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Directory structure:
gitextract_0mmsfh5n/
├── CODE_OF_CONDUCT.md
├── CONTRIBUTING.md
├── LICENSE
├── README.md
├── split_data.py
├── src/
│ ├── __init__.py
│ ├── envs/
│ │ ├── __init__.py
│ │ └── ode.py
│ ├── evaluator.py
│ ├── logger.py
│ ├── model/
│ │ ├── __init__.py
│ │ └── transformer.py
│ ├── optim.py
│ ├── slurm.py
│ ├── trainer.py
│ └── utils.py
└── train.py
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FILE CONTENTS
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FILE: CODE_OF_CONDUCT.md
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# Code of Conduct
Facebook has adopted a Code of Conduct that we expect project participants to adhere to.
Please read the [full text](https://code.fb.com/codeofconduct/)
so that you can understand what actions will and will not be tolerated.
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FILE: CONTRIBUTING.md
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# Contributing to this repo
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## License
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under the LICENSE file in the root directory of this source tree.
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FILE: LICENSE
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FILE: README.md
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# Maths from examples - Learning advanced mathematical computations from examples
This is the source code and data sets relevant to the paper Learning advanced mathematical computations from examples, by Amaury hayat, François Charton and Guillaume Lample, published by ICLR 2021. https://arxiv.org/abs/2006.06462
We provide code for
* data generation
* model training
* model evaluation
We also provide
* 7 datasets
* 7 pretrained models
### Dependencies
* Python (3.8+)
* Numpy (1.16.4+)
* Sympy (1.4+)
* Pytorch (1.7.1+)
* Control library (0.8.4, from conda-forge)
* CUDA (i.e. a NVIDIA chip) if you intend to use a GPU
* Apex for half-precision training
## Important notes
### Learning with and without GPU
All the code can run on CPU only (set parameter --cpu to true). Data generation is to be done on CPU only. Model training and model evaluation can be done on CPU, but training will be extremely slow. To train or evaluate with a GPU, you need a CUDA-enabled GPU (i.e. a NVIDIA chip).
We support:
* Half-Precision (with NVIDIA Apex library): set parameters `--fp16 true --amp 2`, to disable, set `--fp16 false --amp -1`
* Multi-GPU training: to run an experiment with several GPU on a unique machine, use
```bash
export NGPU=8; python -m torch.distributed.launch --nproc_per_node=$NGPU train.py # parameters for your experiment
```
* Multi-node training: using GPU on different machines is handled by SLURM (see code)
On GPU with limited video memory, you will need to reduce memory usage by adjusting `--batch_size`. Try to set it to the largest value that will fit in your CUDA memory. Since model optimization is performed at the end of each minibatch, smaller batch sizes will gratly slow learning. You can compensate for this by increasing `--accumulate_gradient`, which controls the number of mini-batches the model sees before optimizing the model.
### Dump paths and experiment names
All paths should be absolute : `--dump_path ./mydump` might not work, `--dump_path c:/Users/me/mydump` should be fine.
The directories where your datasets, models, and logfiles will be generated are constructed from the parameters --dump_path --exp_name and --exp_id, as {dump_path}/{exp_name}/{exp_id}/, if you do not specify an exp_id, a random unique name will be created for you. If you reuse the same dump_path/exp/name/exp_id, generation or training will resume there (adding new examples, or loading the previous model for training).
All results will be logged in file `train.log`of the experiment path.
All models and datasets can be downloaded from https://dl.fbaipublicfiles.com/MathsFromExamples/. By convention, in all code examples, datasets and models use the path `/checkpoint/fcharton/dumped/`. You will need to adjust this to the correct path on your local machine.
## Data sets
We provide 7 datasets, all can be found on https://dl.fbaipublicfiles.com/MathsFromExamples/data/ as tar.gz archives.
### Stability : balanced sample of systems of degree 2 to 5 (50% stable), predicting speed of convergence at 0.01 (largest real part of eigenvalue):
in archive https://dl.fbaipublicfiles.com/MathsFromExamples/data/ddss_stability_balanced.tar.gz
* ddss_stability_balanced.prefix_counts.train : 25,544,975 systems
* ddss_stability_balanced.prefix_counts.valid.final : 10,000 systems
* ddss_stability_balanced.prefix_counts.test.final : 10,000 systems
### Stability : random sample of systems of degree 2 to 6, predicting speed of convergence at 0.01
in archive https://dl.fbaipublicfiles.com/MathsFromExamples/data/ddss_stability.tar.gz
* ddss_stability.prefix_counts.train : 92,994,423 systems
* ddss_stability.prefix_counts.valid.final : 10,000 systems
* ddss_stability.prefix_counts.test.final : 10,000 systems
### Controllability: balanced sample of systems of degree 3 to 5 (50% stable), predicting controllability (a binary value)
in archive https://dl.fbaipublicfiles.com/MathsFromExamples/data/ddss_control.tar.gz
* ddss_control.prefix_counts.train : 26,577,934 systems
* ddss_control.prefix_counts.valid.final : 10,000 systems
* ddss_control.prefix_counts.test.final : 10,000 systems
### Controllability: sample of controllable systems of degree 3 to 6, predicting a control matrix
in archive https://dl.fbaipublicfiles.com/MathsFromExamples/data/ddss_gram.tar.gz
* ddss_gram.prefix_counts.train : 53,680,092 systems
* ddss_gram.prefix_counts.valid.final : 10,000 systems
* ddss_gram.prefix_counts.test.final : 10,000 systems
### Non autonomous controllability: random sample (82.4% controllable) of systems of degree 2 and 3, predicting controllability
in archive https://dl.fbaipublicfiles.com/MathsFromExamples/data/ddss_control_t.tar.gz
* ddss_control_t.prefix_counts.train : 65,754,655 systems
* ddss_control_t.prefix_counts.valid.final : 10,000 systems
* ddss_control_t.prefix_counts.test.final : 10,000 systems
### Non autonomous controllability: balanced sample (50/50) of systems of degree 2 and 3, predicting controllability
in archive https://dl.fbaipublicfiles.com/MathsFromExamples/data/ddss_control_t_bal.tar.gz
* ddss_control_t_bal.prefix_counts.train : 23,125,016 systems
* ddss_control_t_bal.prefix_counts.valid.final : 10,000 systems
* ddss_control_t_bal.prefix_counts.test.final : 10,000 systems
### Partial differential equations with initial conditions, predicting existence of a solution and behavior at infinity
in archive https://dl.fbaipublicfiles.com/MathsFromExamples/data/ddss_fourier.tar.gz
* ddss_fourier.prefix_counts.train : 52,285,760 systems
* ddss_fourier.prefix_counts.valid.final : 10,000 systems
* ddss_fourier.prefix_counts.test.final : 10,000 systems
## Training a model from a dataset
```bash
python train.py
# experiment parameters
# the full path of this experiment will be /checkpoint/fcharton/dumped/ddss_ctrl/exp_1
--dump_path '/checkpoint/fcharton/dumped' # path for log files and saved models, avoid ./ and other non absolute paths
--exp_name ddss_ctrl # name
--exp_id exp_1 # id : randomly generated if absent
# dataset
--export_data false
--tasks ode_control # set to `ode_convergence_speed`, `ode_control` or `fourier_cond_init`
# '{tasks},{train_file_path},{valid_file_path},{test_file_path}'
--reload_data 'ode_control,/checkpoint/fcharton/dumped/ddss_gen_ctrl/ddss_control.prefix_counts.train,/checkpoint/fcharton/dumped/ddss_gen_ctrl/ddss_control.prefix_counts.valid.final,/checkpoint/fcharton/dumped/ddss_gen_ctrl/ddss_control.prefix_counts.test.final'
--reload_size 40000000 # nr of records to load
--max_len 512 # max length of input or output
# model parameters
--emb_dim 512
--n_enc_layers 6
--n_dec_layers 6
--n_heads 8
--optimizer 'adam_inverse_sqrt,warmup_updates=10000,lr=0.0001,weight_decay=0.01'
# training parameters
--batch_size 256 # minibatch size, reduce to fit available GPU memory
--epoch_size 300000 # how often evaluation on validation set is performed
--beam_eval 0 # use beam search for evaluation (set to 1 for quantitative tasks)
--eval_size 10000 # size of validation set
--batch_size_eval 256 # batchs for validation, reduce to adjust memory
# validation metrics
# valid_{task}_acc or valid_{task}_beam_acc depending on whether beam search is used
--validation_metrics valid_ode_control_acc
# stop after no increase in 20 epochs
--stopping_criterion 'valid_ode_control_acc,20'
```
## Generating your own data sets
To generate a dataset, use the parameters
```bash
python train.py --cpu true --export_data true --reload_data '' --env_base_seed -1 --num_workers 20 --task # task specific parameters
```
Generated data (exported as sequences of tokens) will be written in file data.prefix in the dump path of the experiment. To be used for training, these files need to be post-processed as shown in the examples below.
