posterior learning.\n\nAll public functions operate on JAX arrays and pytrees and are designed to\nwork with batched agent execution (`vmap`) and fixed-window sequence buffers.\n\"\"\"\n\nimport jax.numpy as jnp\nfrom typing import Any, TypedDict\nfrom pymdp.algos import (\n run_factorized_fpi,\n run_mmp,\n run_vmp,\n hmm_smoother_from_filtered_colstoch,\n)\nfrom pymdp.maths import calc_vfe\nfrom jax import tree_util as jtu, lax\nfrom jax.experimental.sparse._base import JAXSparse\nfrom jax.experimental import sparse\nfrom jaxtyping import Array, ArrayLike\n\neps = jnp.finfo('float').eps\n\nEXACT_METHOD = \"exact\"\nONE_STEP_METHODS = {\"fpi\", \"ovf\", EXACT_METHOD}\nSEQUENCE_METHODS = {\"mmp\", \"vmp\"}\nSMOOTHING_METHODS = {\"ovf\", EXACT_METHOD}\n\n\nclass VFEInfo(TypedDict):\n vfe_t: ArrayLike\n vfe: ArrayLike\n vfe_components: dict[str, ArrayLike]\n\n\ndef _select_current_obs(obs: list[Array] | Array, distr_obs: bool) -> list[Array] | Array:\n def _select_leaf(x: Array) -> Array:\n if x.ndim == 0:\n return x\n if distr_obs:\n # Distributional observations use the last axis for observations, so\n # 1D leaves are already a single-time-step observation.\n return x if x.ndim == 1 else x[-1]\n return x[-1]\n\n return jtu.tree_map(_select_leaf, obs)\n\n\ndef _truncate_for_horizon(\n obs: list[Array], past_actions: Array | None, inference_horizon: int | None\n) -> tuple[list[Array], Array | None]:\n if inference_horizon is None:\n return obs, past_actions\n\n if inference_horizon < 1:\n raise ValueError(\"`inference_horizon` must be >= 1 when provided\")\n\n obs = jtu.tree_map(lambda x: x[-inference_horizon:], obs)\n if past_actions is None:\n return obs, None\n\n action_horizon = max(inference_horizon - 1, 0)\n if action_horizon == 0:\n return obs, past_actions[:0]\n\n return obs, past_actions[-action_horizon:]\n\n\ndef _ensure_action_history_shape(past_actions: Array | None, num_factors: int) -> Array | None:\n if past_actions is None:\n return None\n\n if past_actions.ndim == 1:\n if num_factors == 1:\n return jnp.expand_dims(past_actions, -1)\n raise ValueError(\n \"1D `past_actions` is only supported for single-factor action \"\n \"histories; multi-factor action histories must have shape \"\n \"(T-1, num_factors). For a single timestep across factors, use \"\n \"`past_actions[None, :]`.\"\n )\n\n if past_actions.ndim != 2:\n raise ValueError(\"`past_actions` must have shape (T-1, num_factors) per batch sample\")\n\n if past_actions.shape[1] != num_factors:\n raise ValueError(\n f\"`past_actions` has second dimension {past_actions.shape[1]}, expected {num_factors}\"\n )\n\n return past_actions\n\n\ndef _build_sequence_validity_masks(\n obs: list[Array], past_actions: Array | None, valid_steps: int | Array | None\n) -> tuple[Array, Array]:\n T = obs[0].shape[0]\n\n if valid_steps is None:\n obs_valid = jnp.ones((T,), dtype=bool)\n else:\n valid_steps = jnp.asarray(valid_steps, dtype=jnp.int32)\n k = jnp.clip(valid_steps, 1, T)\n obs_valid = jnp.arange(T) >= (T - k)\n\n if T <= 1:\n trans_valid = jnp.zeros((0,), dtype=bool)\n else:\n trans_valid = obs_valid[:-1] & obs_valid[1:]\n if past_actions is not None:\n action_valid = jnp.all(past_actions >= 0, axis=-1)\n trans_valid = trans_valid & action_valid\n\n return obs_valid, trans_valid\n\n\ndef _condition_transitions_on_actions(\n B: list[ArrayLike],\n past_actions: Array,\n invalid_action_mode: str = \"neutral\",\n) -> list[Array]:\n nf = len(B)\n past_actions = _ensure_action_history_shape(past_actions, nf)\n actions_tree = [past_actions[:, i] for i in range(nf)]\n\n def _select_transitions_for_actions(b: ArrayLike, action_idx: Array) -> Array:\n if isinstance(b, JAXSparse):\n b = sparse.todense(b)\n\n action_idx = action_idx.astype(jnp.int32)\n safe_idx = jnp.where(action_idx < 0, 0, action_idx)\n selected = jnp.moveaxis(jnp.take(b, safe_idx, axis=-1), -1, 0)\n\n if invalid_action_mode == \"neutral\":\n invalid_transition = jnp.ones_like(b[..., 0], dtype=b.dtype)\n invalid_transition = invalid_transition / jnp.clip(\n invalid_transition.sum(axis=0, keepdims=True), min=eps\n )\n elif invalid_action_mode == \"identity\":\n transition = b[..., 0]\n if transition.ndim != 2 or transition.shape[0] != transition.shape[1]:\n raise ValueError(\n \"`invalid_action_mode='identity'` requires square 2D transitions \"\n \"after action selection\"\n )\n invalid_transition = jnp.eye(transition.shape[0], dtype=transition.dtype)\n else:\n raise ValueError(\n f\"Unsupported invalid_action_mode `{invalid_action_mode}`. \"\n \"Expected one of {'neutral', 'identity'}.\"\n )\n\n invalid_transition = jnp.broadcast_to(invalid_transition, selected.shape)\n\n invalid = (action_idx < 0).reshape((action_idx.shape[0],) + (1,) * (selected.ndim - 1))\n return jnp.where(invalid, invalid_transition, selected)\n\n return [\n _select_transitions_for_actions(b, action_idx)\n for b, action_idx in zip(B, actions_tree)\n ]\n\n\ndef _run_one_step_inference(\n A: list[Array],\n obs: list[Array],\n prior: list[Array] | None,\n A_dependencies: list[list[int]] | None,\n *,\n method: str,\n num_iter: int,\n distr_obs: bool,\n) -> tuple[list[Array], list[Array] | Array]:\n curr_obs = _select_current_obs(obs, distr_obs)\n fpi_num_iter = 1 if method == EXACT_METHOD else num_iter\n qs = run_factorized_fpi(\n A,\n curr_obs,\n prior,\n A_dependencies,\n num_iter=fpi_num_iter,\n distr_obs=distr_obs,\n )\n return qs, curr_obs\n\n\ndef _run_sequence_inference(\n A: list[Array],\n B: list[Array] | None,\n obs: list[Array],\n past_actions: Array | None,\n prior: list[Array] | None,\n A_dependencies: list[list[int]] | None,\n B_dependencies: list[list[int]] | None,\n *,\n method: str,\n num_iter: int,\n distr_obs: bool,\n valid_steps: int | Array | None,\n) -> tuple[list[Array], Array | None, Array | None]:\n if B is None:\n raise ValueError(f\"Sequence inference method `{method}` requires `B`.\")\n\n obs_valid_mask = None\n transition_valid_mask = None\n history_len = max(obs[0].shape[0] - 1, 0)\n\n if past_actions is not None:\n past_actions = _ensure_action_history_shape(past_actions, len(B))\n if past_actions.shape[0] != history_len:\n raise ValueError(\n \"`past_actions` has leading dimension \"\n f\"{past_actions.shape[0]}, expected {history_len}\"\n )\n\n if valid_steps is not None:\n obs_valid_mask, transition_valid_mask = _build_sequence_validity_masks(\n obs, past_actions, valid_steps\n )\n\n conditioned_B = None\n if past_actions is not None:\n conditioned_B = _condition_transitions_on_actions(B, past_actions)\n elif history_len > 0:\n conditioned_B = []\n for b_f in B:\n if b_f.shape[-1] != 1:\n raise ValueError(\n f\"Sequence inference method `{method}` requires `past_actions` \"\n \"when transition tensors have more than one control state\"\n )\n single_transition = b_f[..., 0]\n conditioned_B.append(\n jnp.broadcast_to(single_transition, (history_len,) + single_transition.shape)\n )\n\n if method == \"vmp\":\n qs = run_vmp(\n A,\n conditioned_B,\n obs,\n prior,\n A_dependencies,\n B_dependencies,\n num_iter=num_iter,\n distr_obs=distr_obs,\n obs_valid_mask=obs_valid_mask,\n transition_valid_mask=transition_valid_mask,\n )\n else:\n qs = run_mmp(\n A,\n conditioned_B,\n obs,\n prior,\n A_dependencies,\n B_dependencies,\n num_iter=num_iter,\n distr_obs=distr_obs,\n obs_valid_mask=obs_valid_mask,\n transition_valid_mask=transition_valid_mask,\n )\n\n return qs, obs_valid_mask, transition_valid_mask\n\n\ndef _update_qs_history(\n qs_hist: list[Array] | None,\n qs: list[Array],\n *,\n method: str,\n inference_horizon: int | None,\n) -> list[Array]:\n if qs_hist is not None:\n if method in ONE_STEP_METHODS:\n qs_hist = jtu.tree_map(\n lambda x, y: jnp.concatenate([x, jnp.expand_dims(y, 0)], 0),\n qs_hist,\n qs,\n )\n if inference_horizon is not None:\n qs_hist = jtu.tree_map(lambda x: x[-inference_horizon:], qs_hist)\n return qs_hist\n return qs\n\n if method in ONE_STEP_METHODS:\n return jtu.tree_map(lambda x: jnp.expand_dims(x, 0), qs)\n return qs\n\n\ndef _assemble_vfe_kwargs(\n *,\n method: str,\n qs: list[Array],\n prior: list[Array] | None,\n A: list[Array],\n B_for_vfe: list[Array] | None,\n curr_obs: list[Array] | Array | None,\n obs: list[Array],\n past_actions: Array | None,\n A_dependencies: list[list[int]] | None,\n B_dependencies: list[list[int]] | None,\n obs_valid_mask: Array | None,\n transition_valid_mask: Array | None,\n distr_obs: bool,\n) -> dict[str, Any]:\n if method in ONE_STEP_METHODS:\n return {\n \"qs\": qs,\n \"prior\": prior,\n \"obs\": curr_obs,\n \"A\": A,\n \"A_dependencies\": A_dependencies,\n \"distr_obs\": distr_obs,\n }\n\n return {\n \"qs\": qs,\n \"prior\": prior,\n \"obs\": obs,\n \"A\": A,\n \"B\": B_for_vfe,\n \"past_actions\": past_actions,\n \"A_dependencies\": A_dependencies,\n \"B_dependencies\": B_dependencies,\n \"obs_valid_mask\": obs_valid_mask,\n \"transition_valid_mask\": transition_valid_mask,\n \"distr_obs\": distr_obs,\n }\n\ndef update_posterior_states(\n A: list[Array],\n B: list[Array] | None,\n obs: list[Array],\n past_actions: Array | None,\n prior: list[Array] | None = None,\n qs_hist: list[Array] | None = None,\n A_dependencies: list[list[int]] | None = None,\n B_dependencies: list[list[int]] | None = None,\n num_iter: int = 16,\n method: str = \"fpi\",\n distr_obs: bool = True,\n inference_horizon: int | None = None,\n valid_steps: int | Array | None = None,\n return_info: bool = False,\n) -> list[Array] | tuple[list[Array], VFEInfo]:\n \"\"\"Infer posterior beliefs over hidden states from observations.\n\n Parameters\n ----------\n A : list[Array]\n Observation likelihood tensors per modality.\n B : list[Array] | None\n Transition model tensors per hidden-state factor. For one-step methods,\n this can be provided unchanged. For sequence methods and non-`None`\n `past_actions`, transitions are conditioned per timestep.\n obs : pytree\n Observation sequence or single-step observation in distributional form\n (for example, one-hot vectors per modality).\n past_actions : Array | None\n Action history with shape `(T-1, num_factors)` for sequence methods.\n Can be `None` when no valid history is available.\n prior : list[Array], optional\n Prior beliefs over hidden states. Required when `return_info=True`\n so canonical VFE diagnostics can be computed.\n qs_hist : list[Array], optional\n Existing posterior history buffer. If provided, one-step updates append\n to this history.\n A_dependencies : list[list[int]], optional\n Sparse modality-to-factor dependency mapping.\n B_dependencies : list[list[int]], optional\n Sparse transition-factor dependency mapping.\n num_iter : int, default=16\n Number of variational update iterations.\n method : {\"fpi\", \"ovf\", \"mmp\", \"vmp\", \"exact\"}, default=\"fpi\"\n Inference routine to execute.\n distr_obs : bool, default=True\n Whether observations are already distributional.\n inference_horizon : int | None, optional\n Optional truncation horizon for sequence inference.\n valid_steps : int | Array | None, optional\n Number of valid (unpadded) timesteps for fixed-window sequence inputs.\n return_info : bool, default=False\n If `True`, also return an info dictionary containing canonical VFE\n diagnostics (`vfe_t`, `vfe`, and component terms). For forward-only\n methods (`fpi`, `ovf`, `exact`) this reports the current posterior /\n history returned by the inference call; if you need a full smoothed\n sequence VFE for `ovf` or `exact`, first run `smoothing_ovf(...)` or\n `smoothing_exact(...)` and then call `pymdp.maths.calc_vfe(...,\n joint_qs=...)`.\n\n Returns\n -------\n list[Array] or tuple[list[Array], VFEInfo]\n Posterior state beliefs, with shape semantics depending on `method`:\n one-step methods return/append a time axis, sequence methods return full\n sequence posteriors. If `return_info=True`, a second return value\n contains canonical VFE diagnostics.\n \"\"\"\n B_for_vfe = B\n info = None\n curr_obs = None\n obs_valid_mask = None\n transition_valid_mask = None\n\n if return_info and prior is None:\n raise ValueError(\"`prior` must be provided when `return_info=True`\")\n\n if method in SEQUENCE_METHODS:\n obs, past_actions = _truncate_for_horizon(obs, past_actions, inference_horizon)\n\n if method in ONE_STEP_METHODS:\n qs, curr_obs = _run_one_step_inference(\n A,\n obs,\n prior,\n A_dependencies,\n method=method,\n num_iter=num_iter,\n distr_obs=distr_obs,\n )\n elif method in SEQUENCE_METHODS:\n qs, obs_valid_mask, transition_valid_mask = _run_sequence_inference(\n A,\n B,\n obs,\n past_actions,\n prior,\n A_dependencies,\n B_dependencies,\n method=method,\n num_iter=num_iter,\n distr_obs=distr_obs,\n valid_steps=valid_steps,\n )\n else:\n raise ValueError(\n f\"Unsupported inference method `{method}`. \"\n \"Expected one of {'fpi', 'ovf', 'mmp', 'vmp', 'exact'}.\"\n )\n\n qs_hist = _update_qs_history(\n qs_hist,\n qs,\n method=method,\n inference_horizon=inference_horizon,\n )\n\n if return_info:\n vfe_kwargs = _assemble_vfe_kwargs(\n method=method,\n qs=qs,\n prior=prior,\n A=A,\n B_for_vfe=B_for_vfe,\n curr_obs=curr_obs,\n obs=obs,\n past_actions=past_actions,\n A_dependencies=A_dependencies,\n B_dependencies=B_dependencies,\n obs_valid_mask=obs_valid_mask,\n transition_valid_mask=transition_valid_mask,\n distr_obs=distr_obs,\n )\n vfe_t, vfe, decomposition = calc_vfe(\n **vfe_kwargs,\n return_decomposition=True,\n )\n\n info = {\n \"vfe_t\": vfe_t,\n \"vfe\": vfe,\n \"vfe_components\": decomposition,\n }\n\n if return_info:\n return qs_hist, info\n return qs_hist\n\ndef _joint_dist_factor(\n conditioned_transitions: ArrayLike, filtered_qs: list[Array]\n) -> tuple[Array, Array]:\n qs_last = filtered_qs[-1]\n qs_filter = filtered_qs[:-1]\n n_transitions = conditioned_transitions.shape[0]\n\n def step_fn(qs_smooth: Array, xs: tuple[Array, Array]) -> tuple[Array, tuple[Array, Array]]:\n qs_f, time_b = xs\n qs_j = time_b * qs_f\n norm = qs_j.sum(-1, keepdims=True)\n if isinstance(norm, JAXSparse):\n norm = sparse.todense(norm)\n norm = jnp.where(norm == 0, eps, norm)\n qs_backward_cond = qs_j / norm\n qs_joint = qs_backward_cond * jnp.expand_dims(qs_smooth, -1)\n qs_smooth = qs_joint.sum(-2)\n if isinstance(qs_smooth, JAXSparse):\n qs_smooth = sparse.todense(qs_smooth)\n\n return qs_smooth, (qs_smooth, qs_joint)\n\n _, seq_qs = lax.scan(\n step_fn,\n qs_last,\n (qs_filter, conditioned_transitions),\n reverse=True,\n unroll=2\n )\n\n qs_smooth_all = jnp.concatenate([seq_qs[0], jnp.expand_dims(qs_last, 0)], 0)\n qs_joint_all = seq_qs[1]\n if isinstance(qs_joint_all, JAXSparse):\n qs_joint_all.shape = (n_transitions,) + qs_joint_all.shape\n return qs_smooth_all, qs_joint_all\n\n\ndef joint_dist_factor(\n b: ArrayLike,\n filtered_qs: list[Array],\n actions: ArrayLike | None = None,\n) -> tuple[Array, Array]:\n \"\"\"Compute smoothed marginals and pairwise joints for one factor.\n\n Parameters\n ----------\n b : Array\n Either an action-conditioned transition sequence\n `(T-1, K_next, K_curr)` or a transition tensor with action axis\n `(..., K_next, K_curr, n_actions)`.\n filtered_qs : list[Array]\n Filtered posterior sequence for this factor with leading time axis.\n actions : Array | None, optional\n Optional action sequence to select transitions from `b`.\n\n Returns\n -------\n tuple[Array, Array]\n `(smoothed_marginals, pairwise_joints)` where:\n - smoothed marginals have shape `(T, K)`\n - joints have shape `(T-1, K_next, K_curr)`\n \"\"\"\n if actions is None:\n conditioned_transitions = b\n else:\n action_idx = jnp.asarray(actions).astype(jnp.int32)\n conditioned_transitions = jnp.moveaxis(\n jnp.take(b, action_idx, axis=-1), -1, 0\n )\n return _joint_dist_factor(conditioned_transitions, filtered_qs)\n\n\ndef smoothing_ovf(\n filtered_post: list[Array], B: list[Array], past_actions: Array | None\n) -> tuple[list[Array], list[Array]]:\n \"\"\"Run backward smoothing for factorized online variational filtering history.\n\n Parameters\n ----------\n filtered_post : list[Array]\n Filtering posteriors per factor, each with shape `(T, K_f)` (or\n equivalent leading-time layout for a batch element).\n B : list[Array]\n Transition tensors per factor.\n past_actions : Array\n Action history with shape `(T-1, num_factors)`.\n\n Returns\n -------\n tuple[list[Array], list[Array]]\n `(marginals, joints)` per factor.\n \"\"\"\n assert len(filtered_post) == len(B)\n nf = len(B) # number of factors\n\n if past_actions is not None:\n past_actions = _ensure_action_history_shape(past_actions, nf)\n B_seq = _condition_transitions_on_actions(B, past_actions, invalid_action_mode=\"identity\")\n\n marginals_and_joints = ([], [])\n for b_seq, qs in zip(B_seq, filtered_post):\n marginals, joints = joint_dist_factor(b_seq, qs, actions=None)\n marginals_and_joints[0].append(marginals)\n marginals_and_joints[1].append(joints)\n\n return marginals_and_joints\n\n\ndef smoothing_exact(\n filtered_post: list[Array], B: list[Array], past_actions: Array | None\n) -> tuple[list[Array], list[Array]]:\n \"\"\"\n Exact single-factor HMM backward smoothing from online filtering history.\n\n Parameters\n ----------\n filtered_post:\n List containing one `(T, K)` array of filtering marginals.\n B:\n List containing one transition tensor in pymdp column-stochastic orientation.\n past_actions:\n `(T-1, 1)` or `(T-1,)` action history used to select transitions.\n\n Returns\n -------\n (marginals, joints):\n marginals: list with one `(T, K)` smoothed marginal array.\n joints: list with one `(T-1, K_next, K_curr)` pairwise posterior array.\n \"\"\"\n if len(filtered_post) != 1 or len(B) != 1:\n raise ValueError(\"smoothing_exact currently supports only one hidden-state factor\")\n\n filtered = filtered_post[0]\n B_seq = _condition_transitions_on_actions(\n B,\n past_actions,\n invalid_action_mode=\"identity\",\n )[0]\n \n\n smoothed, joint_next_curr, _ = hmm_smoother_from_filtered_colstoch(\n filtered,\n B_seq,\n return_trans_probs=False,\n )\n\n return [smoothed], [joint_next_curr]\n\n\n \n" }, { "path": "pymdp/learning.py", "content": "#!/usr/bin/env python\n# -*- coding: utf-8 -*-\n# pylint: disable=no-member\n\"\"\"Dirichlet-parameter learning updates for modern JAX pymdp models.\"\"\"\n\nfrom pymdp.maths import multidimensional_outer, dirichlet_expected_value\nfrom jax.tree_util import tree_map\nfrom jaxtyping import Array\nfrom jax import vmap, nn, lax\n\ndef update_obs_likelihood_dirichlet_m(\n pA_m: Array, obs_m: Array, qs: list[Array], dependencies_m: list[int], lr: float = 1.0\n) -> tuple[Array, Array]:\n \"\"\"Update one modality's Dirichlet parameters for the observation model.\n\n Parameters\n ----------\n pA_m : Array\n Current Dirichlet concentration parameters for modality `m`.\n obs_m : Array\n Observation sequence for modality `m` in categorical/distributional\n form with leading time axis.\n qs : list[Array]\n Posterior beliefs over hidden-state factors.\n dependencies_m : list[int]\n Hidden-state factors that modality `m` depends on.\n lr : float, default=1.0\n Learning-rate multiplier for concentration updates.\n\n Returns\n -------\n tuple[Array, Array]\n Updated concentration parameters and expected likelihood tensor for\n modality `m`.\n \"\"\"\n # pA_m - parameters of the dirichlet from the prior\n # pA_m.shape = (no_m x num_states[k] x num_states[j] x ... x num_states[n]) where (k, j, n) are indices of the hidden state factors that are parents of modality m\n\n # \\alpha^{*} = \\alpha_{0} + \\kappa * \\sum_{t=t_begin}^{t=T} o_{m,t} \\otimes \\mathbf{s}_{f \\in parents(m), t}\n\n # \\alpha^{*} is the VFE-minimizing solution for the parameters of q(A)\n # \\alpha_{0} are the Dirichlet parameters of p(A)\n # o_{m,t} = observation (one-hot vector) of modality m at time t\n # \\mathbf{s}_{f \\in parents(m), t} = categorical parameters of marginal posteriors over hidden state factors that are parents of modality m, at time t\n # \\otimes is a multidimensional outer product, not just a outer product of two vectors\n # \\kappa is an optional learning rate\n\n relevant_factors = tree_map(lambda f_idx: qs[f_idx], dependencies_m)\n\n dfda = vmap(multidimensional_outer)([obs_m] + relevant_factors).sum(axis=0)\n\n new_pA_m = pA_m + lr * dfda\n A_m = dirichlet_expected_value(new_pA_m)\n\n return new_pA_m, A_m\n \ndef update_obs_likelihood_dirichlet(\n pA: list[Array | None],\n A: list[Array],\n obs: list[Array],\n qs: list[Array],\n *,\n A_dependencies: list[list[int]],\n categorical_obs: bool,\n num_obs: list[int],\n lr: float,\n) -> tuple[list[Array | None], list[Array]]:\n \"\"\"\n Update Dirichlet parameters of the observation likelihood (A matrix) given observations and beliefs.\n\n JAX version of `pymdp.learning.update_obs_likelihood_dirichlet`\n\n Parameters\n ----------\n pA : List[Array]\n Prior Dirichlet parameters for A matrices\n A : List[Array]\n Current A matrices (observation likelihoods)\n obs : List[Array]\n Observations (either discrete indices or categorical distributions depending on categorical_obs)\n qs : List[Array]\n Posterior beliefs over hidden states\n A_dependencies : List[List[int]]\n Dependencies between observation modalities and state factors\n categorical_obs : bool\n If True, observations are probability distributions; if False, discrete indices\n num_obs : List[int]\n Number of observations for each modality\n lr : float\n Learning rate\n\n Returns\n -------\n qA : List[Array]\n Updated Dirichlet parameters\n E_qA : List[Array]\n Expected values (updated A matrices)\n \"\"\"\n\n obs_m = lambda o, dim: nn.one_hot(o, dim) if not categorical_obs else o\n update_A_fn = (\n lambda pA_m, o_m, dim, dependencies_m: None\n if pA_m is None\n else update_obs_likelihood_dirichlet_m(pA_m, obs_m(o_m, dim), qs, dependencies_m, lr=lr)\n )\n result = tree_map(update_A_fn, pA, obs, num_obs, A_dependencies, is_leaf=lambda x: x is None)\n qA = []\n E_qA = []\n for i, r in enumerate(result):\n if r is None:\n qA.append(r)\n E_qA.append(A[i])\n else:\n qA.append(r[0])\n E_qA.append(r[1])\n\n return qA, E_qA\n\ndef update_state_transition_dirichlet_f(\n pB_f: Array, actions_f: Array, joint_qs_f: Array | list[Array], lr: float = 1.0\n) -> tuple[Array, Array]:\n \"\"\"Update one factor's Dirichlet parameters for the transition model.\n\n Parameters\n ----------\n pB_f : Array\n Current Dirichlet concentration parameters for hidden-state factor `f`.\n actions_f : Array\n One-hot action history for factor `f` with leading time axis.\n joint_qs_f : Array | list[Array]\n Pairwise state beliefs (for example, `q(s_t, s_{t-1})`) used for\n transition learning.\n lr : float, default=1.0\n Learning-rate multiplier for concentration updates.\n\n Returns\n -------\n tuple[Array, Array]\n Updated concentration parameters and expected transition tensor.\n \"\"\"\n # pB_f - parameters of the dirichlet from the prior\n # pB_f.shape = (num_states[f] x num_states[f] x num_actions[f]) where f is the index of the hidden state factor\n\n # \\alpha^{*} = \\alpha_{0} + \\kappa * \\sum_{t=t_begin}^{t=T} \\mathbf{s}_{f, t} \\otimes \\mathbf{s}_{f, t-1} \\otimes \\mathbf{a}_{f, t-1}\n\n # \\alpha^{*} is the VFE-minimizing solution for the parameters of q(B)\n # \\alpha_{0} are the Dirichlet parameters of p(B)\n # \\mathbf{s}_{f, t} = categorical parameters of marginal posteriors over hidden state factor f, at time t\n # \\mathbf{a}_{f, t-1} = categorical parameters of marginal posteriors over control factor f, at time t-1\n # \\otimes is a multidimensional outer product, not just a outer product of two vectors\n # \\kappa is an optional learning rate\n\n joint_qs_f = [joint_qs_f] if isinstance(joint_qs_f, Array) else joint_qs_f\n dfdb = vmap(multidimensional_outer)(joint_qs_f + [actions_f]).sum(axis=0)\n qB_f = pB_f + lr * dfdb\n\n return qB_f, dirichlet_expected_value(qB_f)\n\ndef update_state_transition_dirichlet(\n pB: list[Array],\n B: list[Array],\n joint_beliefs: list[Array],\n actions: Array,\n *,\n num_controls: list[int],\n lr: float,\n factors_to_update: str | list[int] = 'all',\n) -> tuple[list[Array], list[Array]]:\n \"\"\"\n Update posterior Diriichlet parameters of the state transition likelihood model (B) given the joint beliefs over hidden states and actions.\n\n Supports selective learning of only particular hidden-state factors via\n `factors_to_update` (either `\"all\"` or a `List[int]`).\n\n Parameters\n ----------\n pB : list[Array]\n Dirichlet concentration parameters for transition model factors.\n B : list[Array]\n Current expected transition tensors.\n joint_beliefs : list[Array]\n Time-aligned joint beliefs per factor for transition learning.\n actions : Array\n Integer action history with shape `(batch, T-1, num_factors)`.\n num_controls : list[int]\n Number of control states per factor.\n lr : float\n Learning-rate multiplier for concentration updates.\n factors_to_update : \"all\" | List[int], default=\"all\"\n Which hidden-state factors should be updated.\n\n Returns\n -------\n tuple[List[Array], List[Array]]\n Updated concentration parameters and expected transition tensors.\n \"\"\"\n nf = len(pB)\n\n actions_onehot_fn = lambda f, dim: nn.one_hot(actions[..., f], dim, axis=-1)\n\n def update_B_f_fn(pB_f: Array, joint_qs_f: Array, f: int, na: int) -> tuple[Array, Array]:\n \"\"\" \n Conditionally-update the Dirichlet posterior over a given single factor's B parameters\n Updating is conditional upon the value of `f`: if the factor index (f) is greater than -1, then use the value of f as the factor index\n to create the appropriate one-hot representation of the action corresponding to the the f-th control factor and perform the update. Otherwise, do not perform the update\n \"\"\"\n qB_f, E_qB_f = lax.cond(\n f>-1,\n lambda: update_state_transition_dirichlet_f(pB_f, actions_onehot_fn(f, na), joint_qs_f, lr=lr),\n lambda: (pB_f, dirichlet_expected_value(pB_f)),\n )\n return qB_f, E_qB_f\n\n if factors_to_update == 'all':\n factors_to_update_sorted = list(range(nf))\n else:\n factors_to_update_sorted = [-1]*nf\n for f_i in sorted(factors_to_update):\n factors_to_update_sorted[f_i] = f_i\n\n\n result = tree_map(\n update_B_f_fn,\n pB, joint_beliefs, factors_to_update_sorted, num_controls,\n )\n\n qB = []\n E_qB = []\n\n for r in result:\n qB.append(r[0])\n E_qB.append(r[1])\n\n return qB, E_qB\n \n# def update_state_prior_dirichlet(\n# pD, qs, lr=1.0, factors=\"all\"\n# ):\n# \"\"\"\n# Update Dirichlet parameters of the initial hidden state distribution \n# (prior beliefs about hidden states at the beginning of the inference window).\n\n# Parameters\n# -----------\n# pD: `numpy.ndarray` of dtype object\n# Prior Dirichlet parameters over initial hidden state prior (same shape as `qs`)\n# qs: 1D `numpy.ndarray` or `numpy.ndarray` of dtype object\n# Marginal posterior beliefs over hidden states at current timepoint\n# lr: float, default `1.0`\n# Learning rate, scale of the Dirichlet pseudo-count update.\n# factors: `list`, default \"all\"\n# Indices (ranging from 0 to `n_factors - 1`) of the hidden state factors to include \n# in learning. Defaults to \"all\", meaning that factor-specific sub-vectors of `pD`\n# are all updated using the corresponding hidden state distributions.\n \n# Returns\n# -----------\n# qD: `numpy.ndarray` of dtype object\n# Posterior Dirichlet parameters over initial hidden state prior (same shape as `qs`), after having updated it with state beliefs.\n# \"\"\"\n\n# num_factors = len(pD)\n\n# qD = copy.deepcopy(pD)\n \n# if factors == \"all\":\n# factors = list(range(num_factors))\n\n# for factor in factors:\n# idx = pD[factor] > 0 # only update those state level indices that have some prior probability\n# qD[factor][idx] += (lr * qs[factor][idx])\n \n# return qD\n\n# def _prune_prior(prior, levels_to_remove, dirichlet = False):\n# \"\"\"\n# Function for pruning a prior Categorical distribution (e.g. C, D)\n\n# Parameters\n# -----------\n# prior: 1D `numpy.ndarray` or `numpy.ndarray` of dtype object\n# The vector(s) containing the priors over hidden states of a generative model, e.g. the prior over hidden states (`D` vector). \n# levels_to_remove: `list` of `int`, `list` of `list`\n# A `list` of the levels (indices of the support) to remove. If the prior in question has multiple hidden state factors / multiple observation modalities, \n# then this will be a `list` of `list`, where each sub-list within `levels_to_remove` will contain the levels to prune for a particular hidden state factor or modality \n# dirichlet: `Bool`, default `False`\n# A Boolean flag indicating whether the input vector(s) is/are a Dirichlet distribution, and therefore should not be normalized at the end. \n# @TODO: Instead, the dirichlet parameters from the pruned levels should somehow be re-distributed among the remaining levels\n\n# Returns\n# -----------\n# reduced_prior: 1D `numpy.ndarray` or `numpy.ndarray` of dtype object\n# The prior vector(s), after pruning, that lacks the hidden state or modality levels indexed by `levels_to_remove`\n# \"\"\"\n\n# if utils.is_obj_array(prior): # in case of multiple hidden state factors\n\n# assert all([type(levels) == list for levels in levels_to_remove])\n\n# num_factors = len(prior)\n\n# reduced_prior = utils.obj_array(num_factors)\n\n# factors_to_remove = []\n# for f, s_i in enumerate(prior): # loop over factors (or modalities)\n \n# ns = len(s_i)\n# levels_to_keep = list(set(range(ns)) - set(levels_to_remove[f]))\n# if len(levels_to_keep) == 0:\n# print(f'Warning... removing ALL levels of factor {f} - i.e. the whole hidden state factor is being removed\\n')\n# factors_to_remove.append(f)\n# else:\n# if not dirichlet:\n# reduced_prior[f] = utils.norm_dist(s_i[levels_to_keep])\n# else:\n# raise(NotImplementedError(\"Need to figure out how to re-distribute concentration parameters from pruned levels, across remaining levels\"))\n\n\n# if len(factors_to_remove) > 0:\n# factors_to_keep = list(set(range(num_factors)) - set(factors_to_remove))\n# reduced_prior = reduced_prior[factors_to_keep]\n\n# else: # in case of one hidden state factor\n\n# assert all([type(level_i) == int for level_i in levels_to_remove])\n\n# ns = len(prior)\n# levels_to_keep = list(set(range(ns)) - set(levels_to_remove))\n\n# if not dirichlet:\n# reduced_prior = utils.norm_dist(prior[levels_to_keep])\n# else:\n# raise(NotImplementedError(\"Need to figure out how to re-distribute concentration parameters from pruned levels, across remaining levels\"))\n\n# return reduced_prior\n\n# def _prune_A(A, obs_levels_to_prune, state_levels_to_prune, dirichlet = False):\n# \"\"\"\n# Function for pruning a observation likelihood model (with potentially multiple hidden state factors)\n# :meta private:\n# Parameters\n# -----------\n# A: `numpy.ndarray` with `ndim >= 2`, or `numpy.ndarray` of dtype object\n# Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element `A[m]` of\n# stores an `numpy.ndarray` multidimensional array for observation modality `m`, whose entries `A[m][i, j, k, ...]` store \n# the probability of observation level `i` given hidden state levels `j, k, ...`\n# obs_levels_to_prune: `list` of int or `list` of `list`: \n# A `list` of the observation levels to remove. If the likelihood in question has multiple observation modalities, \n# then this will be a `list` of `list`, where each sub-list within `obs_levels_to_prune` will contain the observation levels \n# to remove for a particular observation modality \n# state_levels_to_prune: `list` of `int`\n# A `list` of the hidden state levels to remove (this will be the same across modalities)\n# dirichlet: `Bool`, default `False`\n# A Boolean flag indicating whether the input array(s) is/are a Dirichlet distribution, and therefore should not be normalized at the end. \n# @TODO: Instead, the dirichlet parameters from the pruned columns should somehow be re-distributed among the remaining columns\n\n# Returns\n# -----------\n# reduced_A: `numpy.ndarray` with ndim >= 2, or `numpy.ndarray `of dtype object\n# The observation model, after pruning, which lacks the observation or hidden state levels given by the arguments `obs_levels_to_prune` and `state_levels_to_prune`\n# \"\"\"\n\n# columns_to_keep_list = []\n# if utils.is_obj_array(A):\n# num_states = A[0].shape[1:]\n# for f, ns in enumerate(num_states):\n# indices_f = np.array( list(set(range(ns)) - set(state_levels_to_prune[f])), dtype = np.intp)\n# columns_to_keep_list.append(indices_f)\n# else:\n# num_states = A.shape[1]\n# indices = np.array( list(set(range(num_states)) - set(state_levels_to_prune)), dtype = np.intp )\n# columns_to_keep_list.append(indices)\n\n# if utils.is_obj_array(A): # in case of multiple observation modality\n\n# assert all([type(o_m_levels) == list for o_m_levels in obs_levels_to_prune])\n\n# num_modalities = len(A)\n\n# reduced_A = utils.obj_array(num_modalities)\n \n# for m, A_i in enumerate(A): # loop over modalities\n \n# no = A_i.shape[0]\n# rows_to_keep = np.array(list(set(range(no)) - set(obs_levels_to_prune[m])), dtype = np.intp)\n \n# reduced_A[m] = A_i[np.ix_(rows_to_keep, *columns_to_keep_list)]\n# if not dirichlet: \n# reduced_A = utils.norm_dist_obj_arr(reduced_A)\n# else:\n# raise(NotImplementedError(\"Need to figure out how to re-distribute concentration parameters from pruned rows/columns, across remaining rows/columns\"))\n# else: # in case of one observation modality\n\n# assert all([type(o_levels_i) == int for o_levels_i in obs_levels_to_prune])\n\n# no = A.shape[0]\n# rows_to_keep = np.array(list(set(range(no)) - set(obs_levels_to_prune)), dtype = np.intp)\n \n# reduced_A = A[np.ix_(rows_to_keep, *columns_to_keep_list)]\n\n# if not dirichlet:\n# reduced_A = utils.norm_dist(reduced_A)\n# else:\n# raise(NotImplementedError(\"Need to figure out how to re-distribute concentration parameters from pruned rows/columns, across remaining rows/columns\"))\n\n# return reduced_A\n\n# def _prune_B(B, state_levels_to_prune, action_levels_to_prune, dirichlet = False):\n# \"\"\"\n# Function for pruning a transition likelihood model (with potentially multiple hidden state factors)\n\n# Parameters\n# -----------\n# B: `numpy.ndarray` of `ndim == 3` or `numpy.ndarray` of dtype object\n# Dynamics likelihood mapping or 'transition model', mapping from hidden states at `t` to hidden states at `t+1`, given some control state `u`.\n# Each element B[f] of this object array stores a 3-D tensor for hidden state factor `f`, whose entries `B[f][s, v, u] store the probability\n# of hidden state level `s` at the current time, given hidden state level `v` and action `u` at the previous time.\n# state_levels_to_prune: `list` of `int` or `list` of `list` \n# A `list` of the state levels to remove. If the likelihood in question has multiple hidden state factors, \n# then this will be a `list` of `list`, where each sub-list within `state_levels_to_prune` will contain the state levels \n# to remove for a particular hidden state factor \n# action_levels_to_prune: `list` of `int` or `list` of `list` \n# A `list` of the control state or action levels to remove. If the likelihood in question has multiple control state factors, \n# then this will be a `list` of `list`, where each sub-list within `action_levels_to_prune` will contain the control state levels \n# to remove for a particular control state factor \n# dirichlet: `Bool`, default `False`\n# A Boolean flag indicating whether the input array(s) is/are a Dirichlet distribution, and therefore should not be normalized at the end. \n# @TODO: Instead, the dirichlet parameters from the pruned rows/columns should somehow be re-distributed among the remaining rows/columns\n\n# Returns\n# -----------\n# reduced_B: `numpy.ndarray` of `ndim == 3` or `numpy.ndarray` of dtype object\n# The transition model, after pruning, which lacks the hidden state levels/action levels given by the arguments `state_levels_to_prune` and `action_levels_to_prune`\n# \"\"\"\n\n# slices_to_keep_list = []\n\n# if utils.is_obj_array(B):\n\n# num_controls = [B_arr.shape[2] for _, B_arr in enumerate(B)]\n\n# for c, nc in enumerate(num_controls):\n# indices_c = np.array( list(set(range(nc)) - set(action_levels_to_prune[c])), dtype = np.intp)\n# slices_to_keep_list.append(indices_c)\n# else:\n# num_controls = B.shape[2]\n# slices_to_keep = np.array( list(set(range(num_controls)) - set(action_levels_to_prune)), dtype = np.intp )\n\n# if utils.is_obj_array(B): # in case of multiple hidden state factors\n\n# assert all([type(ns_f_levels) == list for ns_f_levels in state_levels_to_prune])\n\n# num_factors = len(B)\n\n# reduced_B = utils.obj_array(num_factors)\n \n# for f, B_f in enumerate(B): # loop over modalities\n \n# ns = B_f.shape[0]\n# states_to_keep = np.array(list(set(range(ns)) - set(state_levels_to_prune[f])), dtype = np.intp)\n \n# reduced_B[f] = B_f[np.ix_(states_to_keep, states_to_keep, slices_to_keep_list[f])]\n\n# if not dirichlet: \n# reduced_B = utils.norm_dist_obj_arr(reduced_B)\n# else:\n# raise(NotImplementedError(\"Need to figure out how to re-distribute concentration parameters from pruned rows/columns, across remaining rows/columns\"))\n\n# else: # in case of one hidden state factor\n\n# assert all([type(state_level_i) == int for state_level_i in state_levels_to_prune])\n\n# ns = B.shape[0]\n# states_to_keep = np.array(list(set(range(ns)) - set(state_levels_to_prune)), dtype = np.intp)\n \n# reduced_B = B[np.ix_(states_to_keep, states_to_keep, slices_to_keep)]\n\n# if not dirichlet:\n# reduced_B = utils.norm_dist(reduced_B)\n# else:\n# raise(NotImplementedError(\"Need to figure out how to re-distribute concentration parameters from pruned rows/columns, across remaining rows/columns\"))\n\n# return reduced_B\n" }, { "path": "pymdp/legacy/__init__.py", "content": "from . import agent\nfrom . import envs\nfrom . import utils\nfrom . import maths\nfrom . import control\nfrom . import inference\nfrom . import learning\nfrom . import algos\nfrom . import default_models\n" }, { "path": "pymdp/legacy/agent.py", "content": "#!/usr/bin/env python\n# -*- coding: utf-8 -*-\n\n\"\"\" Agent Class\n\n__author__: Conor Heins, Alexander Tschantz, Daphne Demekas, Brennan Klein\n\n\"\"\"\n\nimport warnings\nimport numpy as np\nfrom pymdp.legacy import inference, control, learning\nfrom pymdp.legacy import utils\nimport copy\n\nclass Agent(object):\n \"\"\" \n The Agent class, the highest-level API that wraps together processes for action, perception, and learning under active inference.\n\n The basic usage is as follows:\n\n >>> my_agent = Agent(A = A, B = C, )\n >>> observation = env.step(initial_action)\n >>> qs = my_agent.infer_states(observation)\n >>> q_pi, G = my_agent.infer_policies()\n >>> next_action = my_agent.sample_action()\n >>> next_observation = env.step(next_action)\n\n This represents one timestep of an active inference process. Wrapping this step in a loop with an ``Env()`` class that returns\n observations and takes actions as inputs, would entail a dynamic agent-environment interaction.\n \"\"\"\n\n def __init__(\n self,\n A,\n B,\n C=None,\n D=None,\n E=None,\n H=None,\n pA=None,\n pB=None,\n pD=None,\n num_controls=None,\n policy_len=1,\n inference_horizon=1,\n control_fac_idx=None,\n policies=None,\n gamma=16.0,\n alpha=16.0,\n use_utility=True,\n use_states_info_gain=True,\n use_param_info_gain=False,\n action_selection=\"deterministic\",\n sampling_mode = \"marginal\", # whether to sample from full posterior over policies (\"full\") or from marginal posterior over actions (\"marginal\")\n inference_algo=\"VANILLA\",\n inference_params=None,\n modalities_to_learn=\"all\",\n lr_pA=1.0,\n factors_to_learn=\"all\",\n lr_pB=1.0,\n lr_pD=1.0,\n use_BMA=True,\n policy_sep_prior=False,\n save_belief_hist=False,\n A_factor_list=None,\n B_factor_list=None,\n sophisticated=False,\n si_horizon=3,\n si_policy_prune_threshold=1/16,\n si_state_prune_threshold=1/16,\n si_prune_penalty=512,\n ii_depth=10,\n ii_threshold=1/16,\n ):\n\n ### Constant parameters ###\n\n # policy parameters\n self.policy_len = policy_len\n self.gamma = gamma\n self.alpha = alpha\n self.action_selection = action_selection\n self.sampling_mode = sampling_mode\n self.use_utility = use_utility\n self.use_states_info_gain = use_states_info_gain\n self.use_param_info_gain = use_param_info_gain\n\n # learning parameters\n self.modalities_to_learn = modalities_to_learn\n self.lr_pA = lr_pA\n self.factors_to_learn = factors_to_learn\n self.lr_pB = lr_pB\n self.lr_pD = lr_pD\n\n # sophisticated inference parameters\n self.sophisticated = sophisticated\n if self.sophisticated:\n assert self.policy_len == 1, \"Sophisticated inference only works with policy_len = 1\"\n self.si_horizon = si_horizon\n self.si_policy_prune_threshold = si_policy_prune_threshold\n self.si_state_prune_threshold = si_state_prune_threshold\n self.si_prune_penalty = si_prune_penalty\n\n # Initialise observation model (A matrices)\n if not isinstance(A, np.ndarray):\n raise TypeError(\n 'A matrix must be a numpy array'\n )\n\n self.A = utils.to_obj_array(A)\n\n assert utils.is_normalized(self.A), \"A matrix is not normalized (i.e. A[m].sum(axis = 0) must all equal 1.0 for all modalities)\"\n\n # Determine number of observation modalities and their respective dimensions\n self.num_obs = [self.A[m].shape[0] for m in range(len(self.A))]\n self.num_modalities = len(self.num_obs)\n\n # Assigning prior parameters on observation model (pA matrices)\n self.pA = pA\n\n # Initialise transition model (B matrices)\n if not isinstance(B, np.ndarray):\n raise TypeError(\n 'B matrix must be a numpy array'\n )\n\n self.B = utils.to_obj_array(B)\n\n assert utils.is_normalized(self.B), \"B matrix is not normalized (i.e. B[f].sum(axis = 0) must all equal 1.0 for all factors)\"\n\n # Determine number of hidden state factors and their dimensionalities\n self.num_states = [self.B[f].shape[0] for f in range(len(self.B))]\n self.num_factors = len(self.num_states)\n\n # Assigning prior parameters on transition model (pB matrices) \n self.pB = pB\n\n # If no `num_controls` are given, then this is inferred from the shapes of the input B matrices\n if num_controls is None:\n self.num_controls = [self.B[f].shape[-1] for f in range(self.num_factors)]\n else:\n inferred_num_controls = [self.B[f].shape[-1] for f in range(self.num_factors)]\n assert num_controls == inferred_num_controls, \"num_controls must be consistent with the shapes of the input B matrices\"\n self.num_controls = num_controls\n\n # checking that `A_factor_list` and `B_factor_list` are consistent with `num_factors`, `num_states`, and lagging dimensions of `A` and `B` tensors\n self.factorized = False\n if A_factor_list is None:\n self.A_factor_list = self.num_modalities * [list(range(self.num_factors))] # defaults to having all modalities depend on all factors\n for m in range(self.num_modalities):\n factor_dims = tuple([self.num_states[f] for f in self.A_factor_list[m]])\n assert self.A[m].shape[1:] == factor_dims, f\"Please input an `A_factor_list` whose {m}-th indices pick out the hidden state factors that line up with lagging dimensions of A{m}...\" \n if self.pA is not None:\n assert self.pA[m].shape[1:] == factor_dims, f\"Please input an `A_factor_list` whose {m}-th indices pick out the hidden state factors that line up with lagging dimensions of pA{m}...\" \n else:\n self.factorized = True\n for m in range(self.num_modalities):\n assert max(A_factor_list[m]) <= (self.num_factors - 1), f\"Check modality {m} of A_factor_list - must be consistent with `num_states` and `num_factors`...\"\n factor_dims = tuple([self.num_states[f] for f in A_factor_list[m]])\n assert self.A[m].shape[1:] == factor_dims, f\"Check modality {m} of A_factor_list. It must coincide with lagging dimensions of A{m}...\" \n if self.pA is not None:\n assert self.pA[m].shape[1:] == factor_dims, f\"Check modality {m} of A_factor_list. It must coincide with lagging dimensions of pA{m}...\"\n self.A_factor_list = A_factor_list\n\n # generate a list of the modalities that depend on each factor \n A_modality_list = []\n for f in range(self.num_factors):\n A_modality_list.append( [m for m in range(self.num_modalities) if f in self.A_factor_list[m]] )\n\n # Store thee `A_factor_list` and the `A_modality_list` in a Markov blanket dictionary\n self.mb_dict = {\n 'A_factor_list': self.A_factor_list,\n 'A_modality_list': A_modality_list\n }\n\n if B_factor_list is None:\n self.B_factor_list = [[f] for f in range(self.num_factors)] # defaults to having all factors depend only on themselves\n for f in range(self.num_factors):\n factor_dims = tuple([self.num_states[f] for f in self.B_factor_list[f]])\n assert self.B[f].shape[1:-1] == factor_dims, f\"Please input a `B_factor_list` whose {f}-th indices pick out the hidden state factors that line up with the all-but-final lagging dimensions of B{f}...\" \n if self.pB is not None:\n assert self.pB[f].shape[1:-1] == factor_dims, f\"Please input a `B_factor_list` whose {f}-th indices pick out the hidden state factors that line up with the all-but-final lagging dimensions of pB{f}...\" \n else:\n self.factorized = True\n for f in range(self.num_factors):\n assert max(B_factor_list[f]) <= (self.num_factors - 1), f\"Check factor {f} of B_factor_list - must be consistent with `num_states` and `num_factors`...\"\n factor_dims = tuple([self.num_states[f] for f in B_factor_list[f]])\n assert self.B[f].shape[1:-1] == factor_dims, f\"Check factor {f} of B_factor_list. It must coincide with all-but-final lagging dimensions of B{f}...\" \n if self.pB is not None:\n assert self.pB[f].shape[1:-1] == factor_dims, f\"Check factor {f} of B_factor_list. It must coincide with all-but-final lagging dimensions of pB{f}...\"\n self.B_factor_list = B_factor_list\n\n # Users have the option to make only certain factors controllable.\n # default behaviour is to make all hidden state factors controllable, i.e. `self.num_factors == len(self.num_controls)`\n if control_fac_idx is None:\n self.control_fac_idx = [f for f in range(self.num_factors) if self.num_controls[f] > 1]\n else:\n\n assert max(control_fac_idx) <= (self.num_factors - 1), \"Check control_fac_idx - must be consistent with `num_states` and `num_factors`...\"\n self.control_fac_idx = control_fac_idx\n\n for factor_idx in self.control_fac_idx:\n assert self.num_controls[factor_idx] > 1, \"Control factor (and B matrix) dimensions are not consistent with user-given control_fac_idx\"\n\n # Again, the use can specify a set of possible policies, or\n # all possible combinations of actions and timesteps will be considered\n if policies is None:\n policies = self._construct_policies()\n self.policies = policies\n\n assert all([len(self.num_controls) == policy.shape[1] for policy in self.policies]), \"Number of control states is not consistent with policy dimensionalities\"\n \n all_policies = np.vstack(self.policies)\n\n assert all([n_c >= max_action for (n_c, max_action) in zip(self.num_controls, list(np.max(all_policies, axis =0)+1))]), \"Maximum number of actions is not consistent with `num_controls`\"\n\n # Construct prior preferences (uniform if not specified)\n\n if C is not None:\n if not isinstance(C, np.ndarray):\n raise TypeError(\n 'C vector must be a numpy array'\n )\n self.C = utils.to_obj_array(C)\n\n assert len(self.C) == self.num_modalities, f\"Check C vector: number of sub-arrays must be equal to number of observation modalities: {self.num_modalities}\"\n\n for modality, c_m in enumerate(self.C):\n assert c_m.shape[0] == self.num_obs[modality], f\"Check C vector: number of rows of C vector for modality {modality} should be equal to {self.num_obs[modality]}\"\n else:\n self.C = self._construct_C_prior()\n\n # Construct prior over hidden states (uniform if not specified)\n \n if D is not None:\n if not isinstance(D, np.ndarray):\n raise TypeError(\n 'D vector must be a numpy array'\n )\n self.D = utils.to_obj_array(D)\n\n assert len(self.D) == self.num_factors, f\"Check D vector: number of sub-arrays must be equal to number of hidden state factors: {self.num_factors}\"\n\n for f, d_f in enumerate(self.D):\n assert d_f.shape[0] == self.num_states[f], f\"Check D vector: number of entries of D vector for factor {f} should be equal to {self.num_states[f]}\"\n else:\n if pD is not None:\n self.D = utils.norm_dist_obj_arr(pD)\n else:\n self.D = self._construct_D_prior()\n\n assert utils.is_normalized(self.D), \"D vector is not normalized (i.e. D[f].sum() must all equal 1.0 for all factors)\"\n\n # Assigning prior parameters on initial hidden states (pD vectors)\n self.pD = pD\n\n # Construct prior over policies (uniform if not specified) \n if E is not None:\n if not isinstance(E, np.ndarray):\n raise TypeError(\n 'E vector must be a numpy array'\n )\n self.E = E\n\n assert len(self.E) == len(self.policies), f\"Check E vector: length of E must be equal to number of policies: {len(self.policies)}\"\n\n else:\n self.E = self._construct_E_prior()\n \n # Construct I for backwards induction (if H specified)\n if H is not None:\n self.H = H\n self.I = control.backwards_induction(H, B, B_factor_list, threshold=ii_threshold, depth=ii_depth)\n else:\n self.H = None\n self.I = None\n\n self.edge_handling_params = {}\n self.edge_handling_params['use_BMA'] = use_BMA # creates a 'D-like' moving prior\n self.edge_handling_params['policy_sep_prior'] = policy_sep_prior # carries forward last timesteps posterior, in a policy-conditioned way\n\n # use_BMA and policy_sep_prior can both be False, but both cannot be simultaneously be True. If one of them is True, the other must be False\n if policy_sep_prior:\n if use_BMA:\n warnings.warn(\n \"Inconsistent choice of `policy_sep_prior` and `use_BMA`.\\\n You have set `policy_sep_prior` to True, so we are setting `use_BMA` to False\"\n )\n self.edge_handling_params['use_BMA'] = False\n \n if inference_algo is None:\n self.inference_algo = \"VANILLA\"\n self.inference_params = self._get_default_params()\n if inference_horizon > 1:\n warnings.warn(\n \"If `inference_algo` is VANILLA, then inference_horizon must be 1\\n. \\\n Setting inference_horizon to default value of 1...\\n\"\n )\n self.inference_horizon = 1\n else:\n self.inference_horizon = 1\n else:\n self.inference_algo = inference_algo\n self.inference_params = self._get_default_params()\n self.inference_horizon = inference_horizon\n\n if save_belief_hist:\n self.qs_hist = []\n self.q_pi_hist = []\n \n self.prev_obs = []\n self.reset()\n \n self.action = None\n self.prev_actions = None\n\n def _construct_C_prior(self):\n \n C = utils.obj_array_zeros(self.num_obs)\n\n return C\n\n def _construct_D_prior(self):\n\n D = utils.obj_array_uniform(self.num_states)\n\n return D\n\n def _construct_policies(self):\n \n policies = control.construct_policies(\n self.num_states, self.num_controls, self.policy_len, self.control_fac_idx\n )\n\n return policies\n\n def _construct_num_controls(self):\n num_controls = control.get_num_controls_from_policies(\n self.policies\n )\n \n return num_controls\n \n def _construct_E_prior(self):\n E = np.ones(len(self.policies)) / len(self.policies)\n return E\n\n def reset(self, init_qs=None):\n \"\"\"\n Resets the posterior beliefs about hidden states of the agent to a uniform distribution, and resets time to first timestep of the simulation's temporal horizon.\n Returns the posterior beliefs about hidden states.\n\n Returns\n ---------\n qs: ``numpy.ndarray`` of dtype object\n Initialized posterior over hidden states. Depending on the inference algorithm chosen and other parameters (such as the parameters stored within ``edge_handling_paramss),\n the resulting ``qs`` variable will have additional sub-structure to reflect whether beliefs are additionally conditioned on timepoint and policy.\n For example, in case the ``self.inference_algo == 'MMP' `, the indexing structure of ``qs`` is policy->timepoint-->factor, so that \n ``qs[p_idx][t_idx][f_idx]`` refers to beliefs about marginal factor ``f_idx`` expected under policy ``p_idx`` \n at timepoint ``t_idx``. In this case, the returned ``qs`` will only have entries filled out for the first timestep, i.e. for ``q[p_idx][0]``, for all \n policy-indices ``p_idx``. Subsequent entries ``q[:][1, 2, ...]`` will be initialized to empty ``numpy.ndarray`` objects.\n \"\"\"\n\n self.curr_timestep = 0\n\n if init_qs is None:\n if self.inference_algo == 'VANILLA':\n self.qs = utils.obj_array_uniform(self.num_states)\n else: # in the case you're doing MMP (i.e. you have an inference_horizon > 1), we have to account for policy- and timestep-conditioned posterior beliefs\n self.qs = utils.obj_array(len(self.policies))\n for p_i, _ in enumerate(self.policies):\n self.qs[p_i] = utils.obj_array(self.inference_horizon + self.policy_len + 1) # + 1 to include belief about current timestep\n self.qs[p_i][0] = utils.obj_array_uniform(self.num_states)\n \n first_belief = utils.obj_array(len(self.policies))\n for p_i, _ in enumerate(self.policies):\n first_belief[p_i] = copy.deepcopy(self.D) \n \n if self.edge_handling_params['policy_sep_prior']:\n self.set_latest_beliefs(last_belief = first_belief)\n else:\n self.set_latest_beliefs(last_belief = self.D)\n \n else:\n self.qs = init_qs\n \n if self.pA is not None:\n self.A = utils.norm_dist_obj_arr(self.pA)\n \n if self.pB is not None:\n self.B = utils.norm_dist_obj_arr(self.pB)\n\n return self.qs\n\n def step_time(self):\n \"\"\"\n Advances time by one step. This involves updating the ``self.prev_actions``, and in the case of a moving\n inference horizon, this also shifts the history of post-dictive beliefs forward in time (using ``self.set_latest_beliefs()``),\n so that the penultimate belief before the beginning of the horizon is correctly indexed.