IMPORTANT NOTE : Data generation is very slow, and sometimes results in errors that cause the program to abort and need to be relaunched. Typical generating speeds are one or a few systems per second. Whereas one might want to use this code to experiment with data generation, creating datasets on which our models can be trained (10 million examples or more) requires a lot of computing power (typically 200-300 experiments, with 20 CPU each, running for several days)
Important parameters for data generation are :
* `--tasks` : ode_convergence_speed, ode_control or fourier_cond_init
* `--cpu` : always set to true
* `--num_workers` : set to the number of cores you can use
* `--env_base_seed` : set to -1
* `--min_degree` and `--max_degree` : bounds for the size of the systems generated
For more details, see file 'envs/ode.py' in the source code
### Predicting stability - balanced sample (50% stable), systems of degree 2 to 5
```bash
# Generation command
python train.py --dump_path '/checkpoint/fcharton/dumped' --save_periodic 0 --fp16 false --amp -1 --emb_dim 128 --n_enc_layers 2 --n_dec_layers 2 --n_heads 8 --dropout 0 --attention_dropout 0 --share_inout_emb true --sinusoidal_embeddings false --max_len 512 --batch_size 32 --optimizer 'adam,lr=0.0001' --clip_grad_norm 5 --epoch_size 300000 --max_epoch 100000 --accumulate_gradients 1 --env_name ode --max_int 10 --precision 2 --skip_zero_gradient true --positive false --nonnull true --prob_int 0.3 --min_degree 2 --max_degree 5 --eval_value 0.01 --prob_positive 0.5 --num_workers 20 --cpu true --stopping_criterion '' --validation_metrics '' --export_data true --reload_data '' --tasks ode_convergence_speed --env_base_seed -1 --exp_name ddss_gen_stab_bal
# Post-processing
# assemble raw data file from prefixes
cat */data.prefix \
| awk 'BEGIN{PROCINFO["sorted_in"]="@val_num_desc"}{c[$0]++}END{for (i in c) printf("%i|%s\n",c[i],i)}' \
> ddss_stability_balanced.prefix_counts
# create train, valid and test samples
python ~/MathsFromExamples/split_data.py ddss_stability_balanced.prefix_counts 10000
# check valid and test for duplicates and remove them
awk -F"[|\t]" 'NR==FNR { lines[$2]=1; next } !($2 in lines)' ddss_stability_balanced.prefix_counts.train ddss_stability_balanced.prefix_counts.valid > ddss_stability_balanced.prefix_counts.valid.final
awk -F"[|\t]" 'NR==FNR { lines[$2]=1; next } !($2 in lines)' ddss_stability_balanced.prefix_counts.train ddss_stability_balanced.prefix_counts.test > ddss_stability_balanced.prefix_counts.test.final
```
### Predicting stability - random sample, systems of degree 2 to 6
```bash
# Generation command
python train.py --dump_path '/checkpoint/fcharton/dumped' --save_periodic 0 --fp16 false --amp -1 --emb_dim 128 --n_enc_layers 2 --n_dec_layers 2 --n_heads 8 --dropout 0 --attention_dropout 0 --share_inout_emb true --sinusoidal_embeddings false --max_len 512 --batch_size 32 --optimizer 'adam,lr=0.0001' --clip_grad_norm 5 --epoch_size 300000 --max_epoch 100000 --accumulate_gradients 1 --env_name ode --max_int 10 --precision 2 --skip_zero_gradient true --positive false --nonnull true --prob_int 0.3 --min_degree 2 --max_degree 6 --eval_value 0.01 --num_workers 20 --cpu true --stopping_criterion '' --validation_metrics '' --export_data true --reload_data '' --tasks ode_convergence_speed --env_base_seed -1 --exp_name ddss_gen_stab
# assemble raw data file from prefixes
cat */data.prefix \
| awk 'BEGIN{PROCINFO["sorted_in"]="@val_num_desc"}{c[$0]++}END{for (i in c) printf("%i|%s\n",c[i],i)}' \
> ddss_stability.prefix_counts
# create train, valid and test samples
python ~/MathsFromExamples/split_data.py ddss_stability.prefix_counts 10000
# check valid and test for duplicates and remove them
awk -F"[|\t]" 'NR==FNR { lines[$2]=1; next } !($2 in lines)' ddss_stability.prefix_counts.train ddss_stability.prefix_counts.valid > ddss_stability.prefix_counts.valid.final
awk -F"[|\t]" 'NR==FNR { lines[$2]=1; next } !($2 in lines)' ddss_stability.prefix_counts.train ddss_stability.prefix_counts.test > ddss_stability.prefix_counts.test.final
```
### Predicting controllability - balanced sample, systems of degree 3 to 6
```bash
# generation command
python train.py --dump_path '/checkpoint/fcharton/dumped' --save_periodic 0 --fp16 false --amp -1 --emb_dim 128 --n_enc_layers 2 --n_dec_layers 2 --n_heads 8 --dropout 0 --attention_dropout 0 --share_inout_emb true --sinusoidal_embeddings false --max_len 512 --batch_size 32 --optimizer 'adam,lr=0.0001' --clip_grad_norm 5 --epoch_size 300000 --max_epoch 100000 --accumulate_gradients 1 --env_name ode --max_int 10 --precision 3 --skip_zero_gradient true --positive false --nonnull true --prob_int 0.3 --min_degree 3 --max_degree 6 --eval_value 0.9 --allow_complex false --jacobian_precision 3 --qualitative true --num_workers 20 --cpu true --stopping_criterion '' --validation_metrics '' --export_data true --reload_data '' --tasks ode_control --env_base_seed -1 --exp_name ddss_gen_ctrl
# assemble non controllable cases from prefixes
cat */data.prefix \
| grep '0$' \
| awk 'BEGIN{PROCINFO["sorted_in"]="@val_num_desc"}{c[$0]++}END{for (i in c) printf("%i|%s\n",c[i],i)}' \
> ddss_control.prefix_counts.0
# count them
wc -l ddss_control.prefix_counts.0 # 13,298,967
# assemble controllable cases from prefixes
cat */data.prefix \
| grep '1$' \
| awk 'BEGIN{PROCINFO["sorted_in"]="@val_num_desc"}{c[$0]++}END{for (i in c) printf("%i|%s\n",c[i],i)}' \
| head -n 13298967 > ddss_control.prefix_counts.1
# assemble prefix_counts
cat ddss_control.prefix_counts.0 ddss_control.prefix_counts.1 | shuf > ddss_control.prefix_counts
# create train, valid and test samples
python ~/MathsFromExamples/split_data.py ddss_control.prefix_counts 10000
# check valid and test for duplicates and remove them
awk -F"[|\t]" 'NR==FNR { lines[$2]=1; next } !($2 in lines)' ddss_control.prefix_counts.train ddss_control.prefix_counts.valid > ddss_control.prefix_counts.valid.final
awk -F"[|\t]" 'NR==FNR { lines[$2]=1; next } !($2 in lines)' ddss_control.prefix_counts.train ddss_control.prefix_counts.test > ddss_control.prefix_counts.test.final
```
### Predicting non autonomous controllability: unbalanced sample, systems of 2 to 3 equations
```bash
# generation command
python train.py --dump_path '/checkpoint/fcharton/dumped' --save_periodic 0 --fp16 false --amp -1 --emb_dim 128 --n_enc_layers 2 --n_dec_layers 2 --n_heads 8 --dropout 0 --attention_dropout 0 --share_inout_emb true --sinusoidal_embeddings false --max_len 512 --batch_size 32 --optimizer 'adam,lr=0.0001' --clip_grad_norm 5 --epoch_size 300000 --max_epoch 100000 --accumulate_gradients 1 --env_name ode --max_int 10 --precision 3 --skip_zero_gradient true --positive false --nonnull true --prob_int 0.3 --min_degree 2 --max_degree 3 --eval_value 0.5 --allow_complex false --jacobian_precision 3 --qualitative false --tau 1 --num_workers 20 --cpu true --stopping_criterion '' --validation_metrics '' --export_data true --reload_data '' --tasks ode_control --env_base_seed -1 --exp_name ddss_gen_ctrl_t
# assemble raw data file from prefixes
cat */data.prefix \
| awk 'BEGIN{PROCINFO["sorted_in"]="@val_num_desc"}{c[$0]++}END{for (i in c) printf("%i|%s\n",c[i],i)}' \
> ddss_control_t.prefix_counts
# create train, valid and test samples
python ~/MathsFromExamples/split_data.py ddss_control_t.prefix_counts 10000
# check valid and test for duplicates and remove them
awk -F"[|\t]" 'NR==FNR { lines[$2]=1; next } !($2 in lines)' ddss_control_t.prefix_counts.train ddss_control_t.prefix_counts.valid > ddss_control_t.prefix_counts.valid.final
awk -F"[|\t]" 'NR==FNR { lines[$2]=1; next } !($2 in lines)' ddss_control_t.prefix_counts.train ddss_control_t.prefix_counts.test > ddss_control_t.prefix_counts.test.final
```
### Predicting non autonomous controllability: balanced sample, systems of 2 to 3 equations
```bash
# generation command
python train.py --dump_path '/checkpoint/fcharton/dumped' --save_periodic 0 --fp16 false --amp -1 --emb_dim 128 --n_enc_layers 2 --n_dec_layers 2 --n_heads 8 --dropout 0 --attention_dropout 0 --share_inout_emb true --sinusoidal_embeddings false --max_len 512 --batch_size 32 --optimizer 'adam,lr=0.0001' --clip_grad_norm 5 --epoch_size 300000 --max_epoch 100000 --accumulate_gradients 1 --env_name ode --max_int 10 --precision 3 --skip_zero_gradient true --positive false --nonnull true --prob_int 0.3 --min_degree 2 --max_degree 3 --eval_value 0.5 --allow_complex false --jacobian_precision 3 --qualitative false --tau 1 --num_workers 20 --cpu true --stopping_criterion '' --validation_metrics '' --export_data true --reload_data '' --tasks ode_control --env_base_seed -1 --exp_name ddss_gen_ctrl_t
# assemble non controllable cases from prefixes
cat */data.prefix \
| grep '0$' \
| awk 'BEGIN{PROCINFO["sorted_in"]="@val_num_desc"}{c[$0]++}END{for (i in c) printf("%i|%s\n",c[i],i)}' \
> ddss_control_t.prefix_counts.0
# count them
wc -l ddss_control_t.prefix_counts.0 # 11,572,508
# assemble controllable cases from prefixes
cat */data.prefix \
| grep '1$' \
| awk 'BEGIN{PROCINFO["sorted_in"]="@val_num_desc"}{c[$0]++}END{for (i in c) printf("%i|%s\n",c[i],i)}' \
| head -n 11572508 > ddss_control_t.prefix_counts.1
# assemble prefix_counts
cat ddss_control_t.prefix_counts.0 ddss_control_t.prefix_counts.1 | shuf > ddss_control_t_bal.prefix_counts
# create train, valid and test samples
python ~/MathsFromExamples/split_data.py ddss_control_t_bal.prefix_counts 10000
# check valid and test for duplicates and remove them
awk -F"[|\t]" 'NR==FNR { lines[$2]=1; next } !($2 in lines)' ddss_control_t_bal.prefix_counts.train ddss_control_t_bal.prefix_counts.valid > ddss_control_t_bal.prefix_counts.valid.final
awk -F"[|\t]" 'NR==FNR { lines[$2]=1; next } !($2 in lines)' ddss_control_t_bal.prefix_counts.train ddss_control_t_bal.prefix_counts.test > ddss_control_t_bal.prefix_counts.test.final
```
### Predicting control matrices - sample of controllable systems, of degree 3 to 6
```bash
# generation command
python train.py --dump_path '/checkpoint/fcharton/dumped' --save_periodic 0 --fp16 false --amp -1 --emb_dim 128 --n_enc_layers 2 --n_dec_layers 2 --n_heads 8 --dropout 0 --attention_dropout 0 --share_inout_emb true --sinusoidal_embeddings false --max_len 512 --batch_size 32 --optimizer 'adam,lr=0.0001' --clip_grad_norm 5 --epoch_size 300000 --max_epoch 100000 --accumulate_gradients 1 --env_name ode --max_int 10 --precision 3 --skip_zero_gradient true --positive false --nonnull true --prob_int 0.3 --min_degree 3 --max_degree 6 --eval_value 0.5 --allow_complex false --jacobian_precision 2 --qualitative false --predict_gramian true --prob_positive 1.0 --num_workers 20 --cpu true --stopping_criterion '' --validation_metrics '' --export_data true --reload_data '' --tasks ode_control --env_base_seed -1 --exp_name ddss_gen_gram
# assemble raw data file from prefixes
cat */data.prefix \
| awk 'BEGIN{PROCINFO["sorted_in"]="@val_num_desc"}{c[$0]++}END{for (i in c) printf("%i|%s\n",c[i],i)}' \
> ddss_gram.prefix_counts
# create train, valid and test samples
python ~/MathsFromExamples/split_data.py ddss_gram.prefix_counts 10000
# check valid and test for duplicates and remove them
awk -F"[|\t]" 'NR==FNR { lines[$2]=1; next } !($2 in lines)' ddss_gram.prefix_counts.train ddss_gram.prefix_counts.valid > ddss_gram.prefix_counts.valid.final
awk -F"[|\t]" 'NR==FNR { lines[$2]=1; next } !($2 in lines)' ddss_gram.prefix_counts.train ddss_gram.prefix_counts.test > ddss_gram.prefix_counts.test.final
```
### Predicting the existence of solutions of partial differential equations
```bash
# generation command
python train.py --dump_path '/checkpoint/fcharton/dumped' --save_periodic 0 --fp16 false --amp -1 --emb_dim 128 --n_enc_layers 2 --n_dec_layers 2 --n_heads 8 --dropout 0 --attention_dropout 0 --share_inout_emb true --sinusoidal_embeddings false --max_len 512 --batch_size 32 --optimizer 'adam,lr=0.0001' --clip_grad_norm 5 --epoch_size 300000 --max_epoch 100000 --accumulate_gradients 1 --env_name ode --max_int 10 --precision 2 --jacobian_precision 2 --positive false --nonnull true --allow_complex false --predict_bounds true --skip_zero_gradient true --prob_int 0.3 --min_degree 2 --max_degree 6 --eval_value 0.01 --prob_positive -1.0 --num_workers 20 --cpu true --stopping_criterion '' --validation_metrics '' --export_data true --reload_data '' --tasks fourier_cond_init --env_base_seed -1 --exp_name ddss_gen_fourier
# assemble raw data file from prefixes
cat */data.prefix \
| awk 'BEGIN{PROCINFO["sorted_in"]="@val_num_desc"}{c[$0]++}END{for (i in c) printf("%i|%s\n",c[i],i)}' \
> ddss_fourier.prefix_counts
# create train, valid and test samples
python ~/MathsFromExamples/split_data.py ddss_fourier.prefix_counts 10000
# check valid and test for duplicates and remove them
awk -F"[|\t]" 'NR==FNR { lines[$2]=1; next } !($2 in lines)' ddss_fourier.prefix_counts.train ddss_fourier.prefix_counts.valid > ddss_fourier.prefix_counts.valid.final
awk -F"[|\t]" 'NR==FNR { lines[$2]=1; next } !($2 in lines)' ddss_fourier.prefix_counts.train ddss_fourier.prefix_counts.test > ddss_fourier.prefix_counts.test.final
```
## Pre-trained models
We provide 7 pretrained models for the various problems. Below are the links, the dataset they were trained on, and the parameters used, and the performance on the validation set (valid.final in the same directory, 10 000 held-out examples).