\n\n Returns\n ---------\n curr_timestep: ``int``\n The index in absolute simulation time of the current timestep.\n \"\"\"\n\n if self.prev_actions is None:\n self.prev_actions = [self.action]\n else:\n self.prev_actions.append(self.action)\n\n self.curr_timestep += 1\n\n if self.inference_algo == \"MMP\" and (self.curr_timestep - self.inference_horizon) >= 0:\n self.set_latest_beliefs()\n \n return self.curr_timestep\n \n def set_latest_beliefs(self,last_belief=None):\n \"\"\"\n Both sets and returns the penultimate belief before the first timestep of the backwards inference horizon. \n In the case that the inference horizon includes the first timestep of the simulation, then the ``latest_belief`` is\n simply the first belief of the whole simulation, or the prior (``self.D``). The particular structure of the ``latest_belief``\n depends on the value of ``self.edge_handling_params['use_BMA']``.\n\n Returns\n ---------\n latest_belief: ``numpy.ndarray`` of dtype object\n Penultimate posterior beliefs over hidden states at the timestep just before the first timestep of the inference horizon. \n Depending on the value of ``self.edge_handling_params['use_BMA']``, the shape of this output array will differ.\n If ``self.edge_handling_params['use_BMA'] == True``, then ``latest_belief`` will be a Bayesian model average \n of beliefs about hidden states, where the average is taken with respect to posterior beliefs about policies.\n Otherwise, `latest_belief`` will be the full, policy-conditioned belief about hidden states, and will have indexing structure\n policies->factors, such that ``latest_belief[p_idx][f_idx]`` refers to the penultimate belief about marginal factor ``f_idx``\n under policy ``p_idx``.\n \"\"\"\n\n if last_belief is None:\n last_belief = utils.obj_array(len(self.policies))\n for p_i, _ in enumerate(self.policies):\n last_belief[p_i] = copy.deepcopy(self.qs[p_i][0])\n\n begin_horizon_step = self.curr_timestep - self.inference_horizon\n if self.edge_handling_params['use_BMA'] and (begin_horizon_step >= 0):\n if hasattr(self, \"q_pi_hist\"):\n self.latest_belief = inference.average_states_over_policies(last_belief, self.q_pi_hist[begin_horizon_step]) # average the earliest marginals together using contemporaneous posterior over policies (`self.q_pi_hist[0]`)\n else:\n self.latest_belief = inference.average_states_over_policies(last_belief, self.q_pi) # average the earliest marginals together using posterior over policies (`self.q_pi`)\n else:\n self.latest_belief = last_belief\n\n return self.latest_belief\n \n def get_future_qs(self):\n \"\"\"\n Returns the last ``self.policy_len`` timesteps of each policy-conditioned belief\n over hidden states. This is a step of pre-processing that needs to be done before computing\n the expected free energy of policies. We do this to avoid computing the expected free energy of \n policies using beliefs about hidden states in the past (so-called \"post-dictive\" beliefs).\n\n Returns\n ---------\n future_qs_seq: ``numpy.ndarray`` of dtype object\n Posterior beliefs over hidden states under a policy, in the future. This is a nested ``numpy.ndarray`` object array, with one\n sub-array ``future_qs_seq[p_idx]`` for each policy. The indexing structure is policy->timepoint-->factor, so that \n ``future_qs_seq[p_idx][t_idx][f_idx]`` refers to beliefs about marginal factor ``f_idx`` expected under policy ``p_idx`` \n at future timepoint ``t_idx``, relative to the current timestep.\n \"\"\"\n \n future_qs_seq = utils.obj_array(len(self.qs))\n for p_idx in range(len(self.qs)):\n future_qs_seq[p_idx] = self.qs[p_idx][-(self.policy_len+1):] # this grabs only the last `policy_len`+1 beliefs about hidden states, under each policy\n\n return future_qs_seq\n\n\n def infer_states(self, observation, distr_obs=False):\n \"\"\"\n Update approximate posterior over hidden states by solving variational inference problem, given an observation.\n\n Parameters\n ----------\n observation: ``list`` or ``tuple`` of ints\n The observation input. Each entry ``observation[m]`` stores the index of the discrete\n observation for modality ``m``.\n distr_obs: ``bool``\n Whether the observation is a distribution over possible observations, rather than a single observation.\n\n Returns\n ---------\n qs: ``numpy.ndarray`` of dtype object\n Posterior beliefs over hidden states. Depending on the inference algorithm chosen, the resulting ``qs`` variable will have additional sub-structure to reflect whether\n beliefs are additionally conditioned on timepoint and policy.\n For example, in case the ``self.inference_algo == 'MMP' `` indexing structure is policy->timepoint-->factor, so that \n ``qs[p_idx][t_idx][f_idx]`` refers to beliefs about marginal factor ``f_idx`` expected under policy ``p_idx`` \n at timepoint ``t_idx``.\n \"\"\"\n\n observation = tuple(observation) if not distr_obs else observation\n\n if not hasattr(self, \"qs\"):\n self.reset()\n\n if self.inference_algo == \"VANILLA\":\n if self.action is not None:\n empirical_prior = control.get_expected_states_interactions(\n self.qs, self.B, self.B_factor_list, self.action.reshape(1, -1) \n )[0]\n else:\n empirical_prior = self.D\n qs = inference.update_posterior_states_factorized(\n self.A,\n observation,\n self.num_obs,\n self.num_states,\n self.mb_dict,\n empirical_prior,\n **self.inference_params\n )\n elif self.inference_algo == \"MMP\":\n\n self.prev_obs.append(observation)\n if len(self.prev_obs) > self.inference_horizon:\n latest_obs = self.prev_obs[-self.inference_horizon:]\n latest_actions = self.prev_actions[-(self.inference_horizon-1):]\n else:\n latest_obs = self.prev_obs\n latest_actions = self.prev_actions\n\n qs, F = inference.update_posterior_states_full_factorized(\n self.A,\n self.mb_dict,\n self.B,\n self.B_factor_list,\n latest_obs,\n self.policies, \n latest_actions, \n prior = self.latest_belief, \n policy_sep_prior = self.edge_handling_params['policy_sep_prior'],\n **self.inference_params\n )\n\n self.F = F # variational free energy of each policy \n\n if hasattr(self, \"qs_hist\"):\n self.qs_hist.append(qs)\n self.qs = qs\n\n return qs\n\n def _infer_states_test(self, observation, distr_obs=False):\n \"\"\"\n Test version of ``infer_states()`` that additionally returns intermediate variables of MMP, such as\n the prediction errors and intermediate beliefs from the optimization. Used for benchmarking against SPM outputs.\n \"\"\"\n observation = tuple(observation) if not distr_obs else observation\n\n if not hasattr(self, \"qs\"):\n self.reset()\n\n if self.inference_algo == \"VANILLA\":\n if self.action is not None:\n empirical_prior = control.get_expected_states(\n self.qs, self.B, self.action.reshape(1, -1) \n )[0]\n else:\n empirical_prior = self.D\n qs = inference.update_posterior_states(\n self.A,\n observation,\n empirical_prior,\n **self.inference_params\n )\n elif self.inference_algo == \"MMP\":\n\n self.prev_obs.append(observation)\n if len(self.prev_obs) > self.inference_horizon:\n latest_obs = self.prev_obs[-self.inference_horizon:]\n latest_actions = self.prev_actions[-(self.inference_horizon-1):]\n else:\n latest_obs = self.prev_obs\n latest_actions = self.prev_actions\n\n qs, F, xn, vn = inference._update_posterior_states_full_test(\n self.A,\n self.B, \n latest_obs,\n self.policies, \n latest_actions, \n prior = self.latest_belief, \n policy_sep_prior = self.edge_handling_params['policy_sep_prior'],\n **self.inference_params\n )\n\n self.F = F # variational free energy of each policy \n\n if hasattr(self, \"qs_hist\"):\n self.qs_hist.append(qs)\n\n self.qs = qs\n\n if self.inference_algo == \"MMP\":\n return qs, xn, vn\n else:\n return qs\n \n def infer_policies(self):\n \"\"\"\n Perform policy inference by optimizing a posterior (categorical) distribution over policies.\n This distribution is computed as the softmax of ``G * gamma + lnE`` where ``G`` is the negative expected\n free energy of policies, ``gamma`` is a policy precision and ``lnE`` is the (log) prior probability of policies.\n This function returns the posterior over policies as well as the negative expected free energy of each policy.\n In this version of the function, the expected free energy of policies is computed using known factorized structure \n in the model, which speeds up computation (particular the state information gain calculations).\n\n Returns\n ----------\n q_pi: 1D ``numpy.ndarray``\n Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.\n G: 1D ``numpy.ndarray``\n Negative expected free energies of each policy, i.e. a vector containing one negative expected free energy per policy.\n \"\"\"\n\n if self.inference_algo == \"VANILLA\":\n if self.sophisticated:\n q_pi, G = control.sophisticated_inference_search(\n self.qs, \n self.policies, \n self.A, \n self.B, \n self.C, \n self.A_factor_list, \n self.B_factor_list, \n self.I,\n self.si_horizon,\n self.si_policy_prune_threshold, \n self.si_state_prune_threshold, \n self.si_prune_penalty,\n 1.0,\n self.inference_params,\n n=0\n )\n else:\n q_pi, G = control.update_posterior_policies_factorized(\n self.qs,\n self.A,\n self.B,\n self.C,\n self.A_factor_list,\n self.B_factor_list,\n self.policies,\n self.use_utility,\n self.use_states_info_gain,\n self.use_param_info_gain,\n self.pA,\n self.pB,\n E = self.E,\n I = self.I,\n gamma = self.gamma\n )\n elif self.inference_algo == \"MMP\":\n\n future_qs_seq = self.get_future_qs()\n\n q_pi, G = control.update_posterior_policies_full_factorized(\n future_qs_seq,\n self.A,\n self.B,\n self.C,\n self.A_factor_list,\n self.B_factor_list,\n self.policies,\n self.use_utility,\n self.use_states_info_gain,\n self.use_param_info_gain,\n self.latest_belief,\n self.pA,\n self.pB,\n F=self.F,\n E=self.E,\n I=self.I,\n gamma=self.gamma\n )\n\n if hasattr(self, \"q_pi_hist\"):\n self.q_pi_hist.append(q_pi)\n if len(self.q_pi_hist) > self.inference_horizon:\n self.q_pi_hist = self.q_pi_hist[-(self.inference_horizon-1):]\n\n self.q_pi = q_pi\n self.G = G\n return q_pi, G\n\n def sample_action(self):\n \"\"\"\n Sample or select a discrete action from the posterior over control states.\n This function both sets or cachés the action as an internal variable with the agent and returns it.\n This function also updates time variable (and thus manages consequences of updating the moving reference frame of beliefs)\n using ``self.step_time()``.\n\n \n Returns\n ----------\n action: 1D ``numpy.ndarray``\n Vector containing the indices of the actions for each control factor\n \"\"\"\n\n if self.sampling_mode == \"marginal\":\n action = control.sample_action(\n self.q_pi, self.policies, self.num_controls, action_selection = self.action_selection, alpha = self.alpha\n )\n elif self.sampling_mode == \"full\":\n action = control.sample_policy(self.q_pi, self.policies, self.num_controls,\n action_selection=self.action_selection, alpha=self.alpha)\n\n self.action = action\n\n self.step_time()\n\n return action\n \n def _sample_action_test(self):\n \"\"\"\n Sample or select a discrete action from the posterior over control states.\n This function both sets or cachés the action as an internal variable with the agent and returns it.\n This function also updates time variable (and thus manages consequences of updating the moving reference frame of beliefs)\n using ``self.step_time()``.\n \n Returns\n ----------\n action: 1D ``numpy.ndarray``\n Vector containing the indices of the actions for each control factor\n \"\"\"\n\n if self.sampling_mode == \"marginal\":\n action, p_dist = control._sample_action_test(self.q_pi, self.policies, self.num_controls,\n action_selection=self.action_selection, alpha=self.alpha)\n elif self.sampling_mode == \"full\":\n action, p_dist = control._sample_policy_test(self.q_pi, self.policies, self.num_controls,\n action_selection=self.action_selection, alpha=self.alpha)\n\n self.action = action\n\n self.step_time()\n\n return action, p_dist\n\n def update_A(self, obs):\n \"\"\"\n Update approximate posterior beliefs about Dirichlet parameters that parameterise the observation likelihood or ``A`` array.\n\n Parameters\n ----------\n observation: ``list`` or ``tuple`` of ints\n The observation input. Each entry ``observation[m]`` stores the index of the discrete\n observation for modality ``m``.\n\n Returns\n -----------\n qA: ``numpy.ndarray`` of dtype object\n Posterior Dirichlet parameters over observation model (same shape as ``A``), after having updated it with observations.\n \"\"\"\n\n qA = learning.update_obs_likelihood_dirichlet_factorized(\n self.pA, \n self.A, \n obs, \n self.qs, \n self.A_factor_list,\n self.lr_pA, \n self.modalities_to_learn\n )\n\n self.pA = qA # set new prior to posterior\n self.A = utils.norm_dist_obj_arr(qA) # take expected value of posterior Dirichlet parameters to calculate posterior over A array\n\n return qA\n\n def _update_A_old(self, obs):\n \"\"\"\n Update approximate posterior beliefs about Dirichlet parameters that parameterise the observation likelihood or ``A`` array.\n\n Parameters\n ----------\n observation: ``list`` or ``tuple`` of ints\n The observation input. Each entry ``observation[m]`` stores the index of the discrete\n observation for modality ``m``.\n\n Returns\n -----------\n qA: ``numpy.ndarray`` of dtype object\n Posterior Dirichlet parameters over observation model (same shape as ``A``), after having updated it with observations.\n \"\"\"\n\n qA = learning.update_obs_likelihood_dirichlet(\n self.pA, \n self.A, \n obs, \n self.qs, \n self.lr_pA, \n self.modalities_to_learn\n )\n\n self.pA = qA # set new prior to posterior\n self.A = utils.norm_dist_obj_arr(qA) # take expected value of posterior Dirichlet parameters to calculate posterior over A array\n\n return qA\n\n def update_B(self, qs_prev):\n \"\"\"\n Update posterior beliefs about Dirichlet parameters that parameterise the transition likelihood \n \n Parameters\n -----------\n qs_prev: 1D ``numpy.ndarray`` or ``numpy.ndarray`` of dtype object\n Marginal posterior beliefs over hidden states at previous timepoint.\n \n Returns\n -----------\n qB: ``numpy.ndarray`` of dtype object\n Posterior Dirichlet parameters over transition model (same shape as ``B``), after having updated it with state beliefs and actions.\n \"\"\"\n\n qB = learning.update_state_likelihood_dirichlet_interactions(\n self.pB,\n self.B,\n self.action,\n self.qs,\n qs_prev,\n self.B_factor_list,\n self.lr_pB,\n self.factors_to_learn\n )\n\n self.pB = qB # set new prior to posterior\n self.B = utils.norm_dist_obj_arr(qB) # take expected value of posterior Dirichlet parameters to calculate posterior over B array\n\n return qB\n \n def _update_B_old(self, qs_prev):\n \"\"\"\n Update posterior beliefs about Dirichlet parameters that parameterise the transition likelihood \n \n Parameters\n -----------\n qs_prev: 1D ``numpy.ndarray`` or ``numpy.ndarray`` of dtype object\n Marginal posterior beliefs over hidden states at previous timepoint.\n \n Returns\n -----------\n qB: ``numpy.ndarray`` of dtype object\n Posterior Dirichlet parameters over transition model (same shape as ``B``), after having updated it with state beliefs and actions.\n \"\"\"\n\n qB = learning.update_state_likelihood_dirichlet(\n self.pB,\n self.B,\n self.action,\n self.qs,\n qs_prev,\n self.lr_pB,\n self.factors_to_learn\n )\n\n self.pB = qB # set new prior to posterior\n self.B = utils.norm_dist_obj_arr(qB) # take expected value of posterior Dirichlet parameters to calculate posterior over B array\n\n return qB\n \n def update_D(self, qs_t0 = None):\n \"\"\"\n Update Dirichlet parameters of the initial hidden state distribution \n (prior beliefs about hidden states at the beginning of the inference window).\n\n Parameters\n -----------\n qs_t0: 1D ``numpy.ndarray``, ``numpy.ndarray`` of dtype object, or ``None``\n Marginal posterior beliefs over hidden states at current timepoint. If ``None``, the \n value of ``qs_t0`` is set to ``self.qs_hist[0]`` (i.e. the initial hidden state beliefs at the first timepoint).\n If ``self.inference_algo == \"MMP\"``, then ``qs_t0`` is set to be the Bayesian model average of beliefs about hidden states\n at the first timestep of the backwards inference horizon, where the average is taken with respect to posterior beliefs about policies.\n \n Returns\n -----------\n qD: ``numpy.ndarray`` of dtype object\n Posterior Dirichlet parameters over initial hidden state prior (same shape as ``qs_t0``), after having updated it with state beliefs.\n \"\"\"\n \n if self.inference_algo == \"VANILLA\":\n \n if qs_t0 is None:\n \n try:\n qs_t0 = self.qs_hist[0]\n except ValueError:\n print(\"qs_t0 must either be passed as argument to `update_D` or `save_belief_hist` must be set to True!\") \n\n elif self.inference_algo == \"MMP\":\n \n if self.edge_handling_params['use_BMA']:\n qs_t0 = self.latest_belief\n elif self.edge_handling_params['policy_sep_prior']:\n \n qs_pi_t0 = self.latest_belief\n\n # get beliefs about policies at the time at the beginning of the inference horizon\n if hasattr(self, \"q_pi_hist\"):\n begin_horizon_step = max(0, self.curr_timestep - self.inference_horizon)\n q_pi_t0 = np.copy(self.q_pi_hist[begin_horizon_step])\n else:\n q_pi_t0 = np.copy(self.q_pi)\n \n qs_t0 = inference.average_states_over_policies(qs_pi_t0,q_pi_t0) # beliefs about hidden states at the first timestep of the inference horizon\n \n qD = learning.update_state_prior_dirichlet(self.pD, qs_t0, self.lr_pD, factors = self.factors_to_learn)\n \n self.pD = qD # set new prior to posterior\n self.D = utils.norm_dist_obj_arr(qD) # take expected value of posterior Dirichlet parameters to calculate posterior over D array\n\n return qD\n\n def _get_default_params(self):\n method = self.inference_algo\n default_params = None\n if method == \"VANILLA\":\n default_params = {\"num_iter\": 10, \"dF\": 1.0, \"dF_tol\": 0.001, \"compute_vfe\": True}\n elif method == \"MMP\":\n default_params = {\"num_iter\": 10, \"grad_descent\": True, \"tau\": 0.25}\n elif method == \"VMP\":\n raise NotImplementedError(\"VMP is not implemented\")\n elif method == \"BP\":\n raise NotImplementedError(\"BP is not implemented\")\n elif method == \"EP\":\n raise NotImplementedError(\"EP is not implemented\")\n elif method == \"CV\":\n raise NotImplementedError(\"CV is not implemented\")\n\n return default_params\n\n " }, { "path": "pymdp/legacy/algos/__init__.py", "content": "from .fpi import run_vanilla_fpi, run_vanilla_fpi_factorized\nfrom .mmp import run_mmp, run_mmp_factorized, _run_mmp_testing\n" }, { "path": "pymdp/legacy/algos/fpi.py", "content": "#!/usr/bin/env python\n# -*- coding: utf-8 -*-\n# pylint: disable=no-member\n\nimport numpy as np\nfrom pymdp.legacy.maths import spm_dot, dot_likelihood, get_joint_likelihood, softmax, calc_free_energy, spm_log_single, spm_log_obj_array\nfrom pymdp.legacy.utils import to_obj_array, obj_array, obj_array_uniform\nfrom copy import deepcopy\n\ndef run_vanilla_fpi(A, obs, num_obs, num_states, prior=None, num_iter=10, dF=1.0, dF_tol=0.001, compute_vfe=True):\n \"\"\"\n Update marginal posterior beliefs over hidden states using mean-field variational inference, via\n fixed point iteration. \n\n Parameters\n ----------\n A: ``numpy.ndarray`` of dtype object\n Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of\n stores an ``np.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store \n the probability of observation level ``i`` given hidden state levels ``j, k, ...``\n obs: numpy 1D array or numpy ndarray of dtype object\n The observation (generated by the environment). If single modality, this should be a 1D ``np.ndarray``\n (one-hot vector representation). If multi-modality, this should be ``np.ndarray`` of dtype object whose entries are 1D one-hot vectors.\n num_obs: list of ints\n List of dimensionalities of each observation modality\n num_states: list of ints\n List of dimensionalities of each hidden state factor\n prior: numpy ndarray of dtype object, default None\n Prior over hidden states. If absent, prior is set to be the log uniform distribution over hidden states (identical to the \n initialisation of the posterior)\n num_iter: int, default 10\n Number of variational fixed-point iterations to run until convergence.\n dF: float, default 1.0\n Initial free energy gradient (dF/dt) before updating in the course of gradient descent.\n dF_tol: float, default 0.001\n Threshold value of the time derivative of the variational free energy (dF/dt), to be checked at \n each iteration. If dF <= dF_tol, the iterations are halted pre-emptively and the final \n marginal posterior belief(s) is(are) returned\n compute_vfe: bool, default True\n Whether to compute the variational free energy at each iteration. If False, the function runs through \n all variational iterations.\n \n Returns\n ----------\n qs: numpy 1D array, numpy ndarray of dtype object, optional\n Marginal posterior beliefs over hidden states at current timepoint\n \"\"\"\n\n # get model dimensions\n len(num_obs)\n n_factors = len(num_states)\n\n \"\"\"\n =========== Step 1 ===========\n Loop over the observation modalities and use assumption of independence \n among observation modalitiesto multiply each modality-specific likelihood \n onto a single joint likelihood over hidden factors [size num_states]\n \"\"\"\n\n likelihood = get_joint_likelihood(A, obs, num_states)\n\n likelihood = spm_log_single(likelihood)\n\n \"\"\"\n =========== Step 2 ===========\n Create a flat posterior (and prior if necessary)\n \"\"\"\n\n qs = obj_array_uniform(num_states)\n\n \"\"\"\n If prior is not provided, initialise prior to be identical to posterior \n (namely, a flat categorical distribution). Take the logarithm of it (required for \n FPI algorithm below).\n \"\"\"\n if prior is None:\n prior = obj_array_uniform(num_states)\n \n prior = spm_log_obj_array(prior) # log the prior\n\n\n \"\"\"\n =========== Step 3 ===========\n Initialize initial free energy\n \"\"\"\n if compute_vfe:\n prev_vfe = calc_free_energy(qs, prior, n_factors)\n\n \"\"\"\n =========== Step 4 ===========\n If we have a single factor, we can just add prior and likelihood because there is a unique FE minimum that can reached instantaneously,\n otherwise we run fixed point iteration\n \"\"\"\n\n if n_factors == 1:\n\n qL = spm_dot(likelihood, qs, [0])\n\n return to_obj_array(softmax(qL + prior[0]))\n\n else:\n \"\"\"\n =========== Step 5 ===========\n Run the FPI scheme\n \"\"\"\n\n # change stop condition for fixed point iterations based on whether we are computing the variational free energy or not\n condition_check_both = lambda curr_iter, dF: curr_iter < num_iter and dF >= dF_tol\n condition_check_just_numiter = lambda curr_iter, dF: curr_iter < num_iter\n check_stop_condition = condition_check_both if compute_vfe else condition_check_just_numiter\n\n curr_iter = 0\n\n while check_stop_condition(curr_iter, dF):\n # Initialise variational free energy\n vfe = 0\n\n # arg_list = [likelihood, list(range(n_factors))]\n # arg_list = arg_list + list(chain(*([qs_i,[i]] for i, qs_i in enumerate(qs)))) + [list(range(n_factors))]\n # LL_tensor = np.einsum(*arg_list)\n\n qs_all = qs[0]\n for factor in range(n_factors-1):\n qs_all = qs_all[...,None]*qs[factor+1]\n LL_tensor = likelihood * qs_all\n\n for factor, qs_i in enumerate(qs):\n # qL = np.einsum(LL_tensor, list(range(n_factors)), 1.0/qs_i, [factor], [factor])\n qL = np.einsum(LL_tensor, list(range(n_factors)), [factor])/qs_i\n qs[factor] = softmax(qL + prior[factor])\n\n # print(f'Posteriors at iteration {curr_iter}:\\n')\n # print(qs[0])\n # print(qs[1])\n # List of orders in which marginal posteriors are sequentially multiplied into the joint likelihood:\n # First order loops over factors starting at index = 0, second order goes in reverse\n # factor_orders = [range(n_factors), range((n_factors - 1), -1, -1)]\n\n # iteratively marginalize out each posterior marginal from the joint log-likelihood\n # except for the one associated with a given factor\n # for factor_order in factor_orders:\n # for factor in factor_order:\n # qL = spm_dot(likelihood, qs, [factor])\n # qs[factor] = softmax(qL + prior[factor])\n\n if compute_vfe:\n # calculate new free energy\n vfe = calc_free_energy(qs, prior, n_factors, likelihood)\n\n # print(f'VFE at iteration {curr_iter}: {vfe}\\n')\n # stopping condition - time derivative of free energy\n dF = np.abs(prev_vfe - vfe)\n prev_vfe = vfe\n\n curr_iter += 1\n\n return qs\n\ndef run_vanilla_fpi_factorized(A, obs, num_obs, num_states, mb_dict, prior=None, num_iter=10, dF=1.0, dF_tol=0.001, compute_vfe=True):\n \"\"\"\n Update marginal posterior beliefs over hidden states using mean-field variational inference, via\n fixed point iteration. \n\n Parameters\n ----------\n A: ``numpy.ndarray`` of dtype object\n Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of\n stores an ``np.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store \n the probability of observation level ``i`` given hidden state levels ``j, k, ...``\n obs: numpy 1D array or numpy ndarray of dtype object\n The observation (generated by the environment). If single modality, this should be a 1D ``np.ndarray``\n (one-hot vector representation). If multi-modality, this should be ``np.ndarray`` of dtype object whose entries are 1D one-hot vectors.\n num_obs: ``list`` of ints\n List of dimensionalities of each observation modality\n num_states: ``list`` of ints\n List of dimensionalities of each hidden state factor\n mb_dict: ``Dict``\n Dictionary with two keys (``A_factor_list`` and ``A_modality_list``), that stores the factor indices that influence each modality (``A_factor_list``)\n and the modality indices influenced by each factor (``A_modality_list``).\n prior: numpy ndarray of dtype object, default None\n Prior over hidden states. If absent, prior is set to be the log uniform distribution over hidden states (identical to the \n initialisation of the posterior)\n num_iter: int, default 10\n Number of variational fixed-point iterations to run until convergence.\n dF: float, default 1.0\n Initial free energy gradient (dF/dt) before updating in the course of gradient descent.\n dF_tol: float, default 0.001\n Threshold value of the time derivative of the variational free energy (dF/dt), to be checked at \n each iteration. If dF <= dF_tol, the iterations are halted pre-emptively and the final \n marginal posterior belief(s) is(are) returned\n compute_vfe: bool, default True\n Whether to compute the variational free energy at each iteration. If False, the function runs through \n all variational iterations.\n \n Returns\n ----------\n qs: numpy 1D array, numpy ndarray of dtype object, optional\n Marginal posterior beliefs over hidden states at current timepoint\n \"\"\"\n\n # get model dimensions\n n_modalities = len(num_obs)\n n_factors = len(num_states)\n\n \"\"\"\n =========== Step 1 ===========\n Generate modality-specific log-likelihood tensors (will be tensors of different-shapes,\n where `likelihood[m].ndim` will be equal to `len(mb_dict['A_factor_list'][m])`\n \"\"\"\n\n likelihood = obj_array(n_modalities)\n obs = to_obj_array(obs)\n for (m, A_m) in enumerate(A):\n likelihood[m] = dot_likelihood(A_m, obs[m])\n\n log_likelihood = spm_log_obj_array(likelihood)\n\n \"\"\"\n =========== Step 2 ===========\n Create a flat posterior (and prior if necessary)\n \"\"\"\n\n qs = obj_array_uniform(num_states)\n\n \"\"\"\n If prior is not provided, initialise prior to be identical to posterior \n (namely, a flat categorical distribution). Take the logarithm of it (required for \n FPI algorithm below).\n \"\"\"\n if prior is None:\n prior = obj_array_uniform(num_states)\n \n prior = spm_log_obj_array(prior) # log the prior\n\n\n \"\"\"\n =========== Step 3 ===========\n Initialize initial free energy\n \"\"\"\n prev_vfe = calc_free_energy(qs, prior, n_factors)\n\n \"\"\"\n =========== Step 4 ===========\n If we have a single factor, we can just add prior and likelihood because there is a unique FE minimum that can reached instantaneously,\n otherwise we run fixed point iteration\n \"\"\"\n\n if n_factors == 1:\n\n joint_loglikelihood = np.zeros(tuple(num_states))\n for m in range(n_modalities):\n joint_loglikelihood += log_likelihood[m] # add up all the log-likelihoods, since we know they will all have the same dimension in the case of a single hidden state factor\n qL = spm_dot(joint_loglikelihood, qs, [0])\n\n qs = to_obj_array(softmax(qL + prior[0]))\n\n else:\n \"\"\"\n =========== Step 5 ===========\n Run the factorized FPI scheme\n \"\"\"\n\n A_factor_list, A_modality_list = mb_dict['A_factor_list'], mb_dict['A_modality_list']\n\n if compute_vfe:\n joint_loglikelihood = np.zeros(tuple(num_states))\n for m in range(n_modalities):\n reshape_dims = n_factors*[1]\n for _f_id in A_factor_list[m]:\n reshape_dims[_f_id] = num_states[_f_id]\n\n joint_loglikelihood += log_likelihood[m].reshape(reshape_dims) # add up all the log-likelihoods after reshaping them to the global common dimensions of all hidden state factors\n\n curr_iter = 0\n\n # change stop condition for fixed point iterations based on whether we are computing the variational free energy or not\n condition_check_both = lambda curr_iter, dF: curr_iter < num_iter and dF >= dF_tol\n condition_check_just_numiter = lambda curr_iter, dF: curr_iter < num_iter\n check_stop_condition = condition_check_both if compute_vfe else condition_check_just_numiter\n\n while check_stop_condition(curr_iter, dF):\n \n # vfe = 0 \n\n qs_new = obj_array(n_factors)\n for f in range(n_factors):\n \n '''\n Sum the expected log likelihoods E_q(s_i/f)[ln P(o=obs[m]|s)] for independent modalities together,\n since they may have differing dimension. This obtains a marginal log-likelihood for the current factor index `factor`,\n which includes the evidence for that particular factor afforded by the different modalities. \n '''\n \n qL = np.zeros(num_states[f])\n\n for ii, m in enumerate(A_modality_list[f]):\n \n qL += spm_dot(log_likelihood[m], qs[A_factor_list[m]], [A_factor_list[m].index(f)])\n\n qs_new[f] = softmax(qL + prior[f])\n\n # vfe -= qL.sum() # accuracy part of vfe, sum of factor-level expected energies E_q(s_i/f)[ln P(o=obs|s)]\n \n qs = deepcopy(qs_new)\n # print(f'Posteriors at iteration {curr_iter}:\\n')\n # print(qs[0])\n # print(qs[1])\n # calculate new free energy, leaving out the accuracy term\n # vfe += calc_free_energy(qs, prior, n_factors)\n\n if compute_vfe:\n vfe = calc_free_energy(qs, prior, n_factors, likelihood=joint_loglikelihood)\n\n # print(f'VFE at iteration {curr_iter}: {vfe}\\n')\n # stopping condition - time derivative of free energy\n dF = np.abs(prev_vfe - vfe)\n prev_vfe = vfe\n\n curr_iter += 1\n \n return qs\n\n\ndef _run_vanilla_fpi_faster(A, obs, n_observations, n_states, prior=None, num_iter=10, dF=1.0, dF_tol=0.001):\n \"\"\"\n Update marginal posterior beliefs about hidden states\n using a new version of variational fixed point iteration (FPI). \n @NOTE (Conor, 26.02.2020):\n This method uses a faster algorithm than the traditional 'spm_dot' approach. Instead of\n separately computing a conditional joint log likelihood of an outcome, under the\n posterior probabilities of a certain marginal, instead all marginals are multiplied into one \n joint tensor that gives the joint likelihood of an observation under all hidden states, \n that is then sequentially (and *parallelizably*) marginalized out to get each marginal posterior. \n This method is less RAM-intensive, admits heavy parallelization, and runs (about 2x) faster.\n @NOTE (Conor, 28.02.2020):\n After further testing, discovered interesting differences between this version and the \n original version. It appears that the\n original version (simple 'run_vanilla_fpi') shows mean-field biases or 'explaining away' \n effects, whereas this version spreads probabilities more 'fairly' among possibilities.\n To summarize: it actually matters what order you do the summing across the joint likelihood tensor. \n In this verison, all marginals are multiplied into the likelihood tensor before summing out, \n whereas in the previous version, marginals are recursively multiplied and summed out.\n @NOTE (Conor, 24.04.2020): I would expect that the factor_order approach used above would help \n ameliorate the effects of the mean-field bias. I would also expect that the use of a factor_order \n below is unnnecessary, since the marginalisation w.r.t. each factor is done only after all marginals \n are multiplied into the larger tensor.\n\n Parameters\n ----------\n - 'A' [numpy nd.array (matrix or tensor or array-of-arrays)]:\n Observation likelihood of the generative model, mapping from hidden states to observations. \n Used to invert generative model to obtain marginal likelihood over hidden states, \n given the observation\n - 'obs' [numpy 1D array or array of arrays (with 1D numpy array entries)]:\n The observation (generated by the environment). If single modality, this can be a 1D array \n (one-hot vector representation). If multi-modality, this can be an array of arrays \n (whose entries are 1D one-hot vectors).\n - 'n_observations' [int or list of ints]\n - 'n_states' [int or list of ints]\n - 'prior' [numpy 1D array, array of arrays (with 1D numpy array entries) or None]:\n Prior beliefs of the agent, to be integrated with the marginal likelihood to obtain posterior. \n If absent, prior is set to be a uniform distribution over hidden states \n (identical to the initialisation of the posterior)\n -'num_iter' [int]:\n Number of variational fixed-point iterations to run.\n -'dF' [float]:\n Starting free energy gradient (dF/dt) before updating in the course of gradient descent.\n -'dF_tol' [float]:\n Threshold value of the gradient of the variational free energy (dF/dt), \n to be checked at each iteration. If dF <= dF_tol, the iterations are halted pre-emptively \n and the final marginal posterior belief(s) is(are) returned\n Returns\n ----------\n -'qs' [numpy 1D array or array of arrays (with 1D numpy array entries):\n Marginal posterior beliefs over hidden states (single- or multi-factor) achieved \n via variational fixed point iteration (mean-field)\n \"\"\"\n\n # get model dimensions\n len(n_observations)\n n_factors = len(n_states)\n\n \"\"\"\n =========== Step 1 ===========\n Loop over the observation modalities and use assumption of independence \n among observation modalities to multiply each modality-specific likelihood \n onto a single joint likelihood over hidden factors [size n_states]\n \"\"\"\n\n # likelihood = np.ones(tuple(n_states))\n\n # if n_modalities is 1:\n # likelihood *= spm_dot(A, obs, obs_mode=True)\n # else:\n # for modality in range(n_modalities):\n # likelihood *= spm_dot(A[modality], obs[modality], obs_mode=True)\n likelihood = get_joint_likelihood(A, obs, n_states)\n likelihood = np.log(likelihood + 1e-16)\n\n \"\"\"\n =========== Step 2 ===========\n Create a flat posterior (and prior if necessary)\n \"\"\"\n\n qs = np.empty(n_factors, dtype=object)\n for factor in range(n_factors):\n qs[factor] = np.ones(n_states[factor]) / n_states[factor]\n\n \"\"\"\n If prior is not provided, initialise prior to be identical to posterior \n (namely, a flat categorical distribution). Take the logarithm of it \n (required for FPI algorithm below).\n \"\"\"\n if prior is None:\n prior = np.empty(n_factors, dtype=object)\n for factor in range(n_factors):\n prior[factor] = np.log(np.ones(n_states[factor]) / n_states[factor] + 1e-16)\n\n \"\"\"\n =========== Step 3 ===========\n Initialize initial free energy\n \"\"\"\n prev_vfe = calc_free_energy(qs, prior, n_factors)\n\n \"\"\"\n =========== Step 4 ===========\n If we have a single factor, we can just add prior and likelihood,\n otherwise we run FPI\n \"\"\"\n\n if n_factors == 1:\n qL = spm_dot(likelihood, qs, [0])\n return softmax(qL + prior[0])\n\n else:\n \"\"\"\n =========== Step 5 ===========\n Run the revised fixed-point iteration scheme\n \"\"\"\n\n curr_iter = 0\n\n while curr_iter < num_iter and dF >= dF_tol:\n # Initialise variational free energy\n vfe = 0\n\n # List of orders in which marginal posteriors are sequentially \n # multiplied into the joint likelihood: First order loops over \n # factors starting at index = 0, second order goes in reverse\n factor_orders = [range(n_factors), range((n_factors - 1), -1, -1)]\n\n for factor_order in factor_orders:\n # reset the log likelihood\n L = likelihood.copy()\n\n # multiply each marginal onto a growing single joint distribution\n for factor in factor_order:\n s = np.ones(np.ndim(L), dtype=int)\n s[factor] = len(qs[factor])\n L *= qs[factor].reshape(tuple(s))\n\n # now loop over factors again, and this time divide out the \n # appropriate marginal before summing out.\n # !!! KEY DIFFERENCE BETWEEN THIS AND 'VANILLA' FPI, \n # WHERE THE ORDER OF THE MARGINALIZATION MATTERS !!!\n for f in factor_order:\n s = np.ones(np.ndim(L), dtype=int)\n s[factor] = len(qs[factor]) # type: ignore\n\n # divide out the factor we multiplied into X already\n temp = L * (1.0 / qs[factor]).reshape(tuple(s)) # type: ignore\n dims2sum = tuple(np.where(np.arange(n_factors) != f)[0])\n qL = np.sum(temp, dims2sum)\n\n temp = L * (1.0 / qs[factor]).reshape(tuple(s)) # type: ignore\n qs[factor] = softmax(qL + prior[factor]) # type: ignore\n\n # calculate new free energy\n vfe = calc_free_energy(qs, prior, n_factors, likelihood)\n\n # stopping condition - time derivative of free energy\n dF = np.abs(prev_vfe - vfe)\n prev_vfe = vfe\n\n curr_iter += 1\n\n return qs\n" }, { "path": "pymdp/legacy/algos/mmp.py", "content": "#!/usr/bin/env python\n# -*- coding: utf-8 -*-\n\nimport numpy as np\n\nfrom pymdp.legacy.utils import get_model_dimensions, obj_array, obj_array_zeros, obj_array_uniform\nfrom pymdp.legacy.maths import spm_dot, spm_norm, softmax, calc_free_energy, spm_log_single, factor_dot_flex\n\ndef run_mmp(\n lh_seq, B, policy, prev_actions=None, prior=None, num_iter=10, grad_descent=True, tau=0.25, last_timestep = False):\n \"\"\"\n Marginal message passing scheme for updating marginal posterior beliefs about hidden states over time, \n conditioned on a particular policy.\n\n Parameters\n ----------\n lh_seq: ``numpy.ndarray`` of dtype object\n Log likelihoods of hidden states under a sequence of observations over time. This is assumed to already be log-transformed. Each ``lh_seq[t]`` contains\n the log likelihood of hidden states for a particular observation at time ``t``\n B: ``numpy.ndarray`` of dtype object\n Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.\n Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability\n of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.\n policy: 2D ``numpy.ndarray``\n Matrix of shape ``(policy_len, num_control_factors)`` that indicates the indices of each action (control state index) upon timestep ``t`` and control_factor ``f` in the element ``policy[t,f]`` for a given policy.\n prev_actions: ``numpy.ndarray``, default None\n If provided, should be a matrix of previous actions of shape ``(infer_len, num_control_factors)`` that indicates the indices of each action (control state index) taken in the past (up until the current timestep).\n prior: ``numpy.ndarray`` of dtype object, default None\n If provided, the prior beliefs about initial states (at t = 0, relative to ``infer_len``). If ``None``, this defaults\n to a flat (uninformative) prior over hidden states.\n numiter: int, default 10\n Number of variational iterations.\n grad_descent: Bool, default True\n Flag for whether to use gradient descent (free energy gradient updates) instead of fixed point solution to the posterior beliefs\n tau: float, default 0.25\n Decay constant for use in ``grad_descent`` version. Tunes the size of the gradient descent updates to the posterior.\n last_timestep: Bool, default False\n Flag for whether we are at the last timestep of belief updating\n \n Returns\n ---------\n qs_seq: ``numpy.ndarray`` of dtype object\n Posterior beliefs over hidden states under the policy. Nesting structure is timepoints, factors,\n where e.g. ``qs_seq[t][f]`` stores the marginal belief about factor ``f`` at timepoint ``t`` under the policy in question.\n F: float\n Variational free energy of the policy.\n \"\"\"\n\n # window\n past_len = len(lh_seq)\n future_len = policy.shape[0]\n\n if last_timestep:\n infer_len = past_len + future_len - 1\n else:\n infer_len = past_len + future_len\n \n future_cutoff = past_len + future_len - 2\n\n # dimensions\n _, num_states, _, num_factors = get_model_dimensions(A=None, B=B)\n\n # beliefs\n qs_seq = obj_array(infer_len)\n for t in range(infer_len):\n qs_seq[t] = obj_array_uniform(num_states)\n\n # last message\n qs_T = obj_array_zeros(num_states)\n\n # prior\n if prior is None:\n prior = obj_array_uniform(num_states)\n\n # transposed transition\n trans_B = obj_array(num_factors)\n \n for f in range(num_factors):\n trans_B[f] = spm_norm(np.swapaxes(B[f],0,1))\n\n if prev_actions is not None:\n policy = np.vstack((prev_actions, policy))\n\n for itr in range(num_iter):\n F = 0.0 # reset variational free energy (accumulated over time and factors, but reset per iteration)\n for t in range(infer_len):\n for f in range(num_factors):\n # likelihood\n if t < past_len:\n lnA = spm_log_single(spm_dot(lh_seq[t], qs_seq[t], [f]))\n print(f'Enumerated version: lnA at time {t}: {lnA}') \n else:\n lnA = np.zeros(num_states[f])\n \n # past message\n if t == 0:\n lnB_past = spm_log_single(prior[f])\n else:\n past_msg = B[f][:, :, int(policy[t - 1, f])].dot(qs_seq[t - 1][f])\n lnB_past = spm_log_single(past_msg)\n\n # future message\n if t >= future_cutoff:\n lnB_future = qs_T[f]\n else:\n future_msg = trans_B[f][:, :, int(policy[t, f])].dot(qs_seq[t + 1][f])\n lnB_future = spm_log_single(future_msg)\n \n # inference\n if grad_descent:\n sx = qs_seq[t][f] # save this as a separate variable so that it can be used in VFE computation\n lnqs = spm_log_single(sx)\n coeff = 1 if (t >= future_cutoff) else 2\n err = (coeff * lnA + lnB_past + lnB_future) - coeff * lnqs\n lnqs = lnqs + tau * (err - err.mean()) # for numerical stability, before passing into the softmax\n qs_seq[t][f] = softmax(lnqs)\n if (t == 0) or (t == (infer_len-1)):\n F += sx.dot(0.5*err)\n else:\n F += sx.dot(0.5*(err - (num_factors - 1)*lnA/num_factors)) # @NOTE: not sure why Karl does this in SPM_MDP_VB_X, we should look into this\n else:\n qs_seq[t][f] = softmax(lnA + lnB_past + lnB_future)\n \n if not grad_descent:\n\n if t < past_len:\n F += calc_free_energy(qs_seq[t], prior, num_factors, likelihood = spm_log_single(lh_seq[t]) )\n else:\n F += calc_free_energy(qs_seq[t], prior, num_factors)\n\n return qs_seq, F\n\ndef run_mmp_factorized(\n lh_seq, mb_dict, B, B_factor_list, policy, prev_actions=None, prior=None, num_iter=10, grad_descent=True, tau=0.25, last_timestep = False):\n \"\"\"\n Marginal message passing scheme for updating marginal posterior beliefs about hidden states over time, \n conditioned on a particular policy.\n\n Parameters\n ----------\n lh_seq: ``numpy.ndarray`` of dtype object\n Log likelihoods of hidden states under a sequence of observations over time. This is assumed to already be log-transformed. Each ``lh_seq[t]`` contains\n the log likelihood of hidden states for a particular observation at time ``t``\n mb_dict: ``Dict``\n Dictionary with two keys (``A_factor_list`` and ``A_modality_list``), that stores the factor indices that influence each modality (``A_factor_list``)\n and the modality indices influenced by each factor (``A_modality_list``).\n B: ``numpy.ndarray`` of dtype object\n Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.\n Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability\n of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.\n B_factor_list: ``list`` of ``list`` of ``int``\n List of lists of hidden state factors each hidden state factor depends on. Each element ``B_factor_list[i]`` is a list of the factor indices that factor i's dynamics depend on.\n policy: 2D ``numpy.ndarray``\n Matrix of shape ``(policy_len, num_control_factors)`` that indicates the indices of each action (control state index) upon timestep ``t`` and control_factor ``f` in the element ``policy[t,f]`` for a given policy.\n prev_actions: ``numpy.ndarray``, default None\n If provided, should be a matrix of previous actions of shape ``(infer_len, num_control_factors)`` that indicates the indices of each action (control state index) taken in the past (up until the current timestep).\n prior: ``numpy.ndarray`` of dtype object, default None\n If provided, the prior beliefs about initial states (at t = 0, relative to ``infer_len``). If ``None``, this defaults\n to a flat (uninformative) prior over hidden states.\n numiter: int, default 10\n Number of variational iterations.\n grad_descent: Bool, default True\n Flag for whether to use gradient descent (free energy gradient updates) instead of fixed point solution to the posterior beliefs\n tau: float, default 0.25\n Decay constant for use in ``grad_descent`` version. Tunes the size of the gradient descent updates to the posterior.\n last_timestep: Bool, default False\n Flag for whether we are at the last timestep of belief updating\n \n Returns\n ---------\n qs_seq: ``numpy.ndarray`` of dtype object\n Posterior beliefs over hidden states under the policy. Nesting structure is timepoints, factors,\n where e.g. ``qs_seq[t][f]`` stores the marginal belief about factor ``f`` at timepoint ``t`` under the policy in question.\n F: float\n Variational free energy of the policy.\n \"\"\"\n\n # window\n past_len = len(lh_seq)\n future_len = policy.shape[0]\n\n if last_timestep:\n infer_len = past_len + future_len - 1\n else:\n infer_len = past_len + future_len\n \n future_cutoff = past_len + future_len - 2\n\n # dimensions\n _, num_states, _, num_factors = get_model_dimensions(A=None, B=B)\n\n # beliefs\n qs_seq = obj_array(infer_len)\n for t in range(infer_len):\n qs_seq[t] = obj_array_uniform(num_states)\n\n # last message\n qs_T = obj_array_zeros(num_states)\n\n # prior\n if prior is None:\n prior = obj_array_uniform(num_states)\n\n # transposed transition\n trans_B = obj_array(num_factors)\n \n for f in range(num_factors):\n trans_B[f] = spm_norm(np.swapaxes(B[f],0,1))\n\n if prev_actions is not None:\n policy = np.vstack((prev_actions, policy))\n\n A_factor_list, A_modality_list = mb_dict['A_factor_list'], mb_dict['A_modality_list']\n\n joint_lh_seq = obj_array(len(lh_seq))\n num_modalities = len(A_factor_list)\n for t in range(len(lh_seq)):\n joint_loglikelihood = np.zeros(tuple(num_states))\n for m in range(num_modalities):\n reshape_dims = num_factors*[1]\n for _f_id in A_factor_list[m]:\n reshape_dims[_f_id] = num_states[_f_id]\n joint_loglikelihood += lh_seq[t][m].reshape(reshape_dims) # add up all the log-likelihoods after reshaping them to the global common dimensions of all hidden state factors\n joint_lh_seq[t] = joint_loglikelihood\n\n # compute inverse B dependencies, which is a list that for each hidden state factor, lists the indices of the other hidden state factors that it 'drives' or is a parent of in the HMM graphical model\n inv_B_deps = [[i for i, d in enumerate(B_factor_list) if f in d] for f in range(num_factors)]\n for itr in range(num_iter):\n F = 0.0 # reset variational free energy (accumulated over time and factors, but reset per iteration)\n for t in range(infer_len):\n for f in range(num_factors):\n # likelihood\n lnA = np.zeros(num_states[f])\n if t < past_len:\n for m in A_modality_list[f]:\n lnA += spm_log_single(spm_dot(lh_seq[t][m], qs_seq[t][A_factor_list[m]], [A_factor_list[m].index(f)])) \n print(f'Factorized version: lnA at time {t}: {lnA}') \n \n # past message\n if t == 0:\n lnB_past = spm_log_single(prior[f])\n else:\n past_msg = spm_dot(B[f][...,int(policy[t - 1, f])], qs_seq[t-1][B_factor_list[f]])\n lnB_past = spm_log_single(past_msg)\n\n # future message\n if t >= future_cutoff:\n lnB_future = qs_T[f]\n else:\n # list of future_msgs, one for each of the factors that factor f is driving\n\n B_marg_list = [] # list of the marginalized B matrices, that correspond to mapping between the factor of interest `f` and each of its children factors `i`\n for i in inv_B_deps[f]: #loop over all the hidden state factors that are driven by f\n b = B[i][...,int(policy[t,i])]\n keep_dims = (0,1+B_factor_list[i].index(f))\n dims = []\n idxs = []\n for j, d in enumerate(B_factor_list[i]): # loop over the list of factors that drive each child `i` of factor-of-interest `f` (i.e. the co-parents of `f`, with respect to child `i`)\n if f != d:\n dims.append((1 + j,))\n idxs.append(d)\n xs = [qs_seq[t+1][f_i] for f_i in idxs]\n B_marg_list.append( factor_dot_flex(b, xs, tuple(dims), keep_dims=keep_dims) ) # marginalize out all parents of `i` besides `f`\n\n lnB_future = np.zeros(num_states[f])\n for i, b in enumerate(B_marg_list):\n b_norm_T = spm_norm(b.T)\n lnB_future += spm_log_single(b_norm_T.dot(qs_seq[t + 1][inv_B_deps[f][i]]))\n \n \n lnB_future *= 0.5\n \n # inference\n if grad_descent:\n sx = qs_seq[t][f] # save this as a separate variable so that it can be used in VFE computation\n lnqs = spm_log_single(sx)\n coeff = 1 if (t >= future_cutoff) else 2\n err = (coeff * lnA + lnB_past + lnB_future) - coeff * lnqs\n lnqs = lnqs + tau * (err - err.mean())\n qs_seq[t][f] = softmax(lnqs)\n if (t == 0) or (t == (infer_len-1)):\n F += sx.dot(0.5*err)\n else:\n F += sx.dot(0.5*(err - (num_factors - 1)*lnA/num_factors)) # @NOTE: not sure why Karl does this in SPM_MDP_VB_X, we should look into this\n else:\n qs_seq[t][f] = softmax(lnA + lnB_past + lnB_future)\n \n if not grad_descent:\n\n if t < past_len:\n F += calc_free_energy(qs_seq[t], prior, num_factors, likelihood = spm_log_single(joint_lh_seq[t]) )\n else:\n F += calc_free_energy(qs_seq[t], prior, num_factors)\n\n return qs_seq, F\n\ndef _run_mmp_testing(\n lh_seq, B, policy, prev_actions=None, prior=None, num_iter=10, grad_descent=True, tau=0.25, last_timestep = False):\n \"\"\"\n Marginal message passing scheme for updating marginal posterior beliefs about hidden states over time, \n conditioned on a particular policy.\n\n Parameters\n ----------\n lh_seq: ``numpy.ndarray`` of dtype object\n Log likelihoods of hidden states under a sequence of observations over time. This is assumed to already be log-transformed. Each ``lh_seq[t]`` contains\n the log likelihood of hidden states for a particular observation at time ``t``\n B: ``numpy.ndarray`` of dtype object\n Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.\n Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability\n of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.\n policy: 2D ``numpy.ndarray``\n Matrix of shape ``(policy_len, num_control_factors)`` that indicates the indices of each action (control state index) upon timestep ``t`` and control_factor ``f` in the element ``policy[t,f]`` for a given policy.\n prev_actions: ``numpy.ndarray``, default None\n If provided, should be a matrix of previous actions of shape ``(infer_len, num_control_factors)`` that indicates the indices of each action (control state index) taken in the past (up until the current timestep).\n prior: ``numpy.ndarray`` of dtype object, default None\n If provided, the prior beliefs about initial states (at t = 0, relative to ``infer_len``). If ``None``, this defaults\n to a flat (uninformative) prior over hidden states.\n numiter: int, default 10\n Number of variational iterations.\n grad_descent: Bool, default True\n Flag for whether to use gradient descent (free energy gradient updates) instead of fixed point solution to the posterior beliefs\n tau: float, default 0.25\n Decay constant for use in ``grad_descent`` version. Tunes the size of the gradient descent updates to the posterior.\n last_timestep: Bool, default False\n Flag for whether we are at the last timestep of belief updating\n \n Returns\n ---------\n qs_seq: ``numpy.ndarray`` of dtype object\n Posterior beliefs over hidden states under the policy. Nesting structure is timepoints, factors,\n where e.g. ``qs_seq[t][f]`` stores the marginal belief about factor ``f`` at timepoint ``t`` under the policy in question.\n F: float\n Variational free energy of the policy.\n xn: list\n The sequence of beliefs as they're computed across iterations of marginal message passing (used for benchmarking). Nesting structure is iteration, factor, so ``xn[itr][f]`` \n stores the ``num_states x infer_len`` array of beliefs about hidden states at different time points of inference horizon.\n vn: list\n The sequence of prediction errors as they're computed across iterations of marginal message passing (used for benchmarking). Nesting structure is iteration, factor, so ``vn[itr][f]`` \n stores the ``num_states x infer_len`` array of prediction errors for hidden states at different time points of inference horizon.