### Predicting stability (qualitative)
* Model: https://dl.fbaipublicfiles.com/MathsFromExamples/models/ddss_stab_quali.pth
* Training set: `ddss_stability_balanced.prefix_counts.train`
* Accuracy over validation set: 97.1%
* Training parameters (command line)
```bash
python train.py --dump_path '/checkpoint/fcharton/dumped' --save_periodic 0 --fp16 true --amp 2 --accumulate_gradients 1 --emb_dim 512 --batch_size 128 --batch_size_eval 256 --n_enc_layers 6 --n_dec_layers 6 --n_heads 8 --dropout 0 --attention_dropout 0 --share_inout_emb true --sinusoidal_embeddings false --max_len 512 --optimizer 'adam,lr=0.0001' --clip_grad_norm 5 --epoch_size 300000 --max_epoch 100000 --num_workers 1 --export_data false --env_name ode --max_int 10 --positive false --nonnull true --qualitative true --skip_zero_gradient true --prob_int 0.3 --max_degree 5 --min_degree 2 --eval_verbose 0 --beam_eval 0 --eval_size 10000 --tasks ode_convergence_speed --reload_data 'ode_convergence_speed,/checkpoint/fcharton/dumped/ddss_gen_stab_bal/ddss_stability_balanced.prefix_counts.train,/checkpoint/fcharton/dumped/ddss_gen_stab_bal/ddss_stability_balanced.prefix_counts.valid.final,/checkpoint/fcharton/dumped/ddss_gen_stab_bal/ddss_stability_balanced.prefix_counts.test.final' --reload_size 40000000 --stopping_criterion 'valid_ode_convergence_speed_acc,40' --validation_metrics valid_ode_convergence_speed_acc --env_base_seed -1 --exp_name ddss_stab_quali
```
### Stability: computing convergence speed
* Model: https://dl.fbaipublicfiles.com/MathsFromExamples/models/ddss_stab_quanti.pth
* Training set:`ddss_stability.prefix_counts.train`
* Accuracy over validation set: 87.4%
* Training parameters (command line)
```bash
python train.py --dump_path '/checkpoint/fcharton/dumped' --save_periodic 0 --fp16 true --amp 2 --accumulate_gradients 1 --emb_dim 1024 --batch_size 128 --batch_size_eval 256 --n_enc_layers 8 --n_dec_layers 8 --n_heads 8 --dropout 0 --attention_dropout 0 --share_inout_emb true --sinusoidal_embeddings false --max_len 512 --optimizer 'adam_inverse_sqrt,warmup_updates=10000,lr=0.0001,weight_decay=0.01' --clip_grad_norm 5 --epoch_size 300000 --max_epoch 100000 --num_workers 1 --export_data false --env_name ode --max_int 10 --positive false --nonnull true --skip_zero_gradient true --prob_int 0.3 --max_degree 6 --min_degree 2 --eval_verbose 0 --beam_eval 1 --eval_size 10000 --tasks ode_convergence_speed --reload_data 'ode_convergence_speed,/checkpoint/fcharton/dumped/ddss_gen_stab/ddss_stability.prefix_counts.train,/checkpoint/fcharton/dumped/ddss_gen_stab/ddss_stability.prefix_counts.valid.final,/checkpoint/fcharton/dumped/ddss_gen_stab/ddss_stability.prefix_counts.test.final' --reload_size 40000000 --stopping_criterion 'valid_ode_convergence_speed_beam_acc,40' --validation_metrics valid_ode_convergence_speed_beam_acc --env_base_seed -1 --exp_name ddss_stab_quanti
```
### Predicting autonomous controllability
* Model: https://dl.fbaipublicfiles.com/MathsFromExamples/models/ddss_ctrl.pth
* Training set: `ddss_control.prefix_counts.train`
* Accuracy over validation set: 97.4%
* Training parameters (command line)
```bash
python train.py --dump_path '/checkpoint/fcharton/dumped' --save_periodic 0 --fp16 true --amp 2 --accumulate_gradients 1 --emb_dim 512 --batch_size 256 --batch_size_eval 256 --n_enc_layers 6 --n_dec_layers 6 --n_heads 8 --dropout 0 --attention_dropout 0 --share_inout_emb true --sinusoidal_embeddings false --max_len 512 --optimizer 'adam_inverse_sqrt,warmup_updates=10000,lr=0.0001,weight_decay=0.01' --clip_grad_norm 5 --epoch_size 300000 --max_epoch 100000 --num_workers 1 --export_data false --env_name ode --max_int 10 --positive false --nonnull true --skip_zero_gradient true --prob_int 0.3 --max_degree 6 --min_degree 3 --eval_value 0.9 --qualitative true --eval_verbose 0 --beam_eval 0 --eval_size 10000 --tasks ode_control --reload_data 'ode_control,/checkpoint/fcharton/dumped/ddss_gen_ctrl/ddss_control.prefix_counts.train,/checkpoint/fcharton/dumped/ddss_gen_ctrl/ddss_control.prefix_counts.valid.final,/checkpoint/fcharton/dumped/ddss_gen_ctrl/ddss_control.prefix_counts.test.final' --reload_size 40000000 --stopping_criterion 'valid_ode_control_acc,20' --validation_metrics valid_ode_control_acc --env_base_seed -1 --exp_name ddss_ctrl
```
### Predicting non-autonomous controllability
* Model: https://dl.fbaipublicfiles.com/MathsFromExamples/models/ddss_ctrl_t.pth
* Training set: `ddss_control_t.prefix_counts.train`
* Accuracy over validation set: 99.6%
* Training parameters (command line)
```bash
python train.py --dump_path '/checkpoint/fcharton/dumped' --save_periodic 0 --fp16 true --amp 2 --accumulate_gradients 1 --emb_dim 512 --batch_size 256 --batch_size_eval 256 --n_enc_layers 6 --n_dec_layers 6 --n_heads 8 --dropout 0 --attention_dropout 0 --share_inout_emb true --sinusoidal_embeddings false --max_len 512 --optimizer 'adam_inverse_sqrt,warmup_updates=10000,lr=0.0001,weight_decay=0.01' --clip_grad_norm 5 --epoch_size 300000 --max_epoch 100000 --num_workers 1 --export_data false --env_name ode --max_int 10 --positive false --nonnull true --skip_zero_gradient true --prob_int 0.3 --max_degree 3 --min_degree 2 --eval_value 0.5 --qualitative false --tau 1 --eval_verbose 0 --beam_eval 0 --eval_size 10000 --tasks ode_control --reload_data 'ode_control,/checkpoint/fcharton/dumped/ddss_gen_ctrl_t/ddss_control_t.prefix_counts.train,/checkpoint/fcharton/dumped/ddss_gen_ctrl_t/ddss_control_t.prefix_counts.valid.final,/checkpoint/fcharton/dumped/ddss_gen_ctrl_t/ddss_control_t.prefix_counts.test.final' --reload_size 40000000 --stopping_criterion 'valid_ode_control_acc,60' --validation_metrics valid_ode_control_acc --env_base_seed -1 --exp_name ddss_ctrl_t
```
### Computing control matrices: predicting solution up to 10%
* Model: https://dl.fbaipublicfiles.com/MathsFromExamples/models/ddss_gram_approx.pth
* Training set: `ddss_gram.prefix_counts.train`
* Accuracy over validation set: 24.5%
* Training parameters (command line)
```bash
python /private/home/fcharton/workdir/ddss_gram/2021_03_18_12_05_11/train.py --dump_path '/checkpoint/fcharton/dumped' --save_periodic 0 --fp16 true --amp 2 --accumulate_gradients 1 --emb_dim 512 --batch_size 128 --batch_size_eval 128 --n_enc_layers 6 --n_dec_layers 6 --n_heads 8 --dropout 0 --attention_dropout 0 --share_inout_emb true --sinusoidal_embeddings false --max_len 512 --optimizer 'adam,lr=0.0001' --clip_grad_norm 5 --epoch_size 300000 --max_epoch 100000 --num_workers 1 --export_data false --env_name ode --max_int 10 --positive false --nonnull true --skip_zero_gradient true --prob_int 0.3 --max_degree 6 --min_degree 3 --eval_value 0.5 --predict_gramian true --euclidian_metric true --auxiliary_task false --eval_verbose 0 --beam_eval 1 --eval_size 10000 --tasks ode_control --reload_data 'ode_control,/checkpoint/fcharton/dumped/ddss_gen_gram/ddss_gram.prefix_counts.train,/checkpoint/fcharton/dumped/ddss_gen_gram/ddss_gram.prefix_counts.valid.final,/checkpoint/fcharton/dumped/ddss_gen_gram/ddss_gram.prefix_counts.test.final' --reload_size 50000000 --stopping_criterion 'valid_ode_control_beam_acc,40' --validation_metrics valid_ode_control_beam_acc --env_base_seed -1 --exp_name ddss_gram
```
### Computing control matrices: predicting a correct mathematical solution
* Model: https://dl.fbaipublicfiles.com/MathsFromExamples/models/ddss_gram_math.pth
* Training set: `ddss_gram.prefix_counts.train`
* Accuracy over validation set: 63.5%
* Training parameters (command line)
```bash
python /private/home/fcharton/workdir/ddss_gram/2021_03_09_12_09_38/train.py --dump_path '/checkpoint/fcharton/dumped' --save_periodic 0 --fp16 true --amp 2 --accumulate_gradients 1 --emb_dim 512 --batch_size 128 --batch_size_eval 128 --n_enc_layers 6 --n_dec_layers 6 --n_heads 8 --dropout 0 --attention_dropout 0 --share_inout_emb true --sinusoidal_embeddings false --max_len 512 --optimizer 'adam,lr=0.0001' --clip_grad_norm 5 --epoch_size 300000 --max_epoch 100000 --num_workers 1 --export_data false --env_name ode --max_int 10 --positive false --nonnull true --skip_zero_gradient true --prob_int 0.3 --max_degree 6 --min_degree 3 --eval_value 0.5 --predict_gramian true --euclidian_metric false --auxiliary_task false --eval_verbose 0 --beam_eval 1 --eval_size 10000 --tasks ode_control --reload_data 'ode_control,/checkpoint/fcharton/dumped/ddss_gen_gram/ddss_gram.prefix_counts.train,/checkpoint/fcharton/dumped/ddss_gen_gram/ddss_gram.prefix_counts.valid.final,/checkpoint/fcharton/dumped/ddss_gen_gram/ddss_gram.prefix_counts.test.final' --reload_size 40000000 --stopping_criterion 'valid_ode_control_beam_acc,20' --validation_metrics valid_ode_control_beam_acc --env_base_seed -1 --exp_name ddss_gram
```
### Predicting the existence of solutions of partial differential equations
* Model: https://dl.fbaipublicfiles.com/MathsFromExamples/models/ddss_fourier.pth
* Training set: `ddss_fourier.prefix_counts.train`
* Accuracy over validation set: 98.6%
* Training parameters (command line)
```bash
python train.py --dump_path '/checkpoint/fcharton/dumped' --save_periodic 0 --fp16 false --amp -1 --accumulate_gradients 1 --emb_dim 512 --n_enc_layers 8 --n_dec_layers 8 --batch_size 64 --batch_size_eval 64 --eval_size 10000 --predict_jacobian false --n_heads 8 --dropout 0 --attention_dropout 0 --share_inout_emb true --sinusoidal_embeddings false --max_len 1024 --optimizer 'adam_inverse_sqrt,warmup_updates=10000,lr=0.0001,weight_decay=0.01' --clip_grad_norm 5 --epoch_size 300000 --max_epoch 100000 --num_workers 1 --export_data false --env_name ode --max_int 10 --precision 3 --jacobian_precision 1 --positive false --nonnull true --prob_int '0.3' --max_degree 6 --eval_value 0.5 --allow_complex false --predict_bounds true --skip_zero_gradient true --eval_verbose 0 --beam_eval 0 --tasks fourier_cond_init --reload_data 'fourier_cond_init,/checkpoint/fcharton/dumped/ddss_gen_fourier/ddss_fourier.prefix_counts.train,/checkpoint/fcharton/dumped/ddss_gen_fourier/ddss_fourier.prefix_counts.valid,/checkpoint/fcharton/dumped/ddss_gen_fourier/ddss_fourier.prefix_counts.test' --reload_size 40000000 --stopping_criterion 'valid_fourier_cond_init_acc,20' --validation_metrics valid_fourier_cond_init_acc --env_base_seed -1 --exp_name ddss_fourier
```
## Evaluating trained models
To evaluate over a trained model `model.pth` on a specific test set `test.data`, run the model with the same parameters as training, setting `--eval_only true`and `--reload_model` to the path to your model (e.g. `--reload_model /model_path/model.pth`), and setting the second file `--reload_data`to your test data (e.g. ` --reload_data 'ode_control,/checkpoint/fcharton/dumped/ddss_gen_gram/ddss_gram.prefix_counts.train,/MYPATH/test.data,/checkpoint/fcharton/dumped/ddss_gen_gram/ddss_gram.prefix_counts.test.final'`). Set `--eval_size`to the size of your dataset. At present, only the validation dataset is used for evaluation, but you can change this by toggling comments on lines 367 and 368 of file `evaluator.py`.