\n \"\"\"\n\n # window\n past_len = len(lh_seq)\n future_len = policy.shape[0]\n\n if last_timestep:\n infer_len = past_len + future_len - 1\n else:\n infer_len = past_len + future_len\n \n future_cutoff = past_len + future_len - 2\n\n # dimensions\n _, num_states, _, num_factors = get_model_dimensions(A=None, B=B)\n\n # beliefs\n qs_seq = obj_array(infer_len)\n for t in range(infer_len):\n qs_seq[t] = obj_array_uniform(num_states)\n\n # last message\n qs_T = obj_array_zeros(num_states)\n\n # prior\n if prior is None:\n prior = obj_array_uniform(num_states)\n\n # transposed transition\n trans_B = obj_array(num_factors)\n \n for f in range(num_factors):\n trans_B[f] = spm_norm(np.swapaxes(B[f],0,1))\n\n if prev_actions is not None:\n policy = np.vstack((prev_actions, policy))\n\n xn = [] # list for storing beliefs across iterations\n vn = [] # list for storing prediction errors across iterations\n\n shape_list = [ [num_states[f], infer_len] for f in range(num_factors) ]\n \n for itr in range(num_iter):\n\n xn_itr_all_factors = obj_array_zeros(shape_list) # temporary cache for storing beliefs across different hidden state factors, for a fixed iteration of the belief updating scheme\n vn_itr_all_factors = obj_array_zeros(shape_list) # temporary cache for storing prediction errors across different hidden state factors, for a fixed iteration of the belief updating scheme\n\n F = 0.0 # reset variational free energy (accumulated over time and factors, but reset per iteration)\n for t in range(infer_len):\n\n if t == (infer_len - 1):\n pass\n\n for f in range(num_factors):\n # likelihood\n if t < past_len:\n # if itr == 0:\n # print(f'obs from timestep {t}\\n')\n lnA = spm_log_single(spm_dot(lh_seq[t], qs_seq[t], [f]))\n else:\n lnA = np.zeros(num_states[f])\n \n # past message\n if t == 0:\n lnB_past = spm_log_single(prior[f])\n else:\n past_msg = B[f][:, :, int(policy[t - 1, f])].dot(qs_seq[t - 1][f])\n lnB_past = spm_log_single(past_msg)\n\n # future message\n if t >= future_cutoff:\n lnB_future = qs_T[f]\n else:\n future_msg = trans_B[f][:, :, int(policy[t, f])].dot(qs_seq[t + 1][f])\n lnB_future = spm_log_single(future_msg)\n\n # inference\n if grad_descent:\n sx = qs_seq[t][f] # save this as a separate variable so that it can be used in VFE computation\n lnqs = spm_log_single(sx)\n coeff = 1 if (t >= future_cutoff) else 2\n err = (coeff * lnA + lnB_past + lnB_future) - coeff * lnqs\n vn_tmp = err - err.mean()\n lnqs = lnqs + tau * vn_tmp\n qs_seq[t][f] = softmax(lnqs)\n if (t == 0) or (t == (infer_len-1)):\n F += sx.dot(0.5*err)\n else:\n F += sx.dot(0.5*(err - (num_factors - 1)*lnA/num_factors)) # @NOTE: not sure why Karl does this in SPM_MDP_VB_X, we should look into this\n \n xn_itr_all_factors[f][:,t] = np.copy(qs_seq[t][f])\n vn_itr_all_factors[f][:,t] = np.copy(vn_tmp)\n\n else:\n qs_seq[t][f] = softmax(lnA + lnB_past + lnB_future)\n \n if not grad_descent:\n\n if t < past_len:\n F += calc_free_energy(qs_seq[t], prior, num_factors, likelihood = spm_log_single(lh_seq[t]) )\n else:\n F += calc_free_energy(qs_seq[t], prior, num_factors)\n xn.append(xn_itr_all_factors)\n vn.append(vn_itr_all_factors)\n\n return qs_seq, F, xn, vn\n" }, { "path": "pymdp/legacy/algos/mmp_old.py", "content": "#!/usr/bin/env python\n# -*- coding: utf-8 -*-\n# pylint: disable=no-member\n\nimport numpy as np\n\nfrom pymdp.legacy.maths import spm_dot, get_joint_likelihood, spm_norm, softmax\nfrom pymdp.legacy import utils\n\n\ndef run_mmp_old(\n A,\n B,\n obs_t,\n policy,\n curr_t,\n t_horizon,\n T,\n qs_bma=None,\n prior=None,\n num_iter=10,\n dF=1.0,\n dF_tol=0.001,\n previous_actions=None,\n use_gradient_descent=False,\n tau=0.25,\n):\n \"\"\"\n Optimise marginal posterior beliefs about hidden states using marginal message-passing scheme (MMP) developed\n by Thomas Parr and colleagues, see https://github.com/tejparr/nmpassing\n \n Parameters\n ----------\n - 'A' [numpy nd.array (matrix or tensor or array-of-arrays)]:\n Observation likelihood of the generative model, mapping from hidden states to observations. \n Used in inference to get the likelihood of an observation, under different hidden state configurations.\n - 'B' [numpy.ndarray (tensor or array-of-arrays)]:\n Transition likelihood of the generative model, mapping from hidden states at t to hidden states at t+1.\n Used in inference to get expected future (or past) hidden states, given past (or future) hidden \n states (or expectations thereof).\n - 'obs_t' [list of length t_horizon of numpy 1D array or array of arrays (with 1D numpy array entries)]:\n Sequence of observations sampled from beginning of time horizon the current timestep t. \n The first observation (the start of the time horizon) is either the first timestep of the generative \n process or the first timestep of the policy horizon (whichever is closer to 'curr_t' in time).\n The observations over time are stored as a list of numpy arrays, where in case of multi-modalities \n each numpy array is an array-of-arrays, with one 1D numpy.ndarray for each modality. \n In the case of a single modality, each observation is a single 1D numpy.ndarray.\n - 'policy' [2D np.ndarray]:\n Array of actions constituting a single policy. Policy is a shape \n (n_steps, n_control_factors) numpy.ndarray, the values of which indicate actions along a given control \n factor (column index) at a given timestep (row index).\n - 'curr_t' [int]:\n Current timestep (relative to the 'absolute' time of the generative process).\n - 't_horizon'[int]:\n Temporal horizon of inference for states and policies.\n - 'T' [int]:\n Temporal horizon of the generative process (absolute time)\n - `qs_bma` [numpy 1D array, array of arrays (with 1D numpy array entries) or None]:\n - 'prior' [numpy 1D array, array of arrays (with 1D numpy array entries) or None]:\n Prior beliefs of the agent at the beginning of the time horizon, to be integrated \n with the marginal likelihood to obtain posterior at the first timestep.\n If absent, prior is set to be a uniform distribution over hidden states (identical to the \n initialisation of the posterior.\n -'num_iter' [int]:\n Number of variational iterations to run. (optional)\n -'dF' [float]:\n Starting free energy gradient (dF/dt) before updating in the course of gradient descent. (optional)\n -'dF_tol' [float]:\n Threshold value of the gradient of the variational free energy (dF/dt), to be checked \n at each iteration. If dF <= dF_tol, the iterations are halted pre-emptively and the final \n marginal posterior belief(s) is(are) returned. (optional)\n -'previous_actions' [numpy.ndarray with shape (num_steps, n_control_factors) or None]:\n Array of previous actions, which can be used to constrain the 'past' messages in inference \n to only consider states of affairs that were possible under actions that are known to have been taken. \n The first dimension of previous-arrays (previous_actions.shape[0]) encodes how far back in time the agent is \n considering. The first timestep of this either corresponds to either the first timestep of the generative \n process or the first timestep of the policy horizon (whichever is sooner in time). (optional)\n -'use_gradient_descent' [bool]:\n Flag to indicate whether to use gradient descent to optimise posterior beliefs.\n -'tau' [float]:\n Learning rate for gradient descent (only used if use_gradient_descent is True)\n \n \n Returns\n ----------\n -'qs' [list of length T of numpy 1D arrays or array of arrays (with 1D numpy array entries):\n Marginal posterior beliefs over hidden states (single- or multi-factor) achieved \n via marginal message pasing\n -'qss' [list of lists of length T of numpy 1D arrays or array of arrays (with 1D numpy array entries):\n Marginal posterior beliefs about hidden states (single- or multi-factor) held at \n each timepoint, *about* each timepoint of the observation\n sequence\n -'F' [2D np.ndarray]:\n Variational free energy of beliefs about hidden states, indexed by time point and variational iteration\n -'F_pol' [float]:\n Total free energy of the policy under consideration.\n \"\"\"\n\n # get temporal window for inference\n min_time = max(0, curr_t - t_horizon)\n max_time = min(T, curr_t + t_horizon)\n window_idxs = np.array([t for t in range(min_time, max_time)])\n window_len = len(window_idxs)\n # TODO: needs a better name - the point at which we ignore future messages\n future_cutoff = window_len - 1\n inference_len = window_len + 1\n len(obs_t)\n\n # get relevant observations, given our current time point\n if curr_t == 0:\n obs_range = [0]\n else:\n min_obs_idx = max(0, curr_t - t_horizon)\n max_obs_idx = curr_t + 1\n obs_range = range(min_obs_idx, max_obs_idx)\n\n # get model dimensions\n # TODO: make a general function in `utils` for extracting model dimensions\n if utils.is_obj_array(obs_t[0]):\n num_obs = [obs.shape[0] for obs in obs_t[0]]\n else:\n num_obs = [obs_t[0].shape[0]]\n\n if utils.is_obj_array(B):\n num_states = [b.shape[0] for b in B]\n else:\n num_states = [B[0].shape[0]]\n B = utils.to_obj_array(B)\n\n len(num_obs)\n num_factors = len(num_states)\n\n \"\"\"\n =========== Step 1 ===========\n Calculate likelihood\n Loop over modalities and use assumption of independence among observation modalities\n to combine each modality-specific likelihood into a single joint likelihood over hidden states \n \"\"\"\n\n # likelihood of observations under configurations of hidden states (over time)\n likelihood = np.empty(len(obs_range), dtype=object)\n for t, obs in enumerate(obs_range):\n # likelihood_t = np.ones(tuple(num_states))\n\n # if num_modalities == 1:\n # likelihood_t *= spm_dot(A[0], obs_t[obs], obs_mode=True)\n # else:\n # for modality in range(num_modalities):\n # likelihood_t *= spm_dot(A[modality], obs_t[obs][modality], obs_mode=True)\n \n likelihood_t = get_joint_likelihood(A, obs_t, num_states)\n\n # The Thomas Parr MMP version, you log the likelihood first\n # likelihood[t] = np.log(likelihood_t + 1e-16)\n\n # Karl SPM version, logging doesn't happen until *after* the dotting with the posterior\n likelihood[t] = likelihood_t\n\n \"\"\"\n =========== Step 2 ===========\n Initialise a flat posterior (and prior if necessary)\n If a prior is not provided, initialise a uniform prior\n \"\"\"\n\n qs = [np.empty(num_factors, dtype=object) for i in range(inference_len)]\n\n for t in range(inference_len):\n # if t == window_len:\n # # final message is zeros - has no effect on inference\n # # TODO: this may be redundant now that we skip last step\n # for f in range(num_factors):\n # qs[t][f] = np.zeros(num_states[f])\n # else:\n # for f in range(num_factors):\n # qs[t][f] = np.ones(num_states[f]) / num_states[f]\n for f in range(num_factors):\n qs[t][f] = np.ones(num_states[f]) / num_states[f]\n\n if prior is None:\n prior = np.empty(num_factors, dtype=object)\n for f in range(num_factors):\n prior[f] = np.ones(num_states[f]) / num_states[f]\n\n \"\"\" \n =========== Step 3 ===========\n Create a normalized transpose of the transition distribution `B_transposed`\n Used for computing backwards messages 'from the future'\n \"\"\"\n\n B_transposed = np.empty(num_factors, dtype=object)\n for f in range(num_factors):\n B_transposed[f] = np.zeros_like(B[f])\n for u in range(B[f].shape[2]):\n B_transposed[f][:, :, u] = spm_norm(B[f][:, :, u].T)\n\n # zero out final message\n # TODO: may be redundant now we skip final step\n last_message = np.empty(num_factors, dtype=object)\n for f in range(num_factors):\n last_message[f] = np.zeros(num_states[f])\n\n # if previous actions not given, zero out to stop any influence on inference\n if previous_actions is None:\n previous_actions = np.zeros((1, policy.shape[1]))\n\n full_policy = np.vstack((previous_actions, policy))\n\n # print(full_policy.shape)\n\n \"\"\"\n =========== Step 3 ===========\n Loop over time indices of time window, updating posterior as we go\n This includes past time steps and future time steps\n \"\"\"\n\n qss = [[] for i in range(num_iter)]\n free_energy = np.zeros((len(qs), num_iter))\n free_energy_pol = 0.0\n\n # print(obs_seq_len)\n\n print('Full policy history')\n print('------------------')\n print(full_policy)\n\n for n in range(num_iter):\n for t in range(inference_len):\n\n lnB_past_tensor = np.empty(num_factors, dtype=object)\n for f in range(num_factors):\n\n # if t == 0 and n == 0:\n # print(f\"qs at time t = {t}, factor f = {f}, iteration i = {n}: {qs[t][f]}\")\n\n \"\"\"\n =========== Step 3.a ===========\n Calculate likelihood\n \"\"\"\n if t < len(obs_range):\n # if t < len(obs_seq_len):\n # Thomas Parr MMP version\n # lnA = spm_dot(likelihood[t], qs[t], [f])\n\n # Karl SPM version\n lnA = np.log(spm_dot(likelihood[t], qs[t], [f]) + 1e-16)\n else:\n lnA = np.zeros(num_states[f])\n\n if t == 1 and n == 0:\n # pass\n print(f\"lnA at time t = {t}, factor f = {f}, iteration i = {n}: {lnA}\")\n\n # print(f\"lnA at time t = {t}, factor f = {f}, iteration i = {n}: {lnA}\")\n\n \"\"\"\n =========== Step 3.b ===========\n Calculate past message\n \"\"\"\n if t == 0 and window_idxs[0] == 0:\n lnB_past = np.log(prior[f] + 1e-16)\n else:\n # Thomas Parr MMP version\n # lnB_past = 0.5 * np.log(B[f][:, :, full_policy[t - 1, f]].dot(qs[t - 1][f]) + 1e-16)\n\n # Karl SPM version\n if t == 1 and n == 0 and f == 1:\n print('past action:')\n print('-------------')\n print(full_policy[t - 1, :])\n print(B[f][:,:,0])\n print(B[f][:,:,1])\n print(qs[t - 1][f])\n lnB_past = np.log(B[f][:, :, full_policy[t - 1, f]].dot(qs[t - 1][f]) + 1e-16)\n # if t == 0:\n # print(\n # f\"qs_t_1 at time t = {t}, factor f = {f}, iteration i = {n}: {qs[t - 1][f]}\"\n # )\n\n if t == 1 and n == 0:\n print(\n f\"lnB_past at time t = {t}, factor f = {f}, iteration i = {n}: {lnB_past}\"\n )\n\n \"\"\"\n =========== Step 3.c ===========\n Calculate future message\n \"\"\"\n if t >= future_cutoff:\n # TODO: this is redundant - not used in code\n lnB_future = last_message[f]\n else:\n # Thomas Parr MMP version\n # B_future = B_transposed[f][:, :, int(full_policy[t, f])].dot(qs[t + 1][f])\n # lnB_future = 0.5 * np.log(B_future + 1e-16)\n\n # Karl Friston SPM version\n B_future = B_transposed[f][:, :, int(full_policy[t, f])].dot(qs[t + 1][f])\n lnB_future = np.log(B_future + 1e-16)\n \n # Thomas Parr MMP version\n # lnB_past_tensor[f] = 2 * lnBpast\n # Karl SPM version\n lnB_past_tensor[f] = lnB_past\n\n \"\"\"\n =========== Step 3.d ===========\n Update posterior\n \"\"\"\n if use_gradient_descent:\n lns = np.log(qs[t][f] + 1e-16)\n\n # Thomas Parr MMP version\n # error = (lnA + lnBpast + lnBfuture) - lns\n\n # Karl SPM version\n if t >= future_cutoff:\n error = lnA + lnB_past - lns\n\n else:\n error = (2 * lnA + lnB_past + lnB_future) - 2 * lns\n \n\n # print(f\"prediction error at time t = {t}, factor f = {f}, iteration i = {n}: {error}\")\n # print(f\"OG {t} {f} {error}\")\n error -= error.mean()\n lns = lns + tau * error\n qs_t_f = softmax(lns)\n free_energy_pol += 0.5 * qs[t][f].dot(error)\n qs[t][f] = qs_t_f\n else:\n qs[t][f] = softmax(lnA + lnB_past + lnB_future)\n\n # TODO: probably works anyways\n # free_energy[t, n] = calc_free_energy(qs[t], lnB_past_tensor, num_factors, likelihood[t])\n # free_energy_pol += F[t, n]\n qss[n].append(qs)\n\n return qs, qss, free_energy, free_energy_pol\n" }, { "path": "pymdp/legacy/control.py", "content": "#!/usr/bin/env python\n# -*- coding: utf-8 -*-\n# pylint: disable=no-member\n# pylint: disable=not-an-iterable\n\nimport itertools\nimport numpy as np\nfrom pymdp.legacy.maths import softmax, softmax_obj_arr, spm_dot, spm_wnorm, spm_MDP_G, spm_log_single, entropy\nfrom pymdp.legacy.inference import update_posterior_states_factorized, average_states_over_policies\nfrom pymdp.legacy import utils\nimport copy\n\ndef update_posterior_policies_full(\n qs_seq_pi,\n A,\n B,\n C,\n policies,\n use_utility=True,\n use_states_info_gain=True,\n use_param_info_gain=False,\n prior=None,\n pA=None,\n pB=None,\n F=None,\n E=None,\n I=None,\n gamma=16.0\n): \n \"\"\"\n Update posterior beliefs about policies by computing expected free energy of each policy and integrating that\n with the variational free energy of policies ``F`` and prior over policies ``E``. This is intended to be used in conjunction\n with the ``update_posterior_states_full`` method of ``inference.py``, since the full posterior over future timesteps, under all policies, is\n assumed to be provided in the input array ``qs_seq_pi``.\n\n Parameters\n ----------\n qs_seq_pi: ``numpy.ndarray`` of dtype object\n Posterior beliefs over hidden states for each policy. Nesting structure is policies, timepoints, factors,\n where e.g. ``qs_seq_pi[p][t][f]`` stores the marginal belief about factor ``f`` at timepoint ``t`` under policy ``p``.\n A: ``numpy.ndarray`` of dtype object\n Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of\n stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store \n the probability of observation level ``i`` given hidden state levels ``j, k, ...``\n B: ``numpy.ndarray`` of dtype object\n Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.\n Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability\n of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.\n C: ``numpy.ndarray`` of dtype object\n Prior over observations or 'prior preferences', storing the \"value\" of each outcome in terms of relative log probabilities. \n This is softmaxed to form a proper probability distribution before being used to compute the expected utility term of the expected free energy.\n policies: ``list`` of 2D ``numpy.ndarray``\n ``list`` that stores each policy in ``policies[p_idx]``. Shape of ``policies[p_idx]`` is ``(num_timesteps, num_factors)`` where `num_timesteps` is the temporal\n depth of the policy and ``num_factors`` is the number of control factors.\n use_utility: ``Bool``, default ``True``\n Boolean flag that determines whether expected utility should be incorporated into computation of EFE.\n use_states_info_gain: ``Bool``, default ``True``\n Boolean flag that determines whether state epistemic value (info gain about hidden states) should be incorporated into computation of EFE.\n use_param_info_gain: ``Bool``, default ``False`` \n Boolean flag that determines whether parameter epistemic value (info gain about generative model parameters) should be incorporated into computation of EFE. \n prior: ``numpy.ndarray`` of dtype object, default ``None``\n If provided, this is a ``numpy`` object array with one sub-array per hidden state factor, that stores the prior beliefs about initial states. \n If ``None``, this defaults to a flat (uninformative) prior over hidden states.\n pA: ``numpy.ndarray`` of dtype object, default ``None``\n Dirichlet parameters over observation model (same shape as ``A``)\n pB: ``numpy.ndarray`` of dtype object, default ``None``\n Dirichlet parameters over transition model (same shape as ``B``)\n F: 1D ``numpy.ndarray``, default ``None``\n Vector of variational free energies for each policy\n E: 1D ``numpy.ndarray``, default ``None``\n Vector of prior probabilities of each policy (what's referred to in the active inference literature as \"habits\"). If ``None``, this defaults to a flat (uninformative) prior over policies.\n I: ``numpy.ndarray`` of dtype object\n For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability \n of reaching the goal state backwards from state j after i steps.\n gamma: ``float``, default 16.0\n Prior precision over policies, scales the contribution of the expected free energy to the posterior over policies\n\n Returns\n ----------\n q_pi: 1D ``numpy.ndarray``\n Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.\n G: 1D ``numpy.ndarray``\n Negative expected free energies of each policy, i.e. a vector containing one negative expected free energy per policy.\n \"\"\"\n\n num_obs, num_states, num_modalities, num_factors = utils.get_model_dimensions(A, B)\n horizon = len(qs_seq_pi[0])\n num_policies = len(qs_seq_pi)\n\n qo_seq = utils.obj_array(horizon)\n for t in range(horizon):\n qo_seq[t] = utils.obj_array_zeros(num_obs)\n\n # initialise expected observations\n qo_seq_pi = utils.obj_array(num_policies)\n\n # initialize (negative) expected free energies for all policies\n G = np.zeros(num_policies)\n\n if F is None:\n F = spm_log_single(np.ones(num_policies) / num_policies)\n\n if E is None:\n lnE = spm_log_single(np.ones(num_policies) / num_policies)\n else:\n lnE = spm_log_single(E) \n\n if I is not None:\n init_qs_all_pi = [qs_seq_pi[p][0] for p in range(num_policies)]\n qs_bma = average_states_over_policies(init_qs_all_pi, softmax(E))\n\n for p_idx, policy in enumerate(policies):\n\n qo_seq_pi[p_idx] = get_expected_obs(qs_seq_pi[p_idx], A)\n\n if use_utility:\n G[p_idx] += calc_expected_utility(qo_seq_pi[p_idx], C)\n \n if use_states_info_gain:\n G[p_idx] += calc_states_info_gain(A, qs_seq_pi[p_idx])\n \n if use_param_info_gain:\n if pA is not None:\n G[p_idx] += calc_pA_info_gain(pA, qo_seq_pi[p_idx], qs_seq_pi[p_idx])\n if pB is not None:\n G[p_idx] += calc_pB_info_gain(pB, qs_seq_pi[p_idx], prior, policy)\n \n if I is not None:\n G[p_idx] += calc_inductive_cost(qs_bma, qs_seq_pi[p_idx], I)\n\n q_pi = softmax(G * gamma - F + lnE)\n \n return q_pi, G\n\ndef update_posterior_policies_full_factorized(\n qs_seq_pi,\n A,\n B,\n C,\n A_factor_list,\n B_factor_list,\n policies,\n use_utility=True,\n use_states_info_gain=True,\n use_param_info_gain=False,\n prior=None,\n pA=None,\n pB=None,\n F=None,\n E=None,\n I=None,\n gamma=16.0\n): \n \"\"\"\n Update posterior beliefs about policies by computing expected free energy of each policy and integrating that\n with the variational free energy of policies ``F`` and prior over policies ``E``. This is intended to be used in conjunction\n with the ``update_posterior_states_full`` method of ``inference.py``, since the full posterior over future timesteps, under all policies, is\n assumed to be provided in the input array ``qs_seq_pi``.\n\n Parameters\n ----------\n qs_seq_pi: ``numpy.ndarray`` of dtype object\n Posterior beliefs over hidden states for each policy. Nesting structure is policies, timepoints, factors,\n where e.g. ``qs_seq_pi[p][t][f]`` stores the marginal belief about factor ``f`` at timepoint ``t`` under policy ``p``.\n A: ``numpy.ndarray`` of dtype object\n Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of\n stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store \n the probability of observation level ``i`` given hidden state levels ``j, k, ...``\n B: ``numpy.ndarray`` of dtype object\n Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.\n Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability\n of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.\n C: ``numpy.ndarray`` of dtype object\n Prior over observations or 'prior preferences', storing the \"value\" of each outcome in terms of relative log probabilities. \n This is softmaxed to form a proper probability distribution before being used to compute the expected utility term of the expected free energy.\n A_factor_list: ``list`` of ``list``s of ``int``\n ``list`` that stores the indices of the hidden state factor indices that each observation modality depends on. For example, if ``A_factor_list[m] = [0, 1]``, then\n observation modality ``m`` depends on hidden state factors 0 and 1.\n B_factor_list: ``list`` of ``list``s of ``int``\n ``list`` that stores the indices of the hidden state factor indices that each hidden state factor depends on. For example, if ``B_factor_list[f] = [0, 1]``, then\n the transitions in hidden state factor ``f`` depend on hidden state factors 0 and 1.\n policies: ``list`` of 2D ``numpy.ndarray``\n ``list`` that stores each policy in ``policies[p_idx]``. Shape of ``policies[p_idx]`` is ``(num_timesteps, num_factors)`` where `num_timesteps` is the temporal\n depth of the policy and ``num_factors`` is the number of control factors.\n use_utility: ``Bool``, default ``True``\n Boolean flag that determines whether expected utility should be incorporated into computation of EFE.\n use_states_info_gain: ``Bool``, default ``True``\n Boolean flag that determines whether state epistemic value (info gain about hidden states) should be incorporated into computation of EFE.\n use_param_info_gain: ``Bool``, default ``False`` \n Boolean flag that determines whether parameter epistemic value (info gain about generative model parameters) should be incorporated into computation of EFE. \n prior: ``numpy.ndarray`` of dtype object, default ``None``\n If provided, this is a ``numpy`` object array with one sub-array per hidden state factor, that stores the prior beliefs about initial states. \n If ``None``, this defaults to a flat (uninformative) prior over hidden states.\n pA: ``numpy.ndarray`` of dtype object, default ``None``\n Dirichlet parameters over observation model (same shape as ``A``)\n pB: ``numpy.ndarray`` of dtype object, default ``None``\n Dirichlet parameters over transition model (same shape as ``B``)\n F: 1D ``numpy.ndarray``, default ``None``\n Vector of variational free energies for each policy\n E: 1D ``numpy.ndarray``, default ``None``\n Vector of prior probabilities of each policy (what's referred to in the active inference literature as \"habits\"). If ``None``, this defaults to a flat (uninformative) prior over policies.\n I: ``numpy.ndarray`` of dtype object\n For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability \n of reaching the goal state backwards from state j after i steps.\n gamma: ``float``, default 16.0\n Prior precision over policies, scales the contribution of the expected free energy to the posterior over policies\n\n Returns\n ----------\n q_pi: 1D ``numpy.ndarray``\n Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.\n G: 1D ``numpy.ndarray``\n Negative expected free energies of each policy, i.e. a vector containing one negative expected free energy per policy.\n \"\"\"\n\n num_obs, num_states, num_modalities, num_factors = utils.get_model_dimensions(A, B)\n horizon = len(qs_seq_pi[0])\n num_policies = len(qs_seq_pi)\n\n qo_seq = utils.obj_array(horizon)\n for t in range(horizon):\n qo_seq[t] = utils.obj_array_zeros(num_obs)\n\n # initialise expected observations\n qo_seq_pi = utils.obj_array(num_policies)\n\n # initialize (negative) expected free energies for all policies\n G = np.zeros(num_policies)\n\n if F is None:\n F = spm_log_single(np.ones(num_policies) / num_policies)\n\n if E is None:\n lnE = spm_log_single(np.ones(num_policies) / num_policies)\n else:\n lnE = spm_log_single(E) \n\n if I is not None:\n init_qs_all_pi = [qs_seq_pi[p][0] for p in range(num_policies)]\n qs_bma = average_states_over_policies(init_qs_all_pi, softmax(E))\n\n for p_idx, policy in enumerate(policies):\n\n qo_seq_pi[p_idx] = get_expected_obs_factorized(qs_seq_pi[p_idx], A, A_factor_list)\n\n if use_utility:\n G[p_idx] += calc_expected_utility(qo_seq_pi[p_idx], C)\n \n if use_states_info_gain:\n G[p_idx] += calc_states_info_gain_factorized(A, qs_seq_pi[p_idx], A_factor_list)\n \n if use_param_info_gain:\n if pA is not None:\n G[p_idx] += calc_pA_info_gain_factorized(pA, qo_seq_pi[p_idx], qs_seq_pi[p_idx], A_factor_list)\n if pB is not None:\n G[p_idx] += calc_pB_info_gain_interactions(pB, qs_seq_pi[p_idx], qs_seq_pi[p_idx], B_factor_list, policy)\n \n if I is not None:\n G[p_idx] += calc_inductive_cost(qs_bma, qs_seq_pi[p_idx], I)\n \n q_pi = softmax(G * gamma - F + lnE)\n \n return q_pi, G\n\n\ndef update_posterior_policies(\n qs,\n A,\n B,\n C,\n policies,\n use_utility=True,\n use_states_info_gain=True,\n use_param_info_gain=False,\n pA=None,\n pB=None,\n E=None,\n I=None,\n gamma=16.0\n):\n \"\"\"\n Update posterior beliefs about policies by computing expected free energy of each policy and integrating that\n with the prior over policies ``E``. This is intended to be used in conjunction\n with the ``update_posterior_states`` method of the ``inference`` module, since only the posterior about the hidden states at the current timestep\n ``qs`` is assumed to be provided, unconditional on policies. The predictive posterior over hidden states under all policies Q(s, pi) is computed \n using the starting posterior about states at the current timestep ``qs`` and the generative model (e.g. ``A``, ``B``, ``C``)\n\n Parameters\n ----------\n qs: ``numpy.ndarray`` of dtype object\n Marginal posterior beliefs over hidden states at current timepoint (unconditioned on policies)\n A: ``numpy.ndarray`` of dtype object\n Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of\n stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store \n the probability of observation level ``i`` given hidden state levels ``j, k, ...