## Citation
This code is released under a Creative Commons License, see LICENCE file for more details.
If you use this code, consider citing
@misc{charton2021learning,
title={Learning advanced mathematical computations from examples},
author={François Charton and Amaury Hayat and Guillaume Lample},
year={2021},
eprint={2006.06462},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
================================================
FILE: split_data.py
================================================
# Copyright (c) 2020-present, Facebook, Inc.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
#
import io
import os
import sys
import math
if __name__ == "__main__":
assert len(sys.argv) == 3
data_path = sys.argv[1]
trn_path = sys.argv[1] + ".train"
vld_path = sys.argv[1] + ".valid"
tst_path = sys.argv[1] + ".test"
vld_tst_size = int(sys.argv[2])
assert not os.path.isfile(trn_path)
assert not os.path.isfile(vld_path)
assert not os.path.isfile(tst_path)
assert vld_tst_size > 0
print(f"Reading data from {data_path} ...")
with io.open(data_path, mode="r", encoding="utf-8") as f:
lines = [line for line in f]
total_size = len(lines)
print(f"Read {total_size} lines.")
assert 2 * vld_tst_size < total_size
alpha = math.log(total_size - 0.5) / math.log(2 * vld_tst_size)
assert int((2 * vld_tst_size) ** alpha) == total_size - 1
vld_tst_indices = [int(i ** alpha) for i in range(1, 2 * vld_tst_size + 1)]
vld_indices = set(vld_tst_indices[::2])
tst_indices = set(vld_tst_indices[1::2])
assert len(vld_tst_indices) == 2 * vld_tst_size
assert max(vld_tst_indices) == total_size - 1
assert len(vld_indices) == vld_tst_size
assert len(tst_indices) == vld_tst_size
# sanity check
total = 0
power = 0
while True:
a = 10 ** power
b = 10 * a
s = len([True for x in vld_tst_indices if a <= x < b and x <= total_size])
if s == 0:
break
print("[%12i %12i[: %i" % (a, b, s))
total += s
power += 1
assert total == 2 * vld_tst_size
print(f"Writing train data to {trn_path} ...")
print(f"Writing valid data to {vld_path} ...")
print(f"Writing test data to {tst_path} ...")
f_train = io.open(trn_path, mode="w", encoding="utf-8")
f_valid = io.open(vld_path, mode="w", encoding="utf-8")
f_test = io.open(tst_path, mode="w", encoding="utf-8")
for i, line in enumerate(lines):
if i in vld_indices:
f_valid.write(line)
elif i in tst_indices:
f_test.write(line)
else:
f_train.write(line)
if i % 1000000 == 0:
print(i, end="...", flush=True)
f_train.close()
f_valid.close()
f_test.close()
================================================
FILE: src/__init__.py
================================================
================================================
FILE: src/envs/__init__.py
================================================
# Copyright (c) 2020-present, Facebook, Inc.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
#
from logging import getLogger
from .ode import ODEEnvironment
logger = getLogger()
ENVS = {
'ode': ODEEnvironment,
}
def build_env(params):
"""
Build environment.
"""
env = ENVS[params.env_name](params)
# tasks
tasks = [x for x in params.tasks.split(',') if len(x) > 0]
assert len(tasks) == len(set(tasks)) > 0
assert all(task in env.TRAINING_TASKS for task in tasks)
params.tasks = tasks
logger.info(f'Training tasks: {", ".join(tasks)}')
return env
================================================
FILE: src/envs/ode.py
================================================
# Copyright (c) 2020-present, Facebook, Inc.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
#
from logging import getLogger
import os
import io
import sys
from collections import OrderedDict
import numpy as np
import torch
from torch.utils.data.dataset import Dataset
from torch.utils.data import DataLoader
import sympy as sp
from sympy.core.cache import clear_cache
import control as ctrl
from scipy.linalg import expm
from scipy.integrate import cumtrapz
import scipy.optimize as opt
from ..utils import bool_flag
from ..utils import timeout, TimeoutError
CLEAR_SYMPY_CACHE_FREQ = 10000
SPECIAL_WORDS = ["<s>", "</s>", "<pad>", "(", ")"]
SPECIAL_WORDS = SPECIAL_WORDS + [f"<SPECIAL_{i}>" for i in range(10)]
logger = getLogger()
class UnknownSymPyOperator(Exception):
pass
class InvalidPrefixExpression(Exception):
def __init__(self, data):
self.data = data
def __str__(self):
return repr(self.data)
def has_inf_nan(*args):
"""
Detect whether some SymPy expressions contain a NaN / Infinity symbol.
"""
for f in args:
if f.has(sp.nan) or f.has(sp.oo) or f.has(-sp.oo) or f.has(sp.zoo):
return True
return False
def second_index(x, bal):
if bal not in x:
return len(x)
p1 = x.index(bal)
if bal not in x[p1 + 1 :]:
return len(x)
p2 = x[p1 + 1 :].index(bal)
return p2 + p1
def simplify(f, seconds):
"""
Simplify an expression.
"""
assert seconds > 0
@timeout(seconds)
def _simplify(f):
try:
f2 = sp.simplify(f)
if any(s.is_Dummy for s in f2.free_symbols):
logger.warning(f"Detected Dummy symbol when simplifying {f} to {f2}")
return f
else:
return f2
except TimeoutError:
return f
except Exception as e:
logger.warning(f"{type(e).__name__} exception when simplifying {f}")
return f
return _simplify(f)
def expr_to_fun_real(x, fun, dimension):
# for i in range(dimension):
# v='x'+str(i+1)
# v=sp.symbols('x'+str(i))
# f=f.subs(v,x[i])
Eval = OrderedDict({sp.Symbol(f"x{i}"): x[i] for i in range(dimension)})
fun = sp.re(fun.subs(Eval)).evalf()
fun = min(fun, 1e15)
fun = max(fun, -1e15)
return fun
class Node:
def __init__(self, value, children=None):
self.value = value
self.children = children if children else []
def push_child(self, child):
self.children.append(child)
def prefix(self):
s = str(self.value)
for c in self.children:
s += ", " + c.prefix()
return s
# export to latex qtree format: prefix with \Tree, use package qtree
def qtree_prefix(self):
s = "[.$" + str(self.value) + "$ "
for c in self.children:
s += c.qtree_prefix()
s += "]"
return s
def infix(self):
nb_children = len(self.children)
if nb_children <= 1:
s = str(self.value)
if nb_children == 1:
s += "(" + self.children[0].infix() + ")"
return s
s = "(" + self.children[0].infix()
for c in self.children[1:]:
s = s + " " + str(self.value) + " " + c.infix()
return s + ")"
def __len__(self):
lenc = 1
for c in self.children:
lenc += len(c)
return lenc
def __str__(self):
# infix a default print
return self.infix()
class ODEEnvironment(object):
TRAINING_TASKS = {
"ode_convergence_speed",
"ode_control",
"fourier_cond_init",
}
def __init__(self, params):
self.max_degree = params.max_degree
self.min_degree = params.min_degree
assert self.min_degree >= 2
assert self.max_degree >= self.min_degree
self.max_ops = 200
self.max_int = params.max_int
self.positive = params.positive
self.nonnull = params.nonnull
self.predict_jacobian = params.predict_jacobian
self.predict_gramian = params.predict_gramian
self.qualitative = params.qualitative
self.allow_complex = params.allow_complex
self.reversed_eval = params.reversed_eval
self.euclidian_metric = params.euclidian_metric
self.auxiliary_task = params.auxiliary_task
self.tau = params.tau
self.gramian_norm1 = params.gramian_norm1
self.gramian_tolerance = params.gramian_tolerance
self.min_expr_len_factor_cspeed = params.min_expr_len_factor_cspeed
self.max_expr_len_factor_cspeed = params.max_expr_len_factor_cspeed
self.custom_unary_probs = params.custom_unary_probs
self.prob_trigs = params.prob_trigs
self.prob_arc_trigs = params.prob_arc_trigs
self.prob_logs = params.prob_logs
self.prob_others = 1.0 - self.prob_trigs - self.prob_arc_trigs - self.prob_logs
assert self.prob_others >= 0.0
self.prob_int = params.prob_int
self.precision = params.precision
self.jacobian_precision = params.jacobian_precision
self.max_len = params.max_len
self.eval_value = params.eval_value
self.skip_zero_gradient = params.skip_zero_gradient
self.prob_positive = params.prob_positive
self.np_positive = np.zeros(self.max_degree + 1, dtype=int)
self.np_total = np.zeros(self.max_degree + 1, dtype=int)
self.complex_input = "fourier" in params.tasks
self.SYMPY_OPERATORS = {
# Elementary functions
sp.Add: "+",
sp.Mul: "*",
sp.Pow: "^",
sp.exp: "exp",
sp.log: "ln",
# sp.Abs: 'abs',
# sp.sign: 'sign',
# Trigonometric Functions
sp.sin: "sin",
sp.cos: "cos",
sp.tan: "tan",
# sp.cot: 'cot',
# sp.sec: 'sec',
# sp.csc: 'csc',
# Trigonometric Inverses
sp.asin: "asin",
sp.acos: "acos",
sp.atan: "atan",
# sp.acot: 'acot',
# sp.asec: 'asec',
# sp.acsc: 'acsc',
sp.DiracDelta: "delta0",
}
self.operators_conv = {
"+": 2,
"-": 2,
"*": 2,
"/": 2,
"sqrt": 1,
"exp": 1,
"ln": 1,
"sin": 1,
"cos": 1,
"tan": 1,
"asin": 1,
"acos": 1,
"atan": 1,
}
self.trig_ops = ["sin", "cos", "tan"]
self.arctrig_ops = ["asin", "acos", "atan"]
self.exp_ops = ["exp", "ln"]
self.other_ops = ["sqrt"]
self.operators_lyap = {
"+": 2,
"-": 2,
"*": 2,
"/": 2,
"^": 2,
"sqrt": 1,
"exp": 1,
"ln": 1,
"sin": 1,
"cos": 1,
"tan": 1,
"asin": 1,
"acos": 1,
"atan": 1,
"delta0": 1,
}
self.operators = (
self.operators_lyap if "fourier" in params.tasks else self.operators_conv
)
self.unaries = [o for o in self.operators.keys() if self.operators[o] == 1]
self.binaries = [o for o in self.operators.keys() if self.operators[o] == 2]
self.unary = len(self.unaries) > 0
self.predict_bounds = params.predict_bounds
assert self.max_int >= 1
assert self.precision >= 2
# variables
self.variables = OrderedDict(
{f"x{i}": sp.Symbol(f"x{i}") for i in range(2 * self.max_degree)}
)
self.eval_point = OrderedDict(
{
self.variables[f"x{i}"]: self.eval_value
for i in range(2 * self.max_degree)
}
)
# symbols / elements
self.constants = ["pi", "E"]
self.symbols = ["I", "INT+", "INT-", "FLOAT+", "FLOAT-", ".", "10^"]
self.elements = [str(i) for i in range(10)]
# SymPy elements
self.local_dict = {}
for k, v in list(self.variables.items()):
assert k not in self.local_dict
self.local_dict[k] = v
# vocabulary
self.words = (
SPECIAL_WORDS
+ self.constants
+ list(self.variables.keys())
+ list(self.operators.keys())
+ self.symbols
+ self.elements
)
self.id2word = {i: s for i, s in enumerate(self.words)}
self.word2id = {s: i for i, s in self.id2word.items()}
assert len(self.words) == len(set(self.words))
# number of words / indices
self.n_words = params.n_words = len(self.words)
self.eos_index = params.eos_index = 0
self.pad_index = params.pad_index = 1
self.func_separator = "<SPECIAL_3>" # separate equations in a system
self.line_separator = "<SPECIAL_4>" # separate lines in a matrix
self.list_separator = "<SPECIAL_5>" # separate elements in a list
self.mtrx_separator = "<SPECIAL_6>" # end of a matrix
self.neg_inf = "<SPECIAL_7>" # negative infinity
self.pos_inf = "<SPECIAL_8>" # positive infinity
logger.info(f"words: {self.word2id}")
# initialize distribution for binary and unary-binary trees
# self.max_ops + 1 should be enough
self.distrib = self.generate_dist(2 * self.max_ops)
def get_integer(self, cplex=False):
if cplex:
i1 = self.rng.randint(1, 100000) / 100000
sign = 1 if self.rng.randint(2) == 0 else -1
e = self.rng.randint(2)
if e == 0:
return i1 * sign
else:
return complex(0.0, i1 * sign)
# i2 = self.rng.randint(1, 100000) / 100000
# sign2 = 1 if self.rng.randint(2) == 0 else -1
# return complex(i1 * sign, i2 * sign2)
if self.positive and self.nonnull:
return self.rng.randint(1, self.max_int + 1)
if self.positive:
return self.rng.randint(0, self.max_int + 1)
if self.nonnull:
s = self.rng.randint(1, 2 * self.max_int + 1)
return s if s <= self.max_int else (self.max_int - s)
return self.rng.randint(-self.max_int, self.max_int + 1)
def generate_leaf(self, degree, index):
if self.rng.rand() < self.prob_int:
return self.get_integer()
elif degree == 1:
return self.variables[f"x{index}"]
else:
return self.variables[f"x{self.rng.randint(degree)}"]
def generate_ops(self, arity):
if arity == 1:
if self.custom_unary_probs:
w = [
self.prob_trigs,
self.prob_arc_trigs,
self.prob_logs,
self.prob_others,
]
s = [self.trig_ops, self.arctrig_ops, self.exp_ops, self.other_ops]
return self.rng.choice(s, p=w)
else:
return self.rng.choice(self.unaries)
else:
return self.rng.choice(self.binaries)
def generate_dist(self, max_ops):
"""
`max_ops`: maximum number of operators
Enumerate the number of possible unary-binary trees
that can be generated from empty nodes.
D[e][n] represents the number of different binary trees with n nodes that
can be generated from e empty nodes, using the following recursion:
D(n, 0) = 0
D(0, e) = 1
D(n, e) = D(n, e - 1) + p_1 * D(n- 1, e) + D(n - 1, e + 1)
p1 = if binary trees, 1 if unary binary
"""
p1 = 1 if self.unary else 0
# enumerate possible trees
D = []
D.append([0] + ([1 for i in range(1, 2 * max_ops + 1)]))
for n in range(1, 2 * max_ops + 1): # number of operators
s = [0]
for e in range(1, 2 * max_ops - n + 1): # number of empty nodes
s.append(s[e - 1] + p1 * D[n - 1][e] + D[n - 1][e + 1])
D.append(s)
assert all(len(D[i]) >= len(D[i + 1]) for i in range(len(D) - 1))
return D
def sample_next_pos(self, nb_empty, nb_ops):
"""
Sample the position of the next node (binary case).
Sample a position in {0, ..., `nb_empty` - 1}.
"""
assert nb_empty > 0
assert nb_ops > 0
probs = []
if self.unary:
for i in range(nb_empty):
probs.append(self.distrib[nb_ops - 1][nb_empty - i])
for i in range(nb_empty):
probs.append(self.distrib[nb_ops - 1][nb_empty - i + 1])
probs = [p / self.distrib[nb_ops][nb_empty] for p in probs]
probs = np.array(probs, dtype=np.float64)
e = self.rng.choice(len(probs), p=probs)
arity = 1 if self.unary and e < nb_empty else 2
e %= nb_empty
return e, arity
def generate_tree(self, nb_ops, degree, index=0):
tree = Node(0)
empty_nodes = [tree]
next_en = 0
nb_empty = 1
while nb_ops > 0:
next_pos, arity = self.sample_next_pos(nb_empty, nb_ops)
for n in empty_nodes[next_en : next_en + next_pos]:
n.value = self.generate_leaf(degree, index)
next_en += next_pos
empty_nodes[next_en].value = self.generate_ops(arity)
for _ in range(arity):
e = Node(0)
empty_nodes[next_en].push_child(e)
empty_nodes.append(e)
nb_empty += arity - 1 - next_pos
nb_ops -= 1
next_en += 1
for n in empty_nodes[next_en:]:
n.value = self.generate_leaf(degree, index)
return tree
def generate_polynomial(
self, nterm, max_factor, degree, unaries, noconstant=True, complex_coeffs=False
):
pol = set()
for i in range(nterm):
nfactor = self.rng.randint(1, max_factor + 1)
vars = set()
for j in range(nfactor):
vars.add(
(self.rng.randint(0, degree), self.rng.randint(0, len(unaries)))
)
pol.add(tuple(vars))
for i in range(len(pol)):
v = list(pol)[i]
for j in range(len(v)):
op = unaries[v[j][1]]
var = Node(self.variables[f"x{v[j][0]}"])
if op == "id":
term = var
elif op == "ln":
term = Node("ln", [Node("+", [Node(1), var])])
elif len(op) > 3 and op[:3] == "pow":
term = Node("^", [var, Node(int(op[3:]))])
else:
term = Node(op, [var])
p = term if j == 0 else Node("*", [p, term])
coeff = self.get_integer(complex_coeffs)
if complex_coeffs:
p = Node("*", [Node(coeff), p])
tree = p if i == 0 else Node("+", [tree, p])
else:
if abs(coeff) != 1:
p = Node("*", [Node(abs(coeff)), p])
tree = p if i == 0 else Node("+" if coeff > 0 else "-", [tree, p])
if not noconstant:
coeff = self.get_integer(complex_coeffs)
if complex_coeffs:
tree = Node("+", [tree, Node(coeff)])
else:
tree = Node("+" if coeff > 0 else "-", [tree, Node(abs(coeff))])
return tree
def batch_sequences(self, sequences):
"""
Take as input a list of n sequences (torch.LongTensor vectors) and return
a tensor of size (slen, n) where slen is the length of the longest
sentence, and a vector lengths containing the length of each sentence.
"""
lengths = torch.LongTensor([len(s) + 2 for s in sequences])
sent = torch.LongTensor(lengths.max().item(), lengths.size(0)).fill_(
self.pad_index
)
assert lengths.min().item() > 2
sent[0] = self.eos_index
for i, s in enumerate(sequences):
sent[1 : lengths[i] - 1, i].copy_(s)
sent[lengths[i] - 1, i] = self.eos_index
return sent, lengths
def write_int(self, val):
"""
Convert a decimal integer to a representation in base 10.
"""
res = []
neg = val < 0
val = -val if neg else val
while True:
rem = val % 10
val = val // 10
res.append(str(rem))
if val == 0:
break
res.append("INT-" if neg else "INT+")
return res[::-1]
def parse_int(self, lst):
"""
Parse a list that starts with an integer.
Return the integer value, and the position it ends in the list.
"""
if len(lst) < 2 or lst[0] not in ["INT+", "INT-"] or not lst[1].isdigit():
raise InvalidPrefixExpression("Invalid integer in prefix expression")
val = int(lst[1])
i = 1
for x in lst[2:]:
if not x.isdigit():
break
val = val * 10 + int(x)
i += 1
if lst[0] == "INT-":
val = -val
return val, i + 1
def write_float(self, value, precision=None):
"""
Write a float number.
"""
precision = self.precision if precision is None else precision
assert value not in [-np.inf, np.inf]
res = ["FLOAT+"] if value >= 0.0 else ["FLOAT-"]
m, e = (f"%.{precision}e" % abs(value)).split("e")
assert e[0] in ["+", "-"]
e = int(e[1:] if e[0] == "+" else e)
return res + list(m) + ["10^"] + self.write_int(e)
def parse_float(self, lst):
"""
Parse a list that starts with a float.
Return the float value, and the position it ends in the list.
"""
if len(lst) < 2 or lst[0] not in ["FLOAT+", "FLOAT-"]:
return np.nan, 0
sign = -1 if lst[0] == "FLOAT-" else 1
if not lst[1].isdigit():
return np.nan, 1
mant = 0.0
i = 1
for x in lst[1:]:
if not (x.isdigit()):
break
mant = mant * 10.0 + int(x)
i += 1
if len(lst) > i and lst[i] == ".":
i += 1
mul = 0.1
for x in lst[i:]:
if not (x.isdigit()):
break
mant += mul * int(x)
mul *= 0.1
i += 1
mant *= sign
if len(lst) > i and lst[i] == "10^":
i += 1
try:
exp, offset = self.parse_int(lst[i:])
except InvalidPrefixExpression:
return np.nan, i
i += offset
else:
exp = 0
return mant * (10.0 ** exp), i
def write_complex(self, value, precision=None):
"""
Write a complex number.
"""
if value == 0:
return self.write_float(0, precision)
res = []
if value.imag != 0:
res = self.write_float(value.imag, precision) + ["I"]
if value.real != 0:
res = res + self.write_float(value.real, precision)
return res
def parse_complex(self, lst):
"""
Parse a list that starts with a complex number.
Return the complex value, and the position it ends in the list.