``\n B: ``numpy.ndarray`` of dtype object\n Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.\n Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability\n of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.\n C: ``numpy.ndarray`` of dtype object\n Prior over observations or 'prior preferences', storing the \"value\" of each outcome in terms of relative log probabilities. \n This is softmaxed to form a proper probability distribution before being used to compute the expected utility term of the expected free energy.\n policies: ``list`` of 2D ``numpy.ndarray``\n ``list`` that stores each policy in ``policies[p_idx]``. Shape of ``policies[p_idx]`` is ``(num_timesteps, num_factors)`` where `num_timesteps` is the temporal\n depth of the policy and ``num_factors`` is the number of control factors.\n use_utility: ``Bool``, default ``True``\n Boolean flag that determines whether expected utility should be incorporated into computation of EFE.\n use_states_info_gain: ``Bool``, default ``True``\n Boolean flag that determines whether state epistemic value (info gain about hidden states) should be incorporated into computation of EFE.\n use_param_info_gain: ``Bool``, default ``False`` \n Boolean flag that determines whether parameter epistemic value (info gain about generative model parameters) should be incorporated into computation of EFE.\n pA: ``numpy.ndarray`` of dtype object, optional\n Dirichlet parameters over observation model (same shape as ``A``)\n pB: ``numpy.ndarray`` of dtype object, optional\n Dirichlet parameters over transition model (same shape as ``B``)\n E: 1D ``numpy.ndarray``, optional\n Vector of prior probabilities of each policy (what's referred to in the active inference literature as \"habits\")\n I: ``numpy.ndarray`` of dtype object\n For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability \n of reaching the goal state backwards from state j after i steps.\n gamma: float, default 16.0\n Prior precision over policies, scales the contribution of the expected free energy to the posterior over policies\n\n Returns\n ----------\n q_pi: 1D ``numpy.ndarray``\n Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.\n G: 1D ``numpy.ndarray``\n Negative expected free energies of each policy, i.e. a vector containing one negative expected free energy per policy.\n \"\"\"\n\n n_policies = len(policies)\n G = np.zeros(n_policies)\n q_pi = np.zeros((n_policies, 1))\n\n if E is None:\n lnE = spm_log_single(np.ones(n_policies) / n_policies)\n else:\n lnE = spm_log_single(E) \n\n for idx, policy in enumerate(policies):\n qs_pi = get_expected_states(qs, B, policy)\n qo_pi = get_expected_obs(qs_pi, A)\n\n if use_utility:\n G[idx] += calc_expected_utility(qo_pi, C)\n\n if use_states_info_gain:\n G[idx] += calc_states_info_gain(A, qs_pi)\n\n if use_param_info_gain:\n if pA is not None:\n G[idx] += calc_pA_info_gain(pA, qo_pi, qs_pi).item()\n if pB is not None:\n G[idx] += calc_pB_info_gain(pB, qs_pi, qs, policy).item()\n \n if I is not None:\n G[idx] += calc_inductive_cost(qs, qs_pi, I)\n\n q_pi = softmax(G * gamma + lnE) \n\n return q_pi, G\n\ndef update_posterior_policies_factorized(\n qs,\n A,\n B,\n C,\n A_factor_list,\n B_factor_list,\n policies,\n use_utility=True,\n use_states_info_gain=True,\n use_param_info_gain=False,\n pA=None,\n pB=None,\n E=None,\n I=None,\n gamma=16.0\n):\n \"\"\"\n Update posterior beliefs about policies by computing expected free energy of each policy and integrating that\n with the prior over policies ``E``. This is intended to be used in conjunction\n with the ``update_posterior_states`` method of the ``inference`` module, since only the posterior about the hidden states at the current timestep\n ``qs`` is assumed to be provided, unconditional on policies. The predictive posterior over hidden states under all policies Q(s, pi) is computed \n using the starting posterior about states at the current timestep ``qs`` and the generative model (e.g. ``A``, ``B``, ``C``)\n\n Parameters\n ----------\n qs: ``numpy.ndarray`` of dtype object\n Marginal posterior beliefs over hidden states at current timepoint (unconditioned on policies)\n A: ``numpy.ndarray`` of dtype object\n Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of\n stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store \n the probability of observation level ``i`` given hidden state levels ``j, k, ...``\n B: ``numpy.ndarray`` of dtype object\n Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.\n Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability\n of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.\n C: ``numpy.ndarray`` of dtype object\n Prior over observations or 'prior preferences', storing the \"value\" of each outcome in terms of relative log probabilities. \n This is softmaxed to form a proper probability distribution before being used to compute the expected utility term of the expected free energy.\n A_factor_list: ``list`` of ``list``s of ``int``\n ``list`` that stores the indices of the hidden state factor indices that each observation modality depends on. For example, if ``A_factor_list[m] = [0, 1]``, then\n observation modality ``m`` depends on hidden state factors 0 and 1.\n B_factor_list: ``list`` of ``list``s of ``int``\n ``list`` that stores the indices of the hidden state factor indices that each hidden state factor depends on. For example, if ``B_factor_list[f] = [0, 1]``, then\n the transitions in hidden state factor ``f`` depend on hidden state factors 0 and 1.\n policies: ``list`` of 2D ``numpy.ndarray``\n ``list`` that stores each policy in ``policies[p_idx]``. Shape of ``policies[p_idx]`` is ``(num_timesteps, num_factors)`` where `num_timesteps` is the temporal\n depth of the policy and ``num_factors`` is the number of control factors.\n use_utility: ``Bool``, default ``True``\n Boolean flag that determines whether expected utility should be incorporated into computation of EFE.\n use_states_info_gain: ``Bool``, default ``True``\n Boolean flag that determines whether state epistemic value (info gain about hidden states) should be incorporated into computation of EFE.\n use_param_info_gain: ``Bool``, default ``False`` \n Boolean flag that determines whether parameter epistemic value (info gain about generative model parameters) should be incorporated into computation of EFE.\n pA: ``numpy.ndarray`` of dtype object, optional\n Dirichlet parameters over observation model (same shape as ``A``)\n pB: ``numpy.ndarray`` of dtype object, optional\n Dirichlet parameters over transition model (same shape as ``B``)\n E: 1D ``numpy.ndarray``, optional\n Vector of prior probabilities of each policy (what's referred to in the active inference literature as \"habits\")\n I: ``numpy.ndarray`` of dtype object\n For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability \n of reaching the goal state backwards from state j after i steps.\n gamma: float, default 16.0\n Prior precision over policies, scales the contribution of the expected free energy to the posterior over policies\n\n Returns\n ----------\n q_pi: 1D ``numpy.ndarray``\n Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.\n G: 1D ``numpy.ndarray``\n Negative expected free energies of each policy, i.e. a vector containing one negative expected free energy per policy.\n \"\"\"\n\n n_policies = len(policies)\n G = np.zeros(n_policies)\n q_pi = np.zeros((n_policies, 1))\n\n if E is None:\n lnE = spm_log_single(np.ones(n_policies) / n_policies)\n else:\n lnE = spm_log_single(E) \n\n for idx, policy in enumerate(policies):\n qs_pi = get_expected_states_interactions(qs, B, B_factor_list, policy)\n qo_pi = get_expected_obs_factorized(qs_pi, A, A_factor_list)\n\n if use_utility:\n G[idx] += calc_expected_utility(qo_pi, C)\n\n if use_states_info_gain:\n G[idx] += calc_states_info_gain_factorized(A, qs_pi, A_factor_list)\n\n if use_param_info_gain:\n if pA is not None:\n G[idx] += calc_pA_info_gain_factorized(pA, qo_pi, qs_pi, A_factor_list).item()\n if pB is not None:\n G[idx] += calc_pB_info_gain_interactions(pB, qs_pi, qs, B_factor_list, policy).item()\n \n if I is not None:\n G[idx] += calc_inductive_cost(qs, qs_pi, I)\n\n q_pi = softmax(G * gamma + lnE) \n\n return q_pi, G\n\ndef get_expected_states(qs, B, policy):\n \"\"\"\n Compute the expected states under a policy, also known as the posterior predictive density over states\n\n Parameters\n ----------\n qs: ``numpy.ndarray`` of dtype object\n Marginal posterior beliefs over hidden states at a given timepoint.\n B: ``numpy.ndarray`` of dtype object\n Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.\n Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability\n of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.\n policy: 2D ``numpy.ndarray``\n Array that stores actions entailed by a policy over time. Shape is ``(num_timesteps, num_factors)`` where ``num_timesteps`` is the temporal\n depth of the policy and ``num_factors`` is the number of control factors.\n\n Returns\n -------\n qs_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about\n hidden states expected under the policy at time ``t``\n \"\"\"\n n_steps = policy.shape[0]\n n_factors = policy.shape[1]\n\n # initialise posterior predictive density as a list of beliefs over time, including current posterior beliefs about hidden states as the first element\n qs_pi = [qs] + [utils.obj_array(n_factors) for t in range(n_steps)]\n \n # get expected states over time\n for t in range(n_steps):\n for control_factor, action in enumerate(policy[t,:]):\n qs_pi[t+1][control_factor] = B[control_factor][:,:,int(action)].dot(qs_pi[t][control_factor])\n\n return qs_pi[1:]\n \ndef get_expected_states_interactions(qs, B, B_factor_list, policy):\n \"\"\"\n Compute the expected states under a policy, also known as the posterior predictive density over states\n\n Parameters\n ----------\n qs: ``numpy.ndarray`` of dtype object\n Marginal posterior beliefs over hidden states at a given timepoint.\n B: ``numpy.ndarray`` of dtype object\n Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.\n Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability\n of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.\n B_factor_list: ``list`` of ``list`` of ``int``\n List of lists of hidden state factors each hidden state factor depends on. Each element ``B_factor_list[i]`` is a list of the factor indices that factor i's dynamics depend on.\n policy: 2D ``numpy.ndarray``\n Array that stores actions entailed by a policy over time. Shape is ``(num_timesteps, num_factors)`` where ``num_timesteps`` is the temporal\n depth of the policy and ``num_factors`` is the number of control factors.\n\n Returns\n -------\n qs_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about\n hidden states expected under the policy at time ``t``\n \"\"\"\n n_steps = policy.shape[0]\n n_factors = policy.shape[1]\n\n # initialise posterior predictive density as a list of beliefs over time, including current posterior beliefs about hidden states as the first element\n qs_pi = [qs] + [utils.obj_array(n_factors) for t in range(n_steps)]\n \n # get expected states over time\n for t in range(n_steps):\n for control_factor, action in enumerate(policy[t,:]):\n factor_idx = B_factor_list[control_factor] # list of the hidden state factor indices that the dynamics of `qs[control_factor]` depend on\n qs_pi[t+1][control_factor] = spm_dot(B[control_factor][...,int(action)], qs_pi[t][factor_idx])\n\n return qs_pi[1:]\n \ndef get_expected_obs(qs_pi, A):\n \"\"\"\n Compute the expected observations under a policy, also known as the posterior predictive density over observations\n\n Parameters\n ----------\n qs_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about\n hidden states expected under the policy at time ``t``\n A: ``numpy.ndarray`` of dtype object\n Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of\n stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store \n the probability of observation level ``i`` given hidden state levels ``j, k, ...``\n\n Returns\n -------\n qo_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over observations expected under the policy, where ``qo_pi[t]`` stores the beliefs about\n observations expected under the policy at time ``t``\n \"\"\"\n\n n_steps = len(qs_pi) # each element of the list is the PPD at a different timestep\n\n # initialise expected observations\n qo_pi = []\n\n for t in range(n_steps):\n qo_pi_t = utils.obj_array(len(A))\n qo_pi.append(qo_pi_t)\n\n # compute expected observations over time\n for t in range(n_steps):\n for modality, A_m in enumerate(A):\n qo_pi[t][modality] = spm_dot(A_m, qs_pi[t])\n\n return qo_pi\n\ndef get_expected_obs_factorized(qs_pi, A, A_factor_list):\n \"\"\"\n Compute the expected observations under a policy, also known as the posterior predictive density over observations\n\n Parameters\n ----------\n qs_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about\n hidden states expected under the policy at time ``t``\n A: ``numpy.ndarray`` of dtype object\n Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of\n stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store \n the probability of observation level ``i`` given hidden state levels ``j, k, ...``\n A_factor_list: ``list`` of ``list`` of ``int``\n List of lists of hidden state factor indices that each observation modality depends on. Each element ``A_factor_list[i]`` is a list of the factor indices that modality i's observation model depends on.\n Returns\n -------\n qo_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over observations expected under the policy, where ``qo_pi[t]`` stores the beliefs about\n observations expected under the policy at time ``t``\n \"\"\"\n\n n_steps = len(qs_pi) # each element of the list is the PPD at a different timestep\n\n # initialise expected observations\n qo_pi = []\n\n for t in range(n_steps):\n qo_pi_t = utils.obj_array(len(A))\n qo_pi.append(qo_pi_t)\n\n # compute expected observations over time\n for t in range(n_steps):\n for modality, A_m in enumerate(A):\n factor_idx = A_factor_list[modality] # list of the hidden state factor indices that observation modality with the index `modality` depends on\n qo_pi[t][modality] = spm_dot(A_m, qs_pi[t][factor_idx])\n\n return qo_pi\n\ndef calc_expected_utility(qo_pi, C):\n \"\"\"\n Computes the expected utility of a policy, using the observation distribution expected under that policy and a prior preference vector.\n\n Parameters\n ----------\n qo_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over observations expected under the policy, where ``qo_pi[t]`` stores the beliefs about\n observations expected under the policy at time ``t``\n C: ``numpy.ndarray`` of dtype object\n Prior over observations or 'prior preferences', storing the \"value\" of each outcome in terms of relative log probabilities. \n This is softmaxed to form a proper probability distribution before being used to compute the expected utility.\n\n Returns\n -------\n expected_util: float\n Utility (reward) expected under the policy in question\n \"\"\"\n n_steps = len(qo_pi)\n \n # initialise expected utility\n expected_util = 0\n\n # loop over time points and modalities\n num_modalities = len(C)\n\n # reformat C to be tiled across timesteps, if it's not already\n modalities_to_tile = [modality_i for modality_i in range(num_modalities) if C[modality_i].ndim == 1]\n\n # make a deepcopy of C where it has been tiled across timesteps\n C_tiled = copy.deepcopy(C)\n for modality in modalities_to_tile:\n C_tiled[modality] = np.tile(C[modality][:,None], (1, n_steps) )\n \n C_prob = softmax_obj_arr(C_tiled) # convert relative log probabilities into proper probability distribution\n\n for t in range(n_steps):\n for modality in range(num_modalities):\n\n lnC = spm_log_single(C_prob[modality][:, t])\n expected_util += qo_pi[t][modality].dot(lnC)\n\n return expected_util\n\n\ndef calc_states_info_gain(A, qs_pi):\n \"\"\"\n Computes the Bayesian surprise or information gain about states of a policy, \n using the observation model and the hidden state distribution expected under that policy.\n\n Parameters\n ----------\n A: ``numpy.ndarray`` of dtype object\n Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of\n stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store \n the probability of observation level ``i`` given hidden state levels ``j, k, ...``\n qs_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about\n hidden states expected under the policy at time ``t``\n\n Returns\n -------\n states_surprise: float\n Bayesian surprise (about states) or salience expected under the policy in question\n \"\"\"\n\n n_steps = len(qs_pi)\n\n states_surprise = 0\n for t in range(n_steps):\n states_surprise += spm_MDP_G(A, qs_pi[t])\n\n return states_surprise\n\ndef calc_states_info_gain_factorized(A, qs_pi, A_factor_list):\n \"\"\"\n Computes the Bayesian surprise or information gain about states of a policy, \n using the observation model and the hidden state distribution expected under that policy.\n\n Parameters\n ----------\n A: ``numpy.ndarray`` of dtype object\n Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of\n stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store \n the probability of observation level ``i`` given hidden state levels ``j, k, ...``\n qs_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about\n hidden states expected under the policy at time ``t``\n A_factor_list: ``list`` of ``list`` of ``int``\n List of lists, where ``A_factor_list[m]`` is a list of the hidden state factor indices that observation modality with the index ``m`` depends on\n\n Returns\n -------\n states_surprise: float\n Bayesian surprise (about states) or salience expected under the policy in question\n \"\"\"\n\n n_steps = len(qs_pi)\n\n states_surprise = 0\n for t in range(n_steps):\n for m, A_m in enumerate(A):\n factor_idx = A_factor_list[m] # list of the hidden state factor indices that observation modality with the index `m` depends on\n states_surprise += spm_MDP_G(A_m, qs_pi[t][factor_idx])\n\n return states_surprise\n\n\ndef calc_pA_info_gain(pA, qo_pi, qs_pi):\n \"\"\"\n Compute expected Dirichlet information gain about parameters ``pA`` under a policy\n\n Parameters\n ----------\n pA: ``numpy.ndarray`` of dtype object\n Dirichlet parameters over observation model (same shape as ``A``)\n qo_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over observations expected under the policy, where ``qo_pi[t]`` stores the beliefs about\n observations expected under the policy at time ``t``\n qs_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about\n hidden states expected under the policy at time ``t``\n\n Returns\n -------\n infogain_pA: float\n Surprise (about Dirichlet parameters) expected under the policy in question\n \"\"\"\n\n n_steps = len(qo_pi)\n \n num_modalities = len(pA)\n wA = utils.obj_array(num_modalities)\n for modality, pA_m in enumerate(pA):\n wA[modality] = spm_wnorm(pA[modality])\n\n pA_infogain = 0\n \n for modality in range(num_modalities):\n wA_modality = wA[modality] * (pA[modality] > 0).astype(\"float\")\n for t in range(n_steps):\n pA_infogain -= qo_pi[t][modality].dot(spm_dot(wA_modality, qs_pi[t])[:, np.newaxis])\n\n return pA_infogain\n\ndef calc_pA_info_gain_factorized(pA, qo_pi, qs_pi, A_factor_list):\n \"\"\"\n Compute expected Dirichlet information gain about parameters ``pA`` under a policy.\n In this version of the function, we assume that the observation model is factorized, i.e. that each observation modality depends on a subset of the hidden state factors.\n\n Parameters\n ----------\n pA: ``numpy.ndarray`` of dtype object\n Dirichlet parameters over observation model (same shape as ``A``)\n qo_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over observations expected under the policy, where ``qo_pi[t]`` stores the beliefs about\n observations expected under the policy at time ``t``\n qs_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about\n hidden states expected under the policy at time ``t``\n A_factor_list: ``list`` of ``list`` of ``int``\n List of lists, where ``A_factor_list[m]`` is a list of the hidden state factor indices that observation modality with the index ``m`` depends on\n\n Returns\n -------\n infogain_pA: float\n Surprise (about Dirichlet parameters) expected under the policy in question\n \"\"\"\n\n n_steps = len(qo_pi)\n \n num_modalities = len(pA)\n wA = utils.obj_array(num_modalities)\n for modality, pA_m in enumerate(pA):\n wA[modality] = spm_wnorm(pA[modality])\n\n pA_infogain = 0\n \n for modality in range(num_modalities):\n wA_modality = wA[modality] * (pA[modality] > 0).astype(\"float\")\n factor_idx = A_factor_list[modality]\n for t in range(n_steps):\n pA_infogain -= qo_pi[t][modality].dot(spm_dot(wA_modality, qs_pi[t][factor_idx])[:, np.newaxis])\n\n return pA_infogain\n\ndef calc_pB_info_gain(pB, qs_pi, qs_prev, policy):\n \"\"\"\n Compute expected Dirichlet information gain about parameters ``pB`` under a given policy\n\n Parameters\n ----------\n pB: ``numpy.ndarray`` of dtype object\n Dirichlet parameters over transition model (same shape as ``B``)\n qs_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about\n hidden states expected under the policy at time ``t``\n qs_prev: ``numpy.ndarray`` of dtype object\n Posterior over hidden states at beginning of trajectory (before receiving observations)\n policy: 2D ``numpy.ndarray``\n Array that stores actions entailed by a policy over time. Shape is ``(num_timesteps, num_factors)`` where ``num_timesteps`` is the temporal\n depth of the policy and ``num_factors`` is the number of control factors.\n \n Returns\n -------\n infogain_pB: float\n Surprise (about dirichlet parameters) expected under the policy in question\n \"\"\"\n\n n_steps = len(qs_pi)\n\n num_factors = len(pB)\n wB = utils.obj_array(num_factors)\n for factor, pB_f in enumerate(pB):\n wB[factor] = spm_wnorm(pB_f)\n\n pB_infogain = 0\n\n for t in range(n_steps):\n # the 'past posterior' used for the information gain about pB here is the posterior\n # over expected states at the timestep previous to the one under consideration\n # if we're on the first timestep, we just use the latest posterior in the\n # entire action-perception cycle as the previous posterior\n if t == 0:\n previous_qs = qs_prev\n # otherwise, we use the expected states for the timestep previous to the timestep under consideration\n else:\n previous_qs = qs_pi[t - 1]\n\n # get the list of action-indices for the current timestep\n policy_t = policy[t, :]\n for factor, a_i in enumerate(policy_t):\n wB_factor_t = wB[factor][:, :, int(a_i)] * (pB[factor][:, :, int(a_i)] > 0).astype(\"float\")\n pB_infogain -= qs_pi[t][factor].dot(wB_factor_t.dot(previous_qs[factor]))\n\n return pB_infogain\n\ndef calc_pB_info_gain_interactions(pB, qs_pi, qs_prev, B_factor_list, policy):\n \"\"\"\n Compute expected Dirichlet information gain about parameters ``pB`` under a given policy\n\n Parameters\n ----------\n pB: ``numpy.ndarray`` of dtype object\n Dirichlet parameters over transition model (same shape as ``B``)\n qs_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about\n hidden states expected under the policy at time ``t``\n qs_prev: ``numpy.ndarray`` of dtype object\n Posterior over hidden states at beginning of trajectory (before receiving observations)\n B_factor_list: ``list`` of ``list`` of ``int``\n List of lists, where ``B_factor_list[f]`` is a list of the hidden state factor indices that hidden state factor with the index ``f`` depends on\n policy: 2D ``numpy.ndarray``\n Array that stores actions entailed by a policy over time. Shape is ``(num_timesteps, num_factors)`` where ``num_timesteps`` is the temporal\n depth of the policy and ``num_factors`` is the number of control factors.\n \n Returns\n -------\n infogain_pB: float\n Surprise (about dirichlet parameters) expected under the policy in question\n \"\"\"\n\n n_steps = len(qs_pi)\n\n num_factors = len(pB)\n wB = utils.obj_array(num_factors)\n for factor, pB_f in enumerate(pB):\n wB[factor] = spm_wnorm(pB_f)\n\n pB_infogain = 0\n\n for t in range(n_steps):\n # the 'past posterior' used for the information gain about pB here is the posterior\n # over expected states at the timestep previous to the one under consideration\n # if we're on the first timestep, we just use the latest posterior in the\n # entire action-perception cycle as the previous posterior\n if t == 0:\n previous_qs = qs_prev\n # otherwise, we use the expected states for the timestep previous to the timestep under consideration\n else:\n previous_qs = qs_pi[t - 1]\n\n # get the list of action-indices for the current timestep\n policy_t = policy[t, :]\n for factor, a_i in enumerate(policy_t):\n wB_factor_t = wB[factor][...,int(a_i)] * (pB[factor][...,int(a_i)] > 0).astype(\"float\")\n f_idx = B_factor_list[factor]\n pB_infogain -= qs_pi[t][factor].dot(spm_dot(wB_factor_t, previous_qs[f_idx]))\n\n return pB_infogain\n\ndef calc_inductive_cost(qs, qs_pi, I, epsilon=1e-3):\n \"\"\"\n Computes the inductive cost of a state.\n\n Parameters\n ----------\n qs: ``numpy.ndarray`` of dtype object\n Marginal posterior beliefs over hidden states at a given timepoint.\n qs_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about\n states expected under the policy at time ``t``\n I: ``numpy.ndarray`` of dtype object\n For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability \n of reaching the goal state backwards from state j after i steps.