"""
first_val, len1 = self.parse_float(lst)
if np.isnan(first_val):
return np.nan, len1
if len(lst) <= len1 or lst[len1] != "I":
return first_val, len1
second_val, len2 = self.parse_float(lst[len1 + 1 :])
if np.isnan(second_val):
return complex(0, first_val), len1 + 1
return complex(second_val, first_val), len1 + 1 + len2
def input_to_infix(self, lst):
res = ""
degree, offset = self.parse_int(lst)
res = str(degree) + "|"
offset += 1
l1 = lst[offset:]
if self.complex_input:
nr_eqs = 1
else:
nr_eqs = degree
for i in range(nr_eqs):
s, l2 = self.prefix_to_infix(l1)
res = res + s + "|"
l1 = l2[1:]
return res[:-1]
def output_to_infix(self, lst):
val, _ = self.parse_float(lst)
return str(val)
def prefix_to_infix(self, expr):
"""
Parse an expression in prefix mode, and output it in either:
- infix mode (returns human readable string)
- develop mode (returns a dictionary with the simplified expression)
"""
cplx = self.complex_input
if len(expr) == 0:
raise InvalidPrefixExpression("Empty prefix list.")
t = expr[0]
if t in self.operators.keys():
args = []
l1 = expr[1:]
for _ in range(self.operators[t]):
i1, l1 = self.prefix_to_infix(l1)
args.append(i1)
if self.operators[t] == 1:
return f"{t}({args[0]})", l1
return f"({args[0]}{t}{args[1]})", l1
# return f'({args[0]}){t}({args[1]})', l1
elif t in self.variables or t in self.constants or t == "I":
return t, expr[1:]
elif t == "FLOAT+" or t == "FLOAT-":
if cplx:
val, i = self.parse_complex(expr)
else:
val, i = self.parse_float(expr)
else:
val, i = self.parse_int(expr)
return str(val), expr[i:]
def _sympy_to_prefix(self, op, expr):
"""
Parse a SymPy expression given an initial root operator.
"""
n_args = len(expr.args)
assert (
(op == "+" or op == "*")
and (n_args >= 2)
or (op != "+" and op != "*")
and (1 <= n_args <= 2)
)
# square root
if (
op == "^"
and isinstance(expr.args[1], sp.Rational)
and expr.args[1].p == 1
and expr.args[1].q == 2
):
return ["sqrt"] + self.sympy_to_prefix(expr.args[0])
# parse children
parse_list = []
for i in range(n_args):
if i == 0 or i < n_args - 1:
parse_list.append(op)
parse_list += self.sympy_to_prefix(expr.args[i])
return parse_list
def sympy_to_prefix(self, expr):
"""
Convert a SymPy expression to a prefix one.
"""
if isinstance(expr, sp.Symbol):
return [str(expr)]
elif isinstance(expr, sp.Integer):
return self.write_int(int(str(expr)))
elif isinstance(expr, sp.Float):
return self.write_float(float(str(expr)))
elif isinstance(expr, sp.Rational):
return ["/"] + self.write_int(int(expr.p)) + self.write_int(int(expr.q))
elif expr == sp.E:
return ["E"]
elif expr == sp.pi:
return ["pi"]
elif expr == sp.I:
raise UnknownSymPyOperator(f"Unknown SymPy operator: {expr}")
# SymPy operator
for op_type, op_name in self.SYMPY_OPERATORS.items():
if isinstance(expr, op_type):
return self._sympy_to_prefix(op_name, expr)
# unknown operator
raise UnknownSymPyOperator(f"Unknown SymPy operator: {expr}")
def encode_expr(self, tree, cplx=False):
pref = tree.prefix().split(", ")
res = []
for p in pref:
if (p.startswith("-") and p[1:].isdigit()) or p.isdigit():
res.extend(self.write_int(int(p)))
elif cplx and (
(p.startswith("-") and p[1:2].isdigit())
or p.startswith("(")
or p[0:1].isdigit()
):
res.extend(self.write_complex(complex(p)))
else:
res.append(p)
return res
@timeout(5)
def compute_gradient(self, expr, point, degree):
values = np.zeros(degree, dtype=complex)
try:
for i in range(degree):
grad = expr.diff(self.variables[f"x{i}"])
values[i] = grad.subs(point).evalf()
except TimeoutError:
raise
except Exception:
raise
return values
def gen_ode_system_convergence(self, return_system=False):
"""
Generate systems of functions, and the corresponding convergence speed in zero.
Start by generating a random system S, use SymPy to compute formal jacobian
and evaluate it in zero, find largest eigenvalue
Encode this as a prefix sensence
"""
degree = self.rng.randint(self.min_degree, self.max_degree + 1)
nb_ops = self.rng.randint(
self.min_expr_len_factor_cspeed * degree + 3,
self.max_expr_len_factor_cspeed * degree + 3,
size=(degree,),
)
while True:
system = []
i = 0
ngen = 0
while i < degree:
# generate expression
expr = self.generate_tree(nb_ops[i], degree)
ngen += 1
# sympy zone
try:
expr_sp = sp.S(expr, locals=self.local_dict)
# skip constant or invalid expressions
if len(expr_sp.free_symbols) == 0 or has_inf_nan(expr_sp):
continue
# evaluate gradient in point
values = self.compute_gradient(expr_sp, self.eval_point, degree)
if np.isnan(values).any() or np.isinf(values).any():
continue
if self.skip_zero_gradient and not values.any():
continue
except TimeoutError:
continue
except (ValueError, TypeError):
continue
except Exception as e:
logger.error(
"An unknown exception of type {0} occurred in line {1} "
'for expression "{2}". Arguments:{3!r}.'.format(
type(e).__name__,
sys.exc_info()[-1].tb_lineno,
expr_sp,
e.args,
)
)
continue
system.append(expr)
if i == 0:
jacobian = values
else:
jacobian = np.vstack((jacobian, values))
i += 1
if self.skip_zero_gradient:
skip = False
for i in range(degree):
if not jacobian[:, [i]].any():
skip = True
break
if skip:
continue
cspeed = -max(np.linalg.eigvals(jacobian).real)
if self.prob_positive == 0 and cspeed > 0:
continue
if self.prob_positive == 1 and cspeed <= 0:
continue
if (
self.prob_positive > 0
and self.prob_positive < 1
and self.np_total[degree] > 10
):
proportion = self.np_positive[degree] / self.np_total[degree]
if cspeed > 0 and proportion > self.prob_positive:
continue
if cspeed <= 0 and proportion < self.prob_positive:
continue
self.np_total[degree] += 1
if cspeed > 0:
self.np_positive[degree] += 1
break
# # debug
# logger.info(str(cspeed))
# logger.info(str(cspeed) + "\t" + " ||||| ".join(str(s) for s in system[:3]))
# print(degree, str(ngen) + " : " + str((ngen - degree) / ngen * 100.0))
# encode input
x = self.write_int(degree)
for s in system:
x.append(self.func_separator)
x.extend(self.encode_expr(s))
# encode output: eigenvalue, and optionally the Jacobian matrix
eigenvalue = self.write_float(cspeed)
if self.predict_jacobian:
y = []
for row in jacobian:
for value in row:
y.extend(
self.write_complex(value, precision=self.jacobian_precision)
)
y.append(self.list_separator)
y.append(self.line_separator)
y.append(self.mtrx_separator)
y.extend(eigenvalue)
else:
y = eigenvalue
if return_system:
return x, y, system
else:
return x, y
@timeout(5)
def compute_gradient_control(self, expr, point, degree, p):
if self.allow_complex:
A = np.zeros(degree, dtype=complex)
B = np.zeros(p, dtype=complex)
else:
A = np.zeros(degree, dtype=float)
B = np.zeros(p, dtype=float)
try:
for i in range(degree + p):
grad = expr.diff(self.variables[f"x{i}"])
val = grad.subs(point).evalf()
if i < degree:
A[i] = val
else:
B[i - degree] = val
except TimeoutError:
raise
except Exception:
raise
return A, B
def gen_control(self, return_system=False, skip_unstable=False):
"""
Generate systems of functions, data for controlability
"""
degree = self.rng.randint(self.min_degree, self.max_degree + 1)
p = self.rng.randint(1, degree // 2 + 1)
nb_ops = self.rng.randint(degree + p, 2 * (degree + p) + 3, size=(degree,))
while True:
system = []
i = 0
ngen = 0
while i < degree:
# generate expression
expr = self.generate_tree(
nb_ops[i], degree + p
) # si tau>0 doit on garantir l'existence de t (x{degree + p})?
ngen += 1
# sympy zone
try:
expr_sp = sp.S(expr, locals=self.local_dict)
# skip constant or invalid expressions
if len(expr_sp.free_symbols) == 0 or has_inf_nan(expr_sp):
continue
# evaluate gradient in point
valA, valB = self.compute_gradient_control(
expr_sp, self.eval_point, degree, p
)
if (
np.isnan(valA).any()
or np.isinf(valA).any()
or np.isnan(valB).any()
or np.isinf(valB).any()
):
continue
if self.skip_zero_gradient and not valA.any():
continue
except TimeoutError:
continue
except (ValueError, TypeError):
continue
except Exception as e:
logger.error(
"An unknown exception of type {0} occurred in line {1} "
'for expression "{2}". Arguments:{3!r}.'.format(
type(e).__name__,
sys.exc_info()[-1].tb_lineno,
expr_sp,
e.args,
)
)
continue
system.append(expr)
if i == 0:
A = valA
B = valB
else:
A = np.vstack((A, valA))
B = np.vstack((B, valB))
i += 1
if self.skip_zero_gradient:
skip = False
for i in range(degree):
if not A[:, [i]].any():
skip = True
break
for i in range(p):
if not B[:, [i]].any():
skip = True
break
if skip:
continue
try:
C = ctrl.ctrb(A, B)
d = degree - np.linalg.matrix_rank(C, 1.0e-6)
if d != 0 and (skip_unstable or self.prob_positive > 0.0):
continue
if self.predict_gramian and d == 0:
# C = ctrl.lyap(A, - B @ B.T)
# K = - B.T @ np.linalg.inv(C)
A = A / np.linalg.norm(A)
B = B / np.linalg.norm(A)
tau = 1
yint = []
# We want to integrate a matrix over [0,tau]
# and all the integrate functions I found are for scalars.
# So we do it term by term
for i in range(degree): # divide in row
yint_line = []
for j in range(degree): # divide in column
dt = np.linspace(
0, tau, num=40
) # integration path [0,tau] and 40 points
yint0 = []
for k in range(len(dt)):
# vector i with the component to be integrated (i,j),
# evaluated at each point of the integration path
res = (
(expm(A * (tau - dt[k])))
@ (B @ B.T)
@ (expm(A.T * (tau - dt[k])))
)[i]
yint0.append(
res[j]
) # vector of the component (i,j) along itegration path
resline = (cumtrapz(yint0, dt, initial=0))[
len(dt) - 1
] # integration with cumulative trapezz
yint_line.append(resline) # reconstruct the line
yint.append(yint_line) # reconstruct the matrix
if np.isnan(yint).any() or np.isinf(yint).any():
continue
Ctau = (
expm(-tau * A) @ np.array(yint) @ expm(-tau * A.T)
) # From the gramian to the true C
if np.isnan(Ctau).any() or np.isinf(Ctau).any():
continue
K = -B.T @ (np.linalg.inv(Ctau + 1e-6 * np.eye(degree)))
if np.isnan(K).any() or np.isinf(K).any():
continue
with np.nditer(K, op_flags=["readwrite"]) as it:
for x in it:
x[...] = float(f"%.{self.jacobian_precision}e" % x)
if max(np.linalg.eigvals(A + B @ K).real) > 0:
# Check that A+B@K is stable, which is equivalent to
# check_gramian
# print("UNSTABLE")
continue
except Exception:
# logger.error("An unknown exception of type {0} occurred
# in line {1} for expression \"{2}\". Arguments:{3!r}.".format(
# type(e).__name__, sys.exc_info()[-1].tb_lineno, expr_sp, e.args))
continue
break
# # debug
# logger.info(str(cspeed))
# logger.info(str(cspeed) + "\t" + " ||||| ".join(str(s) for s in system[:3]))
# print(degree, str(ngen) + " : " + str((ngen - degree) / ngen * 100.0))
# encode input
x = self.write_int(degree)
for s in system:
x.append(self.func_separator)
x.extend(self.encode_expr(s))
# encode output: dimension of control subspace and optionally the Gramian matrix
if self.qualitative:
controlable = 1 if d == 0 else 0
y = self.write_int(controlable)
else:
y = self.write_int(d)
if self.predict_gramian and d == 0:
K = np.array(K)
y.append(self.mtrx_separator)
for row in K:
for value in row:
y.extend(self.write_complex(value, self.jacobian_precision))
y.append(self.list_separator)
y.append(self.line_separator)
if self.max_len > 0 and (len(x) >= self.max_len or len(y) >= self.max_len):
return None
if return_system:
return x, y, system, p
else:
return x, y
@timeout(5)
def compute_gradient_control_t(self, expr, point, degree, p):
A = []
B = []
try:
for i in range(degree + p):
grad = expr.diff(self.variables[f"x{i}"])
val = grad.subs(point).evalf()
val = simplify(val, 2)
if i < degree:
A.append(val)
else:
B.append(val)
except TimeoutError:
raise
except Exception:
raise
return A, B
@timeout(10)
def compute_rank(self, A, B, degree, p, val):
Bi = B
for i in range(1, int(val * degree / p) + 1):
E = B.diff(self.variables[f"x{degree + p}"])
B = E - A * B
Bi = Bi.row_join(B)
d = 1
for i in range(5):
value = (i + 1) * self.tau / 5 - 0.01
# D = w(value)
D = Bi.subs({self.variables[f"x{degree + p}"]: value})
D = np.array(D).astype(np.complex)
if np.isnan(D).any() or np.isinf(D).any():
continue
d = degree - np.linalg.matrix_rank(D, 1.0e-6)
if d == 0:
break
return d
# @timeout(20)
def gen_control_t(self):
"""
Generate systems of functions, data for controlability
"""
while True:
degree = self.rng.randint(self.min_degree, self.max_degree + 1)
p = self.rng.randint(1, degree // 2 + 1)
nb_ops = self.rng.randint(degree + p, 2 * (degree + p) + 3, size=(degree,))
ev_point = OrderedDict(
{self.variables[f"x{i}"]: self.eval_value for i in range(degree + p)}
)
system = []
i = 0
A = sp.Matrix()
B = sp.Matrix()
ngen = 0
while i < degree:
# generate expression
# si tau>0 doit on garantir l'existence de t (x{degree + p}) ?
expr = self.generate_tree(nb_ops[i], degree + p + 1)
ngen += 1
# sympy zone
try:
expr_sp = sp.S(expr, locals=self.local_dict)
# skip constant or invalid expressions
if len(expr_sp.free_symbols) == 0 or has_inf_nan(expr_sp):
continue
# evaluate gradient in point
valA, valB = self.compute_gradient_control_t(
expr_sp, ev_point, degree, p
)
# print('valA', valA)
# print('valB', valB)
if any(has_inf_nan(a) for a in valA) or any(
has_inf_nan(a) for a in valB
):
continue
if self.skip_zero_gradient and all(a == 0 for a in valA):
continue
except TimeoutError:
continue
except (ValueError, TypeError):
continue
except Exception as e:
logger.error(
"An unknown exception of type {0} occurred in line {1} "
'for expression "{2}". '
"Arguments:{3!r}.".format(
type(e).__name__,
sys.exc_info()[-1].tb_lineno,
expr_sp,
e.args,
)
)
continue
system.append(expr)
v1 = sp.Matrix(1, degree, valA)
v2 = sp.Matrix(1, p, valB)
A = A.col_join(v1)
B = B.col_join(v2)
i += 1
if self.skip_zero_gradient:
if any(all(A[j, i] == 0 for j in range(degree)) for i in range(degree)):
continue
if any(all(B[j, i] == 0 for j in range(degree)) for i in range(p)):
continue
try:
d = self.compute_rank(A, B, degree, p, 2)
except TimeoutError:
continue
# except FloatingPointError:
# continue
except Exception as e:
logger.error(
"An unknown exception of type {0} occurred in line {1} "
'for expression "{2}". '
"Arguments:{3!r}.".format(
type(e).__name__, sys.exc_info()[-1].tb_lineno, expr_sp, e.args
)
)
continue
break
# # debug
# logger.info(str(cspeed))
# logger.info(str(cspeed) + "\t" + " ||||| ".join(str(s) for s in system[:3]))
# print(degree, str(ngen) + " : " + str((ngen - degree) / ngen * 100.0))
# print(', '.join(f"{s} {t:.3f}" for s, t in times))
# encode input
x = self.write_int(degree)
for s in system:
x.append(self.func_separator)
x.extend(self.encode_expr(s))
# encode output: dimension of control subspace and optionally the Gramian matrix
controlable = 1 if d == 0 else 0
y = self.write_int(controlable)
if self.max_len > 0 and (len(x) >= self.max_len or len(y) >= self.max_len):
return None
return x, y
def generate_cond_init(self, max_delay, dimension, unariesexp, unariesfk):
pol = set()
nfactor = self.rng.randint(1, max_delay + 1)
# print(nfactor)
delay = np.zeros(dimension)
bounds = []
vars = set()
for j in range(nfactor):
vars.add(
(self.rng.randint(0, dimension), self.rng.randint(0, len(unariesexp)))
)
pol.add(tuple(vars))
# print(pol)
for i in range(len(pol)):
v = list(pol)[i]
# print(len(v))
# print(v[len(v)-1])
# print(v[len(v)-1][0])
# print(v[0][0])
# print(delay)
for j in range(len(v)):
op = unariesexp[v[j][1]]
var = Node(self.variables[f"x{v[j][0]}"])
if op == "id":
term = var
elif len(op) > 3 and op[:3] == "pow":
term = Node("^", [var, Node(int(op[3:]))])
elif op == "expi":
a_d = self.rng.randint(-100, 100)
# b = self.rng.randint(-100, 100)#Not needed for now
b_d = 0
term = Node(
"exp",
[
Node(
"+",
[
Node("*", [Node(a_d), Node("*", [Node("I"), var])]),
Node(b_d),
],
)
],
)
delay[v[j][0]] = delay[v[j][0]] + a_d
# print(delay[v[j][0]])
else:
term = Node(op, [var])
p = term if j == 0 else Node("*", [p, term])
expr_delay = p
# print(sp.S(expr_delay))
for i in range(dimension):
k = self.rng.randint(0, len(unariesfk))
op = unariesfk[k]
var = Node(self.variables[f"x{i}"])
a = self.rng.randint(-100, 100)
# b = self.rng.randint(-100, 100)
# inclure b plus tard not needed now avec les delays
b = 0
var = Node("+", [Node("*", [Node(a), var]), Node(b)])
if op == "sinc":
bounds.append(
[-abs(a) / (2 * np.pi), abs(a) / (2 * np.pi)]
) # fouriertiser
term = Node("/", [Node("sin", [var]), var])
# print(sp.S(term))
elif op == "1":
bounds.append([0, 0])
term = Node(1)
elif op == "delta0":
bounds.append([-np.inf, np.inf])
term = Node(op, [var])
elif op == "gauss":
bounds.append([-np.inf, np.inf])
term = Node(
"exp", [Node("*", [Node(-1), Node("^", [var, Node(2)])])]
) # checker
else:
return None
# Message d'erreur
# print(sp.S(term))
p = term if i == 0 else Node("*", [p, term])
bounds[i][0] = bounds[i][0] + delay[i] / (2 * np.pi)
bounds[i][1] = bounds[i][1] + delay[i] / (2 * np.pi)
# print(delay[i])
u0 = Node("*", [expr_delay, p])
# u0f = Node('*', [exprf, pf])
return u0, bounds
def gen_fourier_cond_init(self):
while True:
try:
dimension = self.rng.randint(self.min_degree, self.max_degree + 1)
nb_ops = self.rng.randint(dimension, 2 * dimension + 3)
# Generate differential operator
unariesd = ["id", "pow2", "pow4"]
expr = self.generate_polynomial(
nb_ops, 4, dimension, unariesd, True, False
)
# print(sp.S(expr))
# Fourier transform of the differential operator
PF = OrderedDict(
{
self.variables[f"x{i}"]: 2
* np.pi
* 1j
* self.variables[f"x{i}"]
for i in range(self.max_degree)
}
)
poly_fourier = sp.S(expr).subs(PF)
# print(poly_fourier)
# Generate initial condition
unariesexp = ["expi"]
unariesfk = ["1", "sinc", "delta0", "gauss"]
max_delay_op = 2 * dimension
expr_u0, bounds = self.generate_cond_init(
max_delay_op, dimension, unariesexp, unariesfk
)
# print(sp.S(expr_u0))
# print(bounds)
# Minimization of the Fourier transform of the differential operator
# on the frequency of the initial conditions
dum_point = np.zeros(dimension, dtype=float) + 0.5
max_f = opt.minimize(
expr_to_fun_real,
dum_point,
args=(poly_fourier, dimension),
method="TNC",
bounds=bounds,
options={"ftol": 1e-15, "gtol": 1e-15},
)
# print(max_f.fun)
if not max_f.success:
# logger.info(f'optimization error')
continue
if max_f.fun < -1e14:
reg = 0 # -1
stab = 0
elif max_f.fun < 0:
reg = 1 # 0
stab = 0
elif max_f.fun >= 0:
reg = 1
stab = 1
else:
# logger.info(f'optimization error in value')
continue
except Exception as e:
print(e)
continue
break
# encode input
x = self.write_int(dimension)
x.append(self.func_separator)
x.extend(self.encode_expr(expr, True))
x.append(self.func_separator)
x.extend(self.encode_expr(expr_u0, True))
# encode output
y = self.write_int(reg)
y.append(self.func_separator)
y.extend(self.write_int(stab))
if self.predict_bounds:
y.append(self.func_separator)
for i in range(len(bounds)):
if bounds[i][0] == np.inf:
y.append(self.pos_inf)
elif bounds[i][0] == -np.inf:
y.append(self.neg_inf)
else:
y.extend(self.write_float(bounds[i][0], 2))
y.append(self.list_separator)
if bounds[i][1] == np.inf:
y.append(self.pos_inf)
elif bounds[i][1] == -np.inf:
y.append(self.neg_inf)
else:
y.extend(self.write_float(bounds[i][1], 2))
y.append(self.line_separator)
return x, y
def create_train_iterator(self, task, data_path, params):
"""
Create a dataset for this environment.
"""
logger.info(f"Creating train iterator for {task} ...")
dataset = EnvDataset(
self,
task,
train=True,
params=params,
path=(None if data_path is None else data_path[task][0]),
)
return DataLoader(
dataset,
timeout=(0 if params.num_workers == 0 else 1800),
batch_size=params.batch_size,
num_workers=(
params.num_workers
if data_path is None or params.num_workers == 0
else 1
),
shuffle=False,
collate_fn=dataset.collate_fn,
)
def create_test_iterator(
self, data_type, task, data_path, batch_size, params, size
):
"""
Create a dataset for this environment.
"""
assert data_type in ["valid", "test"]
logger.info(f"Creating {data_type} iterator for {task} ...")
dataset = EnvDataset(
self,
task,
train=False,
params=params,
path=(
None
if data_path is None
else data_path[task][1 if data_type == "valid" else 2]
),
size=size,
)
return DataLoader(
dataset,
timeout=0,
batch_size=batch_size,
num_workers=1,
shuffle=False,
collate_fn=dataset.collate_fn,
)
@staticmethod
def register_args(parser):
"""
Register environment parameters.