\n\n Returns\n -------\n inductive_cost: float\n Cost of visited this state using backwards induction under the policy in question\n \"\"\"\n n_steps = len(qs_pi)\n \n # initialise inductive cost\n inductive_cost = 0\n\n # loop over time points and modalities\n num_factors = len(I)\n\n for t in range(n_steps):\n for factor in range(num_factors):\n # we also assume precise beliefs here?!\n idx = np.argmax(qs[factor])\n # m = arg max_n p_n < sup p\n # i.e. find first I idx equals 1 and m is the index before\n m = np.where(I[factor][:, idx] == 1)[0]\n # we might find no path to goal (i.e. when no goal specified)\n if len(m) > 0:\n m = max(m[0]-1, 0)\n I_m = (1-I[factor][m, :]) * np.log(epsilon)\n inductive_cost += I_m.dot(qs_pi[t][factor])\n \n return inductive_cost\n\ndef construct_policies(num_states, num_controls = None, policy_len=1, control_fac_idx=None):\n \"\"\"\n Generate a ``list`` of policies. The returned array ``policies`` is a ``list`` that stores one policy per entry.\n A particular policy (``policies[i]``) has shape ``(num_timesteps, num_factors)`` \n where ``num_timesteps`` is the temporal depth of the policy and ``num_factors`` is the number of control factors.\n\n Parameters\n ----------\n num_states: ``list`` of ``int``\n ``list`` of the dimensionalities of each hidden state factor\n num_controls: ``list`` of ``int``, default ``None``\n ``list`` of the dimensionalities of each control state factor. If ``None``, then is automatically computed as the dimensionality of each hidden state factor that is controllable\n policy_len: ``int``, default 1\n temporal depth (\"planning horizon\") of policies\n control_fac_idx: ``list`` of ``int``\n ``list`` of indices of the hidden state factors that are controllable (i.e. those state factors ``i`` where ``num_controls[i] > 1``)\n\n Returns\n ----------\n policies: ``list`` of 2D ``numpy.ndarray``\n ``list`` that stores each policy as a 2D array in ``policies[p_idx]``. Shape of ``policies[p_idx]`` \n is ``(num_timesteps, num_factors)`` where ``num_timesteps`` is the temporal\n depth of the policy and ``num_factors`` is the number of control factors.\n \"\"\"\n\n num_factors = len(num_states)\n if control_fac_idx is None:\n if num_controls is not None:\n control_fac_idx = [f for f, n_c in enumerate(num_controls) if n_c > 1]\n else:\n control_fac_idx = list(range(num_factors))\n\n if num_controls is None:\n num_controls = [num_states[c_idx] if c_idx in control_fac_idx else 1 for c_idx in range(num_factors)]\n \n x = num_controls * policy_len\n policies = list(itertools.product(*[list(range(i)) for i in x]))\n for pol_i in range(len(policies)):\n policies[pol_i] = np.array(policies[pol_i]).reshape(policy_len, num_factors)\n\n return policies\n \ndef get_num_controls_from_policies(policies):\n \"\"\"\n Calculates the ``list`` of dimensionalities of control factors (``num_controls``)\n from the ``list`` or array of policies. This assumes a policy space such that for each control factor, there is at least\n one policy that entails taking the action with the maximum index along that control factor.\n\n Parameters\n ----------\n policies: ``list`` of 2D ``numpy.ndarray``\n ``list`` that stores each policy as a 2D array in ``policies[p_idx]``. Shape of ``policies[p_idx]`` \n is ``(num_timesteps, num_factors)`` where ``num_timesteps`` is the temporal\n depth of the policy and ``num_factors`` is the number of control factors.\n \n Returns\n ----------\n num_controls: ``list`` of ``int``\n ``list`` of the dimensionalities of each control state factor, computed here automatically from a ``list`` of policies.\n \"\"\"\n\n return list(np.max(np.vstack(policies), axis = 0) + 1)\n \n\ndef sample_action(q_pi, policies, num_controls, action_selection=\"deterministic\", alpha = 16.0):\n \"\"\"\n Computes the marginal posterior over actions and then samples an action from it, one action per control factor.\n\n Parameters\n ----------\n q_pi: 1D ``numpy.ndarray``\n Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.\n policies: ``list`` of 2D ``numpy.ndarray``\n ``list`` that stores each policy as a 2D array in ``policies[p_idx]``. Shape of ``policies[p_idx]`` \n is ``(num_timesteps, num_factors)`` where ``num_timesteps`` is the temporal\n depth of the policy and ``num_factors`` is the number of control factors.\n num_controls: ``list`` of ``int``\n ``list`` of the dimensionalities of each control state factor.\n action_selection: ``str``, default \"deterministic\"\n String indicating whether whether the selected action is chosen as the maximum of the posterior over actions,\n or whether it's sampled from the posterior marginal over actions\n alpha: ``float``, default 16.0\n Action selection precision -- the inverse temperature of the softmax that is used to scale the \n action marginals before sampling. This is only used if ``action_selection`` argument is \"stochastic\"\n \n Returns\n ----------\n selected_policy: 1D ``numpy.ndarray``\n Vector containing the indices of the actions for each control factor\n \"\"\"\n\n num_factors = len(num_controls)\n\n action_marginals = utils.obj_array_zeros(num_controls)\n\n # weight each action according to its integrated posterior probability under all policies at the current timestep\n for pol_idx, policy in enumerate(policies):\n for factor_i, action_i in enumerate(policy[0, :]):\n action_marginals[factor_i][action_i] += q_pi[pol_idx]\n \n action_marginals = utils.norm_dist_obj_arr(action_marginals)\n\n selected_policy = np.zeros(num_factors)\n for factor_i in range(num_factors):\n\n # Either you do this:\n if action_selection == 'deterministic':\n selected_policy[factor_i] = select_highest(action_marginals[factor_i])\n elif action_selection == 'stochastic':\n log_marginal_f = spm_log_single(action_marginals[factor_i])\n p_actions = softmax(log_marginal_f * alpha)\n selected_policy[factor_i] = utils.sample(p_actions)\n\n return selected_policy\n\ndef _sample_action_test(q_pi, policies, num_controls, action_selection=\"deterministic\", alpha = 16.0, seed=None):\n \"\"\"\n Computes the marginal posterior over actions and then samples an action from it, one action per control factor.\n Internal testing version that returns the marginal posterior over actions, and also has a seed argument for reproducibility.\n\n Parameters\n ----------\n q_pi: 1D ``numpy.ndarray``\n Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.\n policies: ``list`` of 2D ``numpy.ndarray``\n ``list`` that stores each policy as a 2D array in ``policies[p_idx]``. Shape of ``policies[p_idx]`` \n is ``(num_timesteps, num_factors)`` where ``num_timesteps`` is the temporal\n depth of the policy and ``num_factors`` is the number of control factors.\n num_controls: ``list`` of ``int``\n ``list`` of the dimensionalities of each control state factor.\n action_selection: ``str``, default \"deterministic\"\n String indicating whether whether the selected action is chosen as the maximum of the posterior over actions,\n or whether it's sampled from the posterior marginal over actions\n alpha: float, default 16.0\n Action selection precision -- the inverse temperature of the softmax that is used to scale the \n action marginals before sampling. This is only used if ``action_selection`` argument is \"stochastic\"\n seed: ``int``, default None\n The seed can be set to control the random sampling that occurs when ``action_selection`` is \"deterministic\" but there are more than one actions with the same maximum posterior probability.\n\n\n Returns\n ----------\n selected_policy: 1D ``numpy.ndarray``\n Vector containing the indices of the actions for each control factor\n p_actions: ``numpy.ndarray`` of dtype object\n Marginal posteriors over actions, after softmaxing and scaling with action precision. This distribution will be used to sample actions,\n if``action_selection`` argument is \"stochastic\"\n \"\"\"\n\n num_factors = len(num_controls)\n\n action_marginals = utils.obj_array_zeros(num_controls)\n \n # weight each action according to its integrated posterior probability under all policies at the current timestep\n for pol_idx, policy in enumerate(policies):\n for factor_i, action_i in enumerate(policy[0, :]):\n action_marginals[factor_i][action_i] += q_pi[pol_idx]\n \n action_marginals = utils.norm_dist_obj_arr(action_marginals)\n\n selected_policy = np.zeros(num_factors)\n p_actions = utils.obj_array_zeros(num_controls)\n for factor_i in range(num_factors):\n if action_selection == 'deterministic':\n p_actions[factor_i] = action_marginals[factor_i]\n selected_policy[factor_i] = _select_highest_test(p_actions[factor_i], seed=seed)\n elif action_selection == 'stochastic':\n log_marginal_f = spm_log_single(action_marginals[factor_i])\n p_actions[factor_i] = softmax(log_marginal_f * alpha)\n selected_policy[factor_i] = utils.sample(p_actions[factor_i])\n\n return selected_policy, p_actions\n\ndef sample_policy(q_pi, policies, num_controls, action_selection=\"deterministic\", alpha = 16.0):\n \"\"\"\n Samples a policy from the posterior over policies, taking the action (per control factor) entailed by the first timestep of the selected policy.\n\n Parameters\n ----------\n q_pi: 1D ``numpy.ndarray``\n Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.\n policies: ``list`` of 2D ``numpy.ndarray``\n ``list`` that stores each policy as a 2D array in ``policies[p_idx]``. Shape of ``policies[p_idx]`` \n is ``(num_timesteps, num_factors)`` where ``num_timesteps`` is the temporal\n depth of the policy and ``num_factors`` is the number of control factors.\n num_controls: ``list`` of ``int``\n ``list`` of the dimensionalities of each control state factor.\n action_selection: string, default \"deterministic\"\n String indicating whether whether the selected policy is chosen as the maximum of the posterior over policies,\n or whether it's sampled from the posterior over policies.\n alpha: float, default 16.0\n Action selection precision -- the inverse temperature of the softmax that is used to scale the \n policy posterior before sampling. This is only used if ``action_selection`` argument is \"stochastic\"\n\n Returns\n ----------\n selected_policy: 1D ``numpy.ndarray``\n Vector containing the indices of the actions for each control factor\n \"\"\"\n\n num_factors = len(num_controls)\n\n if action_selection == \"deterministic\":\n policy_idx = select_highest(q_pi)\n elif action_selection == \"stochastic\":\n log_qpi = spm_log_single(q_pi)\n p_policies = softmax(log_qpi * alpha)\n policy_idx = utils.sample(p_policies)\n\n selected_policy = np.zeros(num_factors)\n for factor_i in range(num_factors):\n selected_policy[factor_i] = policies[policy_idx][0, factor_i]\n\n return selected_policy\n\ndef _sample_policy_test(q_pi, policies, num_controls, action_selection=\"deterministic\", alpha = 16.0, seed=None):\n \"\"\"\n Test version of sampling a policy from the posterior over policies, taking the action (per control factor) entailed by the first timestep of the selected policy.\n This test version also returns the probability distribution over policies, and also has a seed argument for reproducibility.\n Parameters\n ----------\n q_pi: 1D ``numpy.ndarray``\n Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.\n policies: ``list`` of 2D ``numpy.ndarray``\n ``list`` that stores each policy as a 2D array in ``policies[p_idx]``. Shape of ``policies[p_idx]`` \n is ``(num_timesteps, num_factors)`` where ``num_timesteps`` is the temporal\n depth of the policy and ``num_factors`` is the number of control factors.\n num_controls: ``list`` of ``int``\n ``list`` of the dimensionalities of each control state factor.\n action_selection: string, default \"deterministic\"\n String indicating whether whether the selected policy is chosen as the maximum of the posterior over policies,\n or whether it's sampled from the posterior over policies.\n alpha: float, default 16.0\n Action selection precision -- the inverse temperature of the softmax that is used to scale the \n policy posterior before sampling. This is only used if ``action_selection`` argument is \"stochastic\"\n seed: ``int``, default None\n The seed can be set to control the random sampling that occurs when ``action_selection`` is \"deterministic\" but there are more than one actions with the same maximum posterior probability.\n\n \n Returns\n ----------\n selected_policy: 1D ``numpy.ndarray``\n Vector containing the indices of the actions for each control factor\n \"\"\"\n\n num_factors = len(num_controls)\n\n if action_selection == \"deterministic\":\n p_policies = q_pi\n policy_idx = _select_highest_test(p_policies, seed=seed)\n elif action_selection == \"stochastic\":\n log_qpi = spm_log_single(q_pi)\n p_policies = softmax(log_qpi * alpha)\n policy_idx = utils.sample(p_policies)\n\n selected_policy = np.zeros(num_factors)\n for factor_i in range(num_factors):\n selected_policy[factor_i] = policies[policy_idx][0, factor_i]\n\n return selected_policy, p_policies\n\n\ndef select_highest(options_array):\n \"\"\"\n Selects the highest value among the provided ones. If the higher value is more than once and they're closer than 1e-5, a random choice is made.\n Parameters\n ----------\n options_array: ``numpy.ndarray``\n The array to examine\n\n Returns\n -------\n The highest value in the given list\n \"\"\"\n options_with_idx = np.array(list(enumerate(options_array)))\n same_prob = options_with_idx[\n abs(options_with_idx[:, 1] - np.amax(options_with_idx[:, 1])) <= 1e-8][:, 0]\n if len(same_prob) > 1:\n # If some of the most likely actions have nearly equal probability, sample from this subset of actions, instead of using argmax\n return int(same_prob[np.random.choice(len(same_prob))])\n\n return int(same_prob[0])\n\ndef _select_highest_test(options_array, seed=None):\n \"\"\"\n (Test version with seed argument for reproducibility) Selects the highest value among the provided ones. If the higher value is more than once and they're closer than 1e-8, a random choice is made.\n Parameters\n ----------\n options_array: ``numpy.ndarray``\n The array to examine\n\n Returns\n -------\n The highest value in the given list\n \"\"\"\n options_with_idx = np.array(list(enumerate(options_array)))\n same_prob = options_with_idx[\n abs(options_with_idx[:, 1] - np.amax(options_with_idx[:, 1])) <= 1e-8][:, 0]\n if len(same_prob) > 1:\n # If some of the most likely actions have nearly equal probability, sample from this subset of actions, instead of using argmax\n rng = np.random.default_rng(seed)\n return int(same_prob[rng.choice(len(same_prob))])\n\n return int(same_prob[0])\n\n\ndef backwards_induction(H, B, B_factor_list, threshold, depth):\n \"\"\"\n Runs backwards induction of reaching a goal state H given a transition model B.\n \n Parameters\n ---------- \n H: ``numpy.ndarray`` of dtype object\n Prior over states\n B: ``numpy.ndarray`` of dtype object\n Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.\n Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability\n of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.\n B_factor_list: ``list`` of ``list`` of ``int``\n List of lists of hidden state factors each hidden state factor depends on. Each element ``B_factor_list[i]`` is a list of the factor indices that factor i's dynamics depend on.\n threshold: ``float``\n The threshold for pruning transitions that are below a certain probability\n depth: ``int``\n The temporal depth of the backward induction\n\n Returns\n ----------\n I: ``numpy.ndarray`` of dtype object\n For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability \n of reaching the goal state backwards from state j after i steps.\n \"\"\"\n # TODO can this be done with arbitrary B_factor_list?\n \n num_factors = len(H)\n I = utils.obj_array(num_factors)\n for factor in range(num_factors):\n I[factor] = np.zeros((depth, H[factor].shape[0]))\n I[factor][0, :] = H[factor]\n\n bf = factor\n if B_factor_list is not None:\n if len(B_factor_list[factor]) > 1:\n raise ValueError(\"Backwards induction with factorized transition model not yet implemented\")\n bf = B_factor_list[factor][0]\n\n num_states, _, _ = B[bf].shape\n b = np.zeros((num_states, num_states))\n \n for state in range(num_states):\n for next_state in range(num_states):\n # If there exists an action that allows transitioning \n # from state to next_state, with probability larger than threshold\n # set b[state, next_state] to 1\n if np.any(B[bf][next_state, state, :] > threshold):\n b[next_state, state] = 1\n\n for i in range(1, depth):\n I[factor][i, :] = np.dot(b, I[factor][i-1, :])\n I[factor][i, :] = np.where(I[factor][i, :] > 0.1, 1.0, 0.0)\n # TODO stop when all 1s?\n\n return I\n\ndef calc_ambiguity_factorized(qs_pi, A, A_factor_list):\n \"\"\"\n Computes the Ambiguity term.\n\n Parameters\n ----------\n qs_pi: ``list`` of ``numpy.ndarray`` of dtype object\n Predictive posterior beliefs over hidden states expected under the policy, where ``qs_pi[t]`` stores the beliefs about\n hidden states expected under the policy at time ``t``\n A: ``numpy.ndarray`` of dtype object\n Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of\n stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store \n the probability of observation level ``i`` given hidden state levels ``j, k, ...``\n A_factor_list: ``list`` of ``list`` of ``int``\n List of lists, where ``A_factor_list[m]`` is a list of the hidden state factor indices that observation modality with the index ``m`` depends on\n\n Returns\n -------\n ambiguity: float\n \"\"\"\n\n n_steps = len(qs_pi)\n\n ambiguity = 0\n # TODO check if we do this correctly!\n H = entropy(A)\n for t in range(n_steps):\n for m, H_m in enumerate(H):\n factor_idx = A_factor_list[m]\n # TODO why does spm_dot return an array here?\n # joint_x = maths.spm_cross(qs_pi[t][factor_idx])\n # ambiguity += (H_m * joint_x).sum()\n ambiguity += np.sum(spm_dot(H_m, qs_pi[t][factor_idx]))\n\n return ambiguity\n\n\ndef sophisticated_inference_search(qs, policies, A, B, C, A_factor_list, B_factor_list, I=None, horizon=1,\n policy_prune_threshold=1/16, state_prune_threshold=1/16, prune_penalty=512, gamma=16,\n inference_params = {\"num_iter\": 10, \"dF\": 1.0, \"dF_tol\": 0.001, \"compute_vfe\": False}, n=0):\n \"\"\"\n Performs sophisticated inference to find the optimal policy for a given generative model and prior preferences.\n\n Parameters\n ----------\n qs: ``numpy.ndarray`` of dtype object\n Marginal posterior beliefs over hidden states at a given timepoint.\n policies: ``list`` of 1D ``numpy.ndarray`` inference_params = {\"num_iter\": 10, \"dF\": 1.0, \"dF_tol\": 0.001, \"compute_vfe\": False}\n\n ``list`` that stores each policy as a 1D array in ``policies[p_idx]``. Shape of ``policies[p_idx]`` \n is ``(num_factors)`` where ``num_factors`` is the number of control factors. \n A: ``numpy.ndarray`` of dtype object\n Sensory likelihood mapping or 'observation model', mapping from hidden states to observations. Each element ``A[m]`` of\n stores an ``numpy.ndarray`` multidimensional array for observation modality ``m``, whose entries ``A[m][i, j, k, ...]`` store \n the probability of observation level ``i`` given hidden state levels ``j, k, ...``\n B: ``numpy.ndarray`` of dtype object\n Dynamics likelihood mapping or 'transition model', mapping from hidden states at ``t`` to hidden states at ``t+1``, given some control state ``u``.\n Each element ``B[f]`` of this object array stores a 3-D tensor for hidden state factor ``f``, whose entries ``B[f][s, v, u]`` store the probability\n of hidden state level ``s`` at the current time, given hidden state level ``v`` and action ``u`` at the previous time.\n C: ``numpy.ndarray`` of dtype object\n Prior over observations or 'prior preferences', storing the \"value\" of each outcome in terms of relative log probabilities. \n This is softmaxed to form a proper probability distribution before being used to compute the expected utility term of the expected free energy.\n A_factor_list: ``list`` of ``list`` of ``int``\n List of lists, where ``A_factor_list[m]`` is a list of the hidden state factor indices that observation modality with the index ``m`` depends on\n B_factor_list: ``list`` of ``list`` of ``int``\n List of lists of hidden state factors each hidden state factor depends on. Each element ``B_factor_list[i]`` is a list of the factor indices that factor i's dynamics depend on.\n I: ``numpy.ndarray`` of dtype object\n For each state factor, contains a 2D ``numpy.ndarray`` whose element i,j yields the probability \n of reaching the goal state backwards from state j after i steps.\n horizon: ``int``\n The temporal depth of the policy\n policy_prune_threshold: ``float``\n The threshold for pruning policies that are below a certain probability\n state_prune_threshold: ``float``\n The threshold for pruning states in the expectation that are below a certain probability\n prune_penalty: ``float``\n Penalty to add to the EFE when a policy is pruned\n gamma: ``float``, default 16.0\n Prior precision over policies, scales the contribution of the expected free energy to the posterior over policies\n n: ``int``\n timestep in the future we are calculating\n \n Returns\n ----------\n q_pi: 1D ``numpy.ndarray``\n Posterior beliefs over policies, i.e. a vector containing one posterior probability per policy.\n \n G: 1D ``numpy.ndarray``\n Negative expected free energies of each policy, i.e. a vector containing one negative expected free energy per policy.\n \"\"\"\n\n n_policies = len(policies)\n G = np.zeros(n_policies)\n q_pi = np.zeros((n_policies, 1))\n qs_pi = utils.obj_array(n_policies)\n qo_pi = utils.obj_array(n_policies)\n\n for idx, policy in enumerate(policies):\n qs_pi[idx] = get_expected_states_interactions(qs, B, B_factor_list, policy)\n qo_pi[idx] = get_expected_obs_factorized(qs_pi[idx], A, A_factor_list)\n\n G[idx] += calc_expected_utility(qo_pi[idx], C)\n G[idx] += calc_states_info_gain_factorized(A, qs_pi[idx], A_factor_list)\n\n if I is not None:\n G[idx] += calc_inductive_cost(qs, qs_pi[idx], I)\n\n q_pi = softmax(G * gamma)\n\n if n < horizon - 1:\n # ignore low probability actions in the search tree\n # TODO shouldnt we have to add extra penalty for branches no longer considered?\n # or assume these are already low EFE (high NEFE) anyway?\n policies_to_consider = list(np.where(q_pi >= policy_prune_threshold)[0])\n for idx in range(n_policies):\n if idx not in policies_to_consider:\n G[idx] -= prune_penalty\n else :\n # average over outcomes\n qo_next = qo_pi[idx][0]\n for k in itertools.product(*[range(s.shape[0]) for s in qo_next]):\n prob = 1.0\n for i in range(len(k)):\n prob *= qo_pi[idx][0][i][k[i]]\n \n # ignore low probability states in the search tree\n if prob < state_prune_threshold:\n continue\n\n qo_one_hot = utils.obj_array(len(qo_next))\n for i in range(len(qo_one_hot)):\n qo_one_hot[i] = utils.onehot(k[i], qo_next[i].shape[0])\n \n num_obs = [A[m].shape[0] for m in range(len(A))]\n num_states = [B[f].shape[0] for f in range(len(B))]\n A_modality_list = []\n for f in range(len(B)):\n A_modality_list.append( [m for m in range(len(A)) if f in A_factor_list[m]] )\n mb_dict = {\n 'A_factor_list': A_factor_list,\n 'A_modality_list': A_modality_list\n }\n qs_next = update_posterior_states_factorized(A, qo_one_hot, num_obs, num_states, mb_dict, qs_pi[idx][0], **inference_params)\n q_pi_next, G_next = sophisticated_inference_search(qs_next, policies, A, B, C, A_factor_list, B_factor_list, I,\n horizon, policy_prune_threshold, state_prune_threshold,\n prune_penalty, gamma, inference_params, n+1)\n G_weighted = np.dot(q_pi_next, G_next) * prob\n G[idx] += G_weighted\n\n q_pi = softmax(G * gamma)\n return q_pi, G " }, { "path": "pymdp/legacy/default_models.py", "content": "\nimport numpy as np\nfrom pymdp.legacy import utils, maths\n\ndef generate_epistemic_MAB_model():\n '''\n Create the generative model matrices (A, B, C, D) for the 'epistemic multi-armed bandit',\n used in the `agent_demo.py` Python file and the `agent_demo.ipynb` notebook.\n ''' \n \n num_states = [2, 3] \n num_obs = [3, 3, 3]\n num_controls = [1, 3] \n A = utils.obj_array_zeros([[o] + num_states for _, o in enumerate(num_obs)])\n\n \"\"\"\n MODALITY 0 -- INFORMATION-ABOUT-REWARD-STATE MODALITY\n \"\"\"\n\n A[0][:, :, 0] = np.ones( (num_obs[0], num_states[0]) ) / num_obs[0]\n A[0][:, :, 1] = np.ones( (num_obs[0], num_states[0]) ) / num_obs[0]\n A[0][:, :, 2] = np.array([[0.8, 0.2], [0.0, 0.0], [0.2, 0.8]])\n\n \"\"\"\n MODALITY 1 -- REWARD MODALITY\n \"\"\"\n\n A[1][2, :, 0] = np.ones(num_states[0])\n A[1][0:2, :, 1] = maths.softmax(np.eye(num_obs[1] - 1)) # bandit statistics (mapping between reward-state (first hidden state factor) and rewards (Good vs Bad))\n A[1][2, :, 2] = np.ones(num_states[0])\n\n \"\"\"\n MODALITY 2 -- LOCATION-OBSERVATION MODALITY\n \"\"\"\n A[2][0,:,0] = 1.0\n A[2][1,:,1] = 1.0\n A[2][2,:,2] = 1.0\n\n control_fac_idx = [1] # this is the controllable control state factor, where there will be a >1-dimensional control state along this factor\n B = utils.obj_array_zeros([[n_s, n_s, num_controls[f]] for f, n_s in enumerate(num_states)])\n\n \"\"\"\n FACTOR 0 -- REWARD STATE DYNAMICS\n \"\"\"\n\n p_stoch = 0.0\n\n # we cannot influence factor zero, set up the 'default' stationary dynamics - \n # one state just maps to itself at the next timestep with very high probability, by default. So this means the reward state can\n # change from one to another with some low probability (p_stoch)\n\n B[0][0, 0, 0] = 1.0 - p_stoch\n B[0][1, 0, 0] = p_stoch\n\n B[0][1, 1, 0] = 1.0 - p_stoch\n B[0][0, 1, 0] = p_stoch\n \n \"\"\"\n FACTOR 1 -- CONTROLLABLE LOCATION DYNAMICS\n \"\"\"\n # setup our controllable factor.\n B[1] = utils.construct_controllable_B(num_states, num_controls)[1]\n\n C = utils.obj_array_zeros(num_obs)\n C[1][0] = 1.0 # make the observation we've a priori named `REWARD` actually desirable, by building a high prior expectation of encountering it \n C[1][1] = -1.0 # make the observation we've a prior named `PUN` actually aversive,by building a low prior expectation of encountering it\n\n control_fac_idx = [1]\n\n return A, B, C, control_fac_idx\n\ndef generate_grid_world_transitions(action_labels, num_rows = 3, num_cols = 3):\n \"\"\" \n Wrapper code for creating the controllable transition matrix \n that an agent can use to navigate in a 2-dimensional grid world\n \"\"\"\n\n num_grid_locs = num_rows * num_cols\n\n transition_matrix = np.zeros( (num_grid_locs, num_grid_locs, len(action_labels)) )\n\n grid = np.arange(num_grid_locs).reshape(num_rows, num_cols)\n it = np.nditer(grid, flags=[\"multi_index\"])\n\n loc_list = []\n while not it.finished:\n loc_list.append(it.multi_index)\n it.iternext()\n\n for action_id, action_label in enumerate(action_labels):\n\n for curr_state, grid_location in enumerate(loc_list):\n\n curr_row, curr_col = grid_location\n \n if action_label == \"LEFT\":\n next_col = curr_col - 1 if curr_col > 0 else curr_col \n next_row = curr_row\n elif action_label == \"DOWN\":\n next_row = curr_row + 1 if curr_row < (num_rows-1) else curr_row \n next_col = curr_col\n elif action_label == \"RIGHT\":\n next_col = curr_col + 1 if curr_col < (num_cols-1) else curr_col \n next_row = curr_row\n elif action_label == \"UP\":\n next_row = curr_row - 1 if curr_row > 0 else curr_row \n next_col = curr_col\n elif action_label == \"STAY\":\n next_row, next_col = curr_row, curr_col\n\n new_location = (next_row, next_col)\n next_state = loc_list.index(new_location)\n transition_matrix[next_state, curr_state, action_id] = 1.0\n \n return transition_matrix\n" }, { "path": "pymdp/legacy/envs/__init__.py", "content": "from .env import Env\nfrom .grid_worlds import GridWorldEnv, DGridWorldEnv\nfrom .visual_foraging import SceneConstruction, RandomDotMotion, initialize_scene_construction_GM, initialize_RDM_GM\nfrom .tmaze import TMazeEnv, TMazeEnvNullOutcome\n" }, { "path": "pymdp/legacy/envs/env.py", "content": "#!/usr/bin/env python\n# -*- coding: utf-8 -*-\n\n\"\"\" Environment Base Class\n\n__author__: Conor Heins, Alexander Tschantz, Brennan Klein\n\n\"\"\"\n\n\nclass Env(object):\n \"\"\" \n The Env base class, loosely-inspired by the analogous ``env`` class of the OpenAIGym framework. \n\n A typical workflow is as follows:\n\n >>> my_env = MyCustomEnv()\n >>> initial_observation = my_env.reset(initial_state)\n >>> my_agent.infer_states(initial_observation)\n >>> my_agent.infer_policies()\n >>> next_action = my_agent.sample_action()\n >>> next_observation = my_env.step(next_action)\n\n This would be the first step of an active inference process, where a sub-class of ``Env``, ``MyCustomEnv`` is initialized, \n an initial observation is produced, and these observations are fed into an instance of ``Agent`` in order to produce an action,\n that can then be fed back into the the ``Env`` instance.\n\n \"\"\"\n\n def reset(self, state=None):\n \"\"\"\n Resets the initial state of the environment. Depending on case, it may be common to return an initial observation as well.\n \"\"\"\n raise NotImplementedError\n\n def step(self, action):\n \"\"\"\n Steps the environment forward using an action.\n\n Parameters\n ----------\n action\n The action, the type/format of which depends on the implementation.\n\n Returns\n ---------\n observation\n Sensory observations for an agent, the type/format of which depends on the implementation of ``step`` and the observation space of the agent.\n \"\"\"\n raise NotImplementedError\n\n def render(self):\n \"\"\"\n Rendering function, that typically creates a visual representation of the state of the environment at the current timestep.\n \"\"\"\n pass\n\n def sample_action(self):\n pass\n\n def get_likelihood_dist(self):\n raise ValueError(\n \"<{}> does not provide a model specification\".format(type(self).__name__)\n )\n\n def get_transition_dist(self):\n raise ValueError(\n \"<{}> does not provide a model specification\".format(type(self).__name__)\n )\n\n def get_uniform_posterior(self):\n raise ValueError(\n \"<{}> does not provide a model specification\".format(type(self).__name__)\n )\n\n def get_rand_likelihood_dist(self):\n raise ValueError(\n \"<{}> does not provide a model specification\".format(type(self).__name__)\n )\n\n def get_rand_transition_dist(self):\n raise ValueError(\n \"<{}> does not provide a model specification\".format(type(self).__name__)\n )\n\n def __str__(self):\n return \"<{} instance>\".format(type(self).__name__)\n" }, { "path": "pymdp/legacy/envs/grid_worlds.py", "content": "#!/usr/bin/env python\n# -*- coding: utf-8 -*-\n\n\"\"\" Cube world environment\n\n__author__: Conor Heins, Alexander Tschantz, Brennan Klein\n\n\"\"\"\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport seaborn as sns\n\n\nfrom pymdp.legacy.envs import Env\n\n\nclass GridWorldEnv(Env):\n \"\"\" 2-dimensional grid-world implementation with 5 actions (the 4 cardinal directions and staying put).\"\"\"\n\n UP = 0\n RIGHT = 1\n DOWN = 2\n LEFT = 3\n STAY = 4\n\n CONTROL_NAMES = [\"UP\", \"RIGHT\", \"DOWN\", \"LEFT\", \"STAY\"]\n\n def __init__(self, shape=[2, 2], init_state=None):\n \"\"\"\n Initialization function for 2-D grid world\n\n Parameters\n ----------\n shape: ``list`` of ``int``, where ``len(shape) == 2``\n The dimensions of the grid world, stored as a list of integers, storing the discrete dimensions of the Y (vertical) and X (horizontal) spatial dimensions, respectively.\n init_state: ``int`` or ``None``\n Initial state of the environment, i.e. the location of the agent in grid world. If not ``None``, must be a discrete index in the range ``(0, (shape[0] * shape[1])-1)``. It is thus a \"linear index\" of the initial location of the agent in grid world.\n If ``None``, then an initial location will be randomly sampled from the grid.\n \"\"\"\n \n self.shape = shape\n self.n_states = np.prod(shape)\n self.n_observations = self.n_states\n self.n_control = 5\n self.max_y = shape[0]\n self.max_x = shape[1]\n self._build()\n self.set_init_state(init_state)\n self.last_action = None\n\n def reset(self, init_state=None):\n \"\"\"\n Reset the state of the 2-D grid world. In other words, resets the location of the agent, and wipes the current action.\n\n Parameters\n ----------\n init_state: ``int`` or ``None``\n Initial state of the environment, i.e. the location of the agent in grid world. If not ``None``, must be a discrete index in the range ``(0, (shape[0] * shape[1])-1)``. It is thus a \"linear index\" of the initial location of the agent in grid world.\n If ``None``, then an initial location will be randomly sampled from the grid.\n\n Returns\n ----------\n self.state: ``int``\n The current state of the environment, i.e. the location of the agent in grid world. Will be a discrete index in the range ``(0, (shape[0] * shape[1])-1)``. It is thus a \"linear index\" of the location of the agent in grid world.\n \"\"\"\n self.set_init_state(init_state)\n self.last_action = None\n return self.state\n\n def set_state(self, state):\n \"\"\"\n Sets the state of the 2-D grid world.\n\n Parameters\n ----------\n state: ``int`` or ``None``\n State of the environment, i.e. the location of the agent in grid world. If not ``None``, must be a discrete index in the range ``(0, (shape[0] * shape[1])-1)``. It is thus a \"linear index\" of the location of the agent in grid world.\n If ``None``, then a location will be randomly sampled from the grid.\n\n Returns\n ----------\n self.state: ``int``\n The current state of the environment, i.e. the location of the agent in grid world. Will be a discrete index in the range ``(0, (shape[0] * shape[1])-1)``. It is thus a \"linear index\" of the location of the agent in grid world.\n \"\"\"\n self.state = state\n return state\n\n def step(self, action):\n \"\"\"\n Updates the state of the environment, i.e. the location of the agent, using an action index that corresponds to one of the 5 possible moves.\n\n Parameters\n ----------\n action: ``int`` \n Action index that refers to which of the 5 actions the agent will take. Actions are, in order: \"UP\", \"RIGHT\", \"DOWN\", \"LEFT\", \"STAY\".\n\n Returns\n ----------\n state: ``int``\n The new, updated state of the environment, i.e. the location of the agent in grid world after the action has been made. Will be discrete index in the range ``(0, (shape[0] * shape[1])-1)``. It is thus a \"linear index\" of the location of the agent in grid world.\n \"\"\"\n state = self.P[self.state][action]\n self.state = state\n self.last_action = action\n return state\n\n def render(self, title=None):\n \"\"\"\n Creates a heatmap showing the current position of the agent in the grid world.\n\n Parameters\n ----------\n title: ``str`` or ``None``\n Optional title for the heatmap.\n \"\"\"\n values = np.zeros(self.shape)\n values[self.position] = 1.0\n _, ax = plt.subplots(figsize=(3, 3))\n if self.shape[0] == 1 or self.shape[1] == 1:\n ax.imshow(values, cmap=\"OrRd\")\n else:\n _ = sns.heatmap(values, cmap=\"OrRd\", linewidth=2.5, cbar=False, ax=ax)\n plt.xticks(range(self.shape[1]))\n plt.yticks(range(self.shape[0]))\n if title is not None:\n plt.title(title)\n plt.show()\n\n def set_init_state(self, init_state=None):\n if init_state is not None:\n if init_state > (self.n_states - 1) or init_state < 0:\n raise ValueError(\"`init_state` is greater than number of states\")\n if not isinstance(init_state, (int, float)):\n raise ValueError(\"`init_state` must be [int/float]\")\n self.init_state = int(init_state)\n else:\n self.init_state = np.random.randint(0, self.n_states)\n self.state = self.init_state\n\n def _build(self):\n P = {}\n grid = np.arange(self.n_states).reshape(self.shape)\n it = np.nditer(grid, flags=[\"multi_index\"])\n\n while not it.finished:\n s = it.iterindex\n y, x = it.multi_index\n P[s] = {a: [] for a in range(self.n_control)}\n\n next_up = s if y == 0 else s - self.max_x\n next_right = s if x == (self.max_x - 1) else s + 1\n next_down = s if y == (self.max_y - 1) else s + self.max_x\n next_left = s if x == 0 else s - 1\n next_stay = s\n\n P[s][self.UP] = next_up\n P[s][self.RIGHT] = next_right\n P[s][self.DOWN] = next_down\n P[s][self.LEFT] = next_left\n P[s][self.STAY] = next_stay\n\n it.iternext()\n\n self.P = P\n\n def get_init_state_dist(self, init_state=None):\n init_state_dist = np.zeros(self.n_states)\n if init_state is None:\n init_state_dist[self.init_state] = 1.0\n else:\n init_state_dist[init_state] = 1.0\n\n def get_transition_dist(self):\n B = np.zeros([self.n_states, self.n_states, self.n_control])\n for s in range(self.n_states):\n for a in range(self.n_control):\n ns = int(self.P[s][a])\n B[ns, s, a] = 1\n return B\n\n def get_likelihood_dist(self):\n A = np.eye(self.n_observations, self.n_states)\n return A\n\n def sample_action(self):\n return np.random.randint(self.n_control)\n\n @property\n def position(self):\n \"\"\" @TODO might be wrong w.r.t (x & y) \"\"\"\n return np.unravel_index(np.array(self.state), self.shape)\n\n\nclass DGridWorldEnv(object):\n \"\"\" 1-dimensional grid-world implementation with 3 possible movement actions (\"LEFT\", \"STAY\", \"RIGHT\")\"\"\"\n\n LEFT = 0\n STAY = 1\n RIGHT = 2\n\n CONTROL_NAMES = [\"LEFT\", \"STAY\", \"RIGHT\"]\n\n def __init__(self, shape=[2, 2], init_state=None):\n self.shape = shape\n self.n_states = np.prod(shape)\n self.n_observations = self.n_states\n self.n_control = 3\n self.max_y = shape[0]\n self.max_x = shape[1]\n self._build()\n self.set_init_state(init_state)\n self.last_action = None\n\n def reset(self, init_state=None):\n self.set_init_state(init_state)\n self.last_action = None\n return self.state\n\n def set_state(self, state):\n self.state = state\n return state\n\n def step(self, action):\n state = self.P[self.state][action]\n self.state = state\n self.last_action = action\n return state\n\n def render(self, title=None):\n values = np.zeros(self.shape)\n values[self.position] = 1.0\n _, ax = plt.subplots(figsize=(3, 3))\n if self.shape[0] == 1 or self.shape[1] == 1:\n ax.imshow(values, cmap=\"OrRd\")\n else:\n _ = sns.heatmap(values, cmap=\"OrRd\", linewidth=2.5, cbar=False, ax=ax)\n plt.xticks(range(self.shape[1]))\n plt.yticks(range(self.shape[0]))\n if title is not None:\n plt.title(title)\n plt.show()\n\n def set_init_state(self, init_state=None):\n if init_state is not None:\n if init_state > (self.n_states - 1) or init_state < 0:\n raise ValueError(\"`init_state` is greater than number of states\")\n if not isinstance(init_state, (int, float)):\n raise ValueError(\"`init_state` must be [int/float]\")\n self.init_state = int(init_state)\n else:\n self.init_state = np.random.randint(0, self.n_states)\n self.state = self.init_state\n\n def _build(self):\n P = {}\n grid = np.arange(self.n_states).reshape(self.shape)\n it = np.nditer(grid, flags=[\"multi_index\"])\n\n while not it.finished:\n s = it.iterindex\n y, x = it.multi_index\n P[s] = {a: [] for a in range(self.n_control)}\n\n next_right = s if x == (self.max_x - 1) else s + 1\n next_left = s if x == 0 else s - 1\n next_stay = s\n\n P[s][self.LEFT] = next_left\n P[s][self.STAY] = next_stay\n P[s][self.RIGHT] = next_right\n\n it.iternext()\n\n self.P = P\n\n def get_init_state_dist(self, init_state=None):\n init_state_dist = np.zeros(self.n_states)\n if init_state is None:\n init_state_dist[self.init_state] = 1.0\n else:\n init_state_dist[init_state] = 1.0\n\n def get_transition_dist(self):\n B = np.zeros([self.n_states, self.n_states, self.n_control])\n for s in range(self.n_states):\n for a in range(self.n_control):\n ns = int(self.P[s][a])\n B[ns, s, a] = 1\n return B\n\n def get_likelihood_dist(self):\n A = np.eye(self.n_observations, self.n_states)\n return A\n\n def sample_action(self):\n return np.random.randint(self.n_control)\n\n @property\n def position(self):\n return self.state\n" }, { "path": "pymdp/legacy/envs/tmaze.py", "content": "#!/usr/bin/env python\n# -*- coding: utf-8 -*-\n\n\"\"\" T Maze Environment (Factorized)\n\n__author__: Conor Heins, Alexander Tschantz, Brennan Klein\n\n\"\"\"\n\nfrom pymdp.legacy.envs import Env\nfrom pymdp.legacy import utils, maths\nimport numpy as np\n\nLOCATION_FACTOR_ID = 0\nTRIAL_FACTOR_ID = 1\n\nLOCATION_MODALITY_ID = 0\nREWARD_MODALITY_ID = 1\nCUE_MODALITY_ID = 2\n\nREWARD_IDX = 1\nLOSS_IDX = 2\n\n\nclass TMazeEnv(Env):\n \"\"\" Implementation of the 3-arm T-Maze environment \"\"\"\n def __init__(self, reward_probs=None):\n\n if reward_probs is None:\n a = 0.98\n b = 1.0 - a\n self.reward_probs = [a, b]\n else:\n if sum(reward_probs) != 1:\n raise ValueError(\"Reward probabilities must sum to 1!\")\n elif len(reward_probs) != 2:\n raise ValueError(\"Only two reward conditions currently supported...\")\n else:\n self.reward_probs = reward_probs\n\n self.num_states = [4, 2]\n self.num_locations = self.num_states[LOCATION_FACTOR_ID]\n self.num_controls = [self.num_locations, 1]\n self.num_reward_conditions = self.num_states[TRIAL_FACTOR_ID]\n self.num_cues = self.num_reward_conditions\n self.num_obs = [self.num_locations, self.num_reward_conditions + 1, self.num_cues]\n self.num_factors = len(self.num_states)\n self.num_modalities = len(self.num_obs)\n\n self._transition_dist = self._construct_transition_dist()\n self._likelihood_dist = self._construct_likelihood_dist()\n\n self._reward_condition = None\n self._state = None\n \n def reset(self, state=None):\n if state is None:\n loc_state = utils.onehot(0, self.num_locations)\n \n self._reward_condition = np.random.randint(self.num_reward_conditions) # randomly select a reward condition\n reward_condition = utils.onehot(self._reward_condition, self.num_reward_conditions)\n\n full_state = utils.obj_array(self.num_factors)\n full_state[LOCATION_FACTOR_ID] = loc_state\n full_state[TRIAL_FACTOR_ID] = reward_condition\n self._state = full_state\n else:\n self._state = state\n return self._get_observation()\n\n def step(self, actions):\n prob_states = utils.obj_array(self.num_factors)\n for factor, state in enumerate(self._state):\n prob_states[factor] = self._transition_dist[factor][:, :, int(actions[factor])].dot(state)\n state = [utils.sample(ps_i) for ps_i in prob_states]\n self._state = self._construct_state(state)\n return self._get_observation()\n\n def render(self):\n pass\n\n def sample_action(self):\n return [np.random.randint(self.num_controls[i]) for i in range(self.num_factors)]\n\n def get_likelihood_dist(self):\n return self._likelihood_dist\n\n def get_transition_dist(self):\n return self._transition_dist\n\n\n def get_rand_likelihood_dist(self):\n pass\n\n def get_rand_transition_dist(self):\n pass\n\n def _get_observation(self):\n\n prob_obs = [maths.spm_dot(A_m, self._state) for A_m in self._likelihood_dist]\n\n obs = [utils.sample(po_i) for po_i in prob_obs]\n return obs\n\n def _construct_transition_dist(self):\n B_locs = np.eye(self.num_locations)\n B_locs = B_locs.reshape(self.num_locations, self.num_locations, 1)\n B_locs = np.tile(B_locs, (1, 1, self.num_locations))\n B_locs = B_locs.transpose(1, 2, 0)\n\n B = utils.obj_array(self.num_factors)\n\n B[LOCATION_FACTOR_ID] = B_locs\n B[TRIAL_FACTOR_ID] = np.eye(self.num_reward_conditions).reshape(\n self.num_reward_conditions, self.num_reward_conditions, 1\n )\n return B\n\n def _construct_likelihood_dist(self):\n\n A = utils.obj_array_zeros([ [obs_dim] + self.num_states for obs_dim in self.num_obs] )\n\n for loc in range(self.num_states[LOCATION_FACTOR_ID]):\n for reward_condition in range(self.num_states[TRIAL_FACTOR_ID]):\n\n # The case when the agent is in the centre location\n if loc == 0:\n # When in the centre location, reward observation is always 'no reward'\n # or the outcome with index 0\n A[REWARD_MODALITY_ID][0, loc, reward_condition] = 1.0\n\n # When in the centre location, cue is totally ambiguous with respect to the reward condition\n A[CUE_MODALITY_ID][:, loc, reward_condition] = 1.0 / self.num_obs[2]\n\n # The case when loc == 3, or the cue location ('bottom arm')\n elif loc == 3:\n\n # When in the cue location, reward observation is always 'no reward'\n # or the outcome with index 0\n A[REWARD_MODALITY_ID][0, loc, reward_condition] = 1.0\n\n # When in the cue location, the cue indicates the reward condition umambiguously\n # signals where the reward is located\n A[CUE_MODALITY_ID][reward_condition, loc, reward_condition] = 1.0\n\n # The case when the agent is in one of the (potentially-) rewarding armS\n else:\n\n # When location is consistent with reward condition\n if loc == (reward_condition + 1):\n # Means highest probability is concentrated over reward outcome\n high_prob_idx = REWARD_IDX\n # Lower probability on loss outcome\n low_prob_idx = LOSS_IDX\n else:\n # Means highest probability is concentrated over loss outcome\n high_prob_idx = LOSS_IDX\n # Lower probability on reward outcome\n low_prob_idx = REWARD_IDX\n\n reward_probs = self.reward_probs[0]\n A[REWARD_MODALITY_ID][high_prob_idx, loc, reward_condition] = reward_probs\n\n reward_probs = self.reward_probs[1]\n A[REWARD_MODALITY_ID][low_prob_idx, loc, reward_condition] = reward_probs\n\n # Cue is ambiguous when in the reward location\n A[CUE_MODALITY_ID][:, loc, reward_condition] = 1.0 / self.num_obs[2]\n\n # The agent always observes its location, regardless of the reward condition\n A[LOCATION_MODALITY_ID][loc, loc, reward_condition] = 1.0\n\n return A\n\n def _construct_state(self, state_tuple):\n\n state = utils.obj_array(self.num_factors)\n for f, ns in enumerate(self.num_states):\n state[f] = utils.onehot(state_tuple[f], ns)\n\n return state\n\n @property\n def state(self):\n return self._state\n\n @property\n def reward_condition(self):\n return self._reward_condition\n\n\nclass TMazeEnvNullOutcome(Env):\n \"\"\" Implementation of the 3-arm T-Maze environment where there is an additional null outcome within the cue modality, so that the agent\n doesn't get a random cue observation, but a null one, when it visits non-cue locations\"\"\"\n\n def __init__(self, reward_probs=None):\n\n if reward_probs is None:\n a = 0.98\n b = 1.0 - a\n self.reward_probs = [a, b]\n else:\n if sum(reward_probs) != 1:\n raise ValueError(\"Reward probabilities must sum to 1!\")\n elif len(reward_probs) != 2:\n raise ValueError(\"Only two reward conditions currently supported...\")\n else:\n self.reward_probs = reward_probs\n\n self.num_states = [4, 2]\n self.num_locations = self.num_states[LOCATION_FACTOR_ID]\n self.num_controls = [self.num_locations, 1]\n self.num_reward_conditions = self.num_states[TRIAL_FACTOR_ID]\n self.num_cues = self.num_reward_conditions\n self.num_obs = [self.num_locations, self.num_reward_conditions + 1, self.num_cues + 1]\n self.num_factors = len(self.num_states)\n self.num_modalities = len(self.num_obs)\n\n self._transition_dist = self._construct_transition_dist()\n self._likelihood_dist = self._construct_likelihood_dist()\n\n self._reward_condition = None\n self._state = None\n\n def reset(self, state=None):\n if state is None:\n loc_state = utils.onehot(0, self.num_locations)\n \n self._reward_condition = np.random.randint(self.num_reward_conditions) # randomly select a reward condition\n reward_condition = utils.onehot(self._reward_condition, self.num_reward_conditions)\n\n full_state = utils.obj_array(self.num_factors)\n full_state[LOCATION_FACTOR_ID] = loc_state\n full_state[TRIAL_FACTOR_ID] = reward_condition\n self._state = full_state\n else:\n self._state = state\n return self._get_observation()\n\n def step(self, actions):\n prob_states = utils.obj_array(self.num_factors)\n for factor, state in enumerate(self._state):\n prob_states[factor] = self._transition_dist[factor][:, :, int(actions[factor])].dot(state)\n state = [utils.sample(ps_i) for ps_i in prob_states]\n self._state = self._construct_state(state)\n return self._get_observation()\n\n\n def sample_action(self):\n return [np.random.randint(self.num_controls[i]) for i in range(self.num_factors)]\n\n def get_likelihood_dist(self):\n return self._likelihood_dist.copy()\n\n def get_transition_dist(self):\n return self._transition_dist.copy()\n\n def _get_observation(self):\n\n prob_obs = [maths.spm_dot(A_m, self._state) for A_m in self._likelihood_dist]\n\n obs = [utils.sample(po_i) for po_i in prob_obs]\n return obs\n\n def _construct_transition_dist(self):\n B_locs = np.eye(self.num_locations)\n B_locs = B_locs.reshape(self.num_locations, self.num_locations, 1)\n B_locs = np.tile(B_locs, (1, 1, self.num_locations))\n B_locs = B_locs.transpose(1, 2, 0)\n\n B = utils.obj_array(self.num_factors)\n\n B[LOCATION_FACTOR_ID] = B_locs\n B[TRIAL_FACTOR_ID] = np.eye(self.num_reward_conditions).reshape(\n self.num_reward_conditions, self.num_reward_conditions, 1\n )\n return B\n\n def _construct_likelihood_dist(self):\n\n A = utils.obj_array_zeros([ [obs_dim] + self.num_states for _, obs_dim in enumerate(self.num_obs)] )\n \n for loc in range(self.num_states[LOCATION_FACTOR_ID]):\n for reward_condition in range(self.num_states[TRIAL_FACTOR_ID]):\n\n if loc == 0: # the case when the agent is in the centre location\n # When in the centre location, reward observation is always 'no reward', or the outcome with index 0\n A[REWARD_MODALITY_ID][0, loc, reward_condition] = 1.0\n\n # When in the center location, cue observation is always 'no cue', or the outcome with index 0\n A[CUE_MODALITY_ID][0, loc, reward_condition] = 1.0\n\n # The case when loc == 3, or the cue location ('bottom arm')\n elif loc == 3:\n\n # When in the cue location, reward observation is always 'no reward', or the outcome with index 0\n A[REWARD_MODALITY_ID][0, loc, reward_condition] = 1.0\n\n # When in the cue location, the cue indicates the reward condition umambiguously\n # signals where the reward is located\n A[CUE_MODALITY_ID][reward_condition + 1, loc, reward_condition] = 1.0\n\n # The case when the agent is in one of the (potentially-) rewarding arms\n else:\n\n # When location is consistent with reward condition\n if loc == (reward_condition + 1):\n # Means highest probability is concentrated over reward outcome\n high_prob_idx = REWARD_IDX\n # Lower probability on loss outcome\n low_prob_idx = LOSS_IDX #\n else:\n # Means highest probability is concentrated over loss outcome\n high_prob_idx = LOSS_IDX\n # Lower probability on reward outcome\n low_prob_idx = REWARD_IDX\n\n reward_probs = self.reward_probs[0]\n A[REWARD_MODALITY_ID][high_prob_idx, loc, reward_condition] = reward_probs\n reward_probs = self.reward_probs[1]\n A[REWARD_MODALITY_ID][low_prob_idx, loc, reward_condition] = reward_probs\n\n # When in the one of the rewarding arms, cue observation is always 'no cue', or the outcome with index 0\n A[CUE_MODALITY_ID][0, loc, reward_condition] = 1.0\n\n # The agent always observes its location, regardless of the reward condition\n A[LOCATION_MODALITY_ID][loc, loc, reward_condition] = 1.0\n\n return A\n\n def _construct_state(self, state_tuple):\n\n state = utils.obj_array(self.num_factors)\n\n for f, ns in enumerate(self.num_states):\n state[f] = utils.onehot(state_tuple[f], ns)\n \n return state\n\n @property\n def state(self):\n return self._state\n\n @property\n def reward_condition(self):\n return self._reward_condition\n" }, { "path": "pymdp/legacy/envs/visual_foraging.py", "content": "#!/usr/bin/env python\n# -*- coding: utf-8 -*-\n\n\"\"\" Visual Foraging Environment\n\n__author__: Conor Heins, Alexander Tschantz, Brennan Klein\n\n\"\"\"\n\nfrom pymdp.legacy.envs import Env\nfrom pymdp.legacy import utils, maths\nimport numpy as np\nfrom itertools import permutations, product\n\nLOCATION_ID = 0\nSCENE_ID = 1\n\nscene_names = [\"UP_RIGHT\", \"RIGHT_DOWN\", \"DOWN_LEFT\", \"LEFT_UP\"] # possible scenes\nquadrant_names = ['1','2','3','4']\nchoice_names = ['choose_UP_RIGHT','choose_RIGHT_DOWN','choose_DOWN_LEFT', 'choose_LEFT_UP'] # possible choices\nconfig_names = list(permutations([1,2,3,4], 2))\nall_scenes_all_configs = list(product(scene_names, config_names))\n\nmotion_dir = ['null','UP','RIGHT','DOWN','LEFT']\nn_states = len(motion_dir)\nsampling_states = ['sample', 'break']\n\nclass SceneConstruction(Env):\n \n def __init__(self, starting_loc = 'start', scene_name = 'UP_RIGHT', config = \"1_2\"):\n\n pos1, pos2 = config.split(\"_\")\n config_tuple = (int(pos1), int(pos2))\n\n assert scene_name in scene_names, f\"{scene_name} is not a possible scene! please choose from {scene_names[0]}, {scene_names[1]}, {scene_names[2]}, or {scene_names[3]}\\n\"\n assert config_tuple in config_names, f\"{config} is not a possible spatial configuration! Please choose an appropriate 2x2 spatial configuration\\n\"\n\n self.current_location = starting_loc\n self.scene_name = scene_name\n self.config = config\n self._create_visual_array()\n\n print(f'Starting location is {self.current_location}, Scene is {self.scene_name}, Configuration is {self.config}\\n')\n\n def step(self,action_label):\n\n\n if action_label == 'start': \n \n new_location = 'start'\n what_obs = 'null'\n\n elif action_label in quadrant_names:\n\n what_obs = self.vis_array_flattened[int(action_label)-1]\n new_location = action_label\n\n elif action_label in choice_names:\n new_location = action_label\n\n chosen_scene_name = new_location.split('_')[1] + '_' + new_location.split('_')[2]\n\n if chosen_scene_name== self.scene_name:\n what_obs = 'correct!'\n else:\n what_obs = 'incorrect!'\n \n self.current_location = new_location # store the new grid location\n\n return what_obs, self.current_location\n\n def reset(self):\n self.current_location = \"start\"\n print('Re-initialized location to Start location')\n what_obs = 'null'\n\n return what_obs, self.current_location\n\n def _create_visual_array(self):\n \"\"\" Create scene array \"\"\"\n\n vis_array_flattened = np.array(['null', 'null', 'null', 'null'],dtype=\"