"""
parser.add_argument(
"--max_int", type=int, default=10, help="Maximum integer value"
)
parser.add_argument(
"--precision", type=int, default=3, help="Float numbers precision"
)
parser.add_argument(
"--jacobian_precision",
type=int,
default=1,
help="Float numbers precision in the Jacobian",
)
parser.add_argument(
"--positive",
type=bool_flag,
default=False,
help="Do not sample negative numbers",
)
parser.add_argument(
"--nonnull", type=bool_flag, default=True, help="Do not sample zeros"
)
parser.add_argument(
"--predict_jacobian",
type=bool_flag,
default=False,
help="Predict the Jacobian matrix",
)
parser.add_argument(
"--predict_gramian",
type=bool_flag,
default=False,
help="Predict the Gramian matrix",
)
parser.add_argument(
"--qualitative",
type=bool_flag,
default=False,
help="Binary output: system is stable or controllable",
)
parser.add_argument(
"--allow_complex",
type=bool_flag,
default=False,
help="Allow complex values in A and B",
)
parser.add_argument(
"--reversed_eval",
type=bool_flag,
default=False,
help="Validation set is dim whereas train set is test control",
)
parser.add_argument(
"--euclidian_metric",
type=bool_flag,
default=False,
help="Simple metric for gramian comparison",
)
parser.add_argument(
"--auxiliary_task",
type=bool_flag,
default=False,
help="Gramian as auxiliary task",
)
parser.add_argument(
"--tau", type=int, default=0, help="if > 0 time span for controllability"
)
parser.add_argument(
"--gramian_norm1",
type=bool_flag,
default=False,
help="Use norm1 as Euclidian distance for Gramian",
)
parser.add_argument(
"--gramian_tolerance",
type=float,
default=0.1,
help="Tolerance level for Gramian euclidian distance",
)
parser.add_argument(
"--predict_bounds",
type=bool_flag,
default=True,
help="Predict bounds for Fourier with initial conditions",
)
parser.add_argument(
"--prob_int",
type=float,
default=0.3,
help="Probability of int vs variables",
)
parser.add_argument(
"--min_degree",
type=int,
default=2,
help="Minimum degree of ode / nb of variables",
)
parser.add_argument(
"--max_degree",
type=int,
default=6,
help="Maximum degree of ode / nb of variables",
)
parser.add_argument(
"--min_expr_len_factor_cspeed",
type=int,
default=0,
help="In cspeed, min nr of operators in system eqs: 3+k degree",
)
parser.add_argument(
"--max_expr_len_factor_cspeed",
type=int,
default=2,
help="In cspeed, min nr of operators in system eqs: 3+k degree",
)
parser.add_argument(
"--custom_unary_probs",
type=bool_flag,
default=False,
help="Lyapunov function is a polynomial",
)
parser.add_argument(
"--prob_trigs",
type=float,
default=0.333,
help="Probability of trig operators",
)
parser.add_argument(
"--prob_arc_trigs",
type=float,
default=0.333,
help="Probability of inverse trig operators",
)
parser.add_argument(
"--prob_logs",
type=float,
default=0.222,
help="Probability of logarithm and exponential operators",
)
parser.add_argument(
"--eval_value",
type=float,
default=0.0,
help="Evaluation point for all variables",
)
parser.add_argument(
"--skip_zero_gradient",
type=bool_flag,
default=False,
help="No gradient can be zero at evaluation point",
)
parser.add_argument(
"--prob_positive",
type=float,
default=-1.0,
help=(
"Proportion of positive convergence speed "
"(for all degrees, -1.0 = no control)"
),
)
parser.add_argument(
"--eval_size",
type=int,
default=10000,
help="Size and valid and test sample",
)
class EnvDataset(Dataset):
def __init__(self, env, task, train, params, path, size=None):
super(EnvDataset).__init__()
self.env = env
self.train = train
self.task = task
self.batch_size = params.batch_size
self.env_base_seed = params.env_base_seed
self.path = path
self.global_rank = params.global_rank
self.count = 0
assert task in ODEEnvironment.TRAINING_TASKS
assert size is None or not self.train
# batching
self.num_workers = params.num_workers
self.batch_size = params.batch_size
# generation, or reloading from file
if path is not None:
assert os.path.isfile(path)
logger.info(f"Loading data from {path} ...")
with io.open(path, mode="r", encoding="utf-8") as f:
# either reload the entire file, or the first N lines
# (for the training set)
if not train:
lines = [line.rstrip().split("|") for line in f]
else:
lines = []
for i, line in enumerate(f):
if i == params.reload_size:
break
if i % params.n_gpu_per_node == params.local_rank:
lines.append(line.rstrip().split("|"))
self.data = [xy.split("\t") for _, xy in lines]
self.data = [xy for xy in self.data if len(xy) == 2]
logger.info(f"Loaded {len(self.data)} equations from the disk.")
if task == "ode_control" and params.reversed_eval and not self.train:
self.data = [
(x, "INT+ 1" if y == "INT+ 0" else "INT+ 0") for (x, y) in self.data
]
if task == "ode_convergence_speed" and params.qualitative:
self.data = [
(x, "INT+ 1" if y[:7] == "FLOAT- " else "INT+ 0")
for (x, y) in self.data
]
if (
task == "fourier_cond_init" and not params.predict_bounds
): # "INT+ X <SPECIAL_3> INT+ X"
self.data = [(x, y[:25]) for (x, y) in self.data]
# if we are not predicting the Jacobian, remove it
if task == "ode_convergence_speed" and not params.predict_jacobian:
self.data = [
(x, y[y.index(env.mtrx_separator) + len(env.mtrx_separator) + 1 :])
if env.mtrx_separator in y
else (x, y)
for (x, y) in self.data
]
# dataset size: infinite iterator for train,
# finite for valid / test (default of 5000 if no file provided)
if self.train:
self.size = 1 << 60
elif size is None:
self.size = 5000 if path is None else len(self.data)
else:
assert size > 0
self.size = size
def collate_fn(self, elements):
"""
Collate samples into a batch.
"""
x, y = zip(*elements)
nb_eqs = [seq.count(self.env.func_separator) for seq in x]
x = [torch.LongTensor([self.env.word2id[w] for w in seq]) for seq in x]
y = [torch.LongTensor([self.env.word2id[w] for w in seq]) for seq in y]
x, x_len = self.env.batch_sequences(x)
y, y_len = self.env.batch_sequences(y)
return (x, x_len), (y, y_len), torch.LongTensor(nb_eqs)
def init_rng(self):
"""
Initialize random generator for training.
"""
if hasattr(self.env, "rng"):
return
if self.train:
worker_id = self.get_worker_id()
self.env.worker_id = worker_id
self.env.rng = np.random.RandomState(
[worker_id, self.global_rank, self.env_base_seed]
)
logger.info(
f"Initialized random generator for worker {worker_id}, with seed "
f"{[worker_id, self.global_rank, self.env_base_seed]} "
f"(base seed={self.env_base_seed})."
)
else:
self.env.rng = np.random.RandomState(0)
def get_worker_id(self):
"""
Get worker ID.
"""
if not self.train:
return 0
worker_info = torch.utils.data.get_worker_info()
assert (worker_info is None) == (self.num_workers == 0)
return 0 if worker_info is None else worker_info.id
def __len__(self):
"""
Return dataset size.
"""
return self.size
def __getitem__(self, index):
"""
Return a training sample.
Either generate it, or read it from file.
"""
self.init_rng()
if self.path is None:
return self.generate_sample()
else:
return self.read_sample(index)
def read_sample(self, index):
"""
Read a sample.
"""
if self.train:
index = self.env.rng.randint(len(self.data))
x, y = self.data[index]
x = x.split()
y = y.split()
assert len(x) >= 1 and len(y) >= 1
return x, y
def generate_sample(self):
"""
Generate a sample.
"""
while True:
try:
if self.task == "ode_convergence_speed":
xy = self.env.gen_ode_system_convergence()
elif self.task == "ode_control":
if self.env.tau == 0:
xy = self.env.gen_control()
else:
xy = self.env.gen_control_t()
elif self.task == "fourier_cond_init":
xy = self.env.gen_fourier_cond_init()
else:
raise Exception(f"Unknown data type: {self.task}")
if xy is None:
continue
x, y = xy
break
except TimeoutError:
continue
except Exception as e:
logger.error(
"An unknown exception of type {0} occurred for worker {4} "
'in line {1} for expression "{2}". Arguments:{3!r}.'.format(
type(e).__name__,
sys.exc_info()[-1].tb_lineno,
"F",
e.args,
self.get_worker_id(),
)
)
continue
self.count += 1
# clear SymPy cache periodically
if CLEAR_SYMPY_CACHE_FREQ > 0 and self.count % CLEAR_SYMPY_CACHE_FREQ == 0:
logger.warning(f"Clearing SymPy cache (worker {self.get_worker_id()})")
clear_cache()
return x, y
================================================
FILE: src/evaluator.py
================================================
# Copyright (c) 2020-present, Facebook, Inc.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
#
from logging import getLogger
from collections import OrderedDict
from concurrent.futures import ProcessPoolExecutor
import os
import time
import torch
import numpy as np
import sympy as sp
from .utils import to_cuda # , timeout
from .utils import TimeoutError
from .envs.ode import second_index
TOLERANCE_THRESHOLD = 1e-1
logger = getLogger()
def check_fourier_cond_init(env, src, tgt, hyp):
try:
nx = src
dimension, pos = env.parse_int(nx)
nx = nx[pos:]
operateur, nx = env.prefix_to_infix(nx[1:])
cond_init, nx = env.prefix_to_infix(nx[1:])
if nx[1:] != []:
logger.info("wrong src")
return False
# read tgt
reg, pos1 = env.parse_int(tgt)
stab, pos2 = env.parse_int(tgt[pos1 + 1 :])
tgt = tgt[pos1 + pos2 :]
# read hyp
reghyp, pos1 = env.parse_int(hyp)
stabhyp, pos2 = env.parse_int(hyp[pos1 + 1 :])
hyp = hyp[pos1 + pos2 :]
# compare hyp and tgt
if (
reghyp != reg or stabhyp != stab
): # First condition on existence and stability
# logger.error("Incorrect reg or stab")
return False
# predict bounds is a subtask, used for training but not for evaluation,
# hence the comment, uncomment if bounds are to be used at evaluations
# if env.predict_bounds:
# # read tgt
# nr_bounds = tgt.count(env.list_separator)
# nr_dimension = tgt.count(env.line_separator)
# if nr_bounds != dimension or nr_dimension != dimension:
# # logger.error("Incorrect form of tgt in read_fourier")
# return False
# bounds = []
# pos = 1
# for i in range(dimension):
# tgt = tgt[pos + 1:]
# if tgt[0] == env.pos_inf:
# bda = np.inf
# pos = 1
# elif tgt[0] == env.neg_inf:
# bda = -np.inf
# pos = 1
# else:
# bda, pos = env.parse_float(tgt)
# tgt = tgt[pos + 1:]
# if tgt[0] == env.pos_inf:
# bdb = np.inf
# pos = 1
# elif tgt[0] == env.neg_inf:
# bdb = -np.inf
# pos = 1
# else:
# bdb, pos = env.parse_float(tgt)
# bounds.append([bda, bdb])
# # read hyp
# nr_bounds = hyp.count(env.list_separator)
# nr_dimension = hyp.count(env.line_separator)
# if nr_bounds != dimension or nr_dimension != dimension:
# # logger.error("Incorrect form of hyp in read_fourier")
# return False
# bounds_hyp = []
# pos = 1
# for i in range(dimension):
# hyp = hyp[pos + 1:]
# if hyp[0] == env.pos_inf:
# bda = np.inf
# pos = 1
# elif hyp[0] == env.neg_inf:
# bda = -np.inf
# pos = 1
# else:
# bda, pos = env.parse_float(hyp)
# hyp = hyp[pos + 1:]
# if hyp[0] == env.pos_inf:
# bdb = np.inf
# pos = 1
# elif hyp[0] == env.neg_inf:
# bdb = -np.inf
# pos = 1
# else:
# bdb, pos = env.parse_float(hyp)
# bounds_hyp.append([bda, bdb])
# # compare hyp and tgt
# for i in range(len(bounds)):
# # Second condition on frequency bounds of initial condition
# for j in range(len(bounds[i])):
# if abs(bounds[i][j]) == np.inf:
# if bounds[i][j] != bounds_hyp[i][j]:
# # logger.error("Incorrect inf bound prediction")
# return False
# elif abs(bounds[i][j]) == 0:
# if bounds_hyp[i][j] != 0:
# # logger.error("Incorrect 0 bound prediction")
# return False
# else:
# if (bounds[i][j] - bounds_hyp[i][j]) / bounds[i][j] > 0.1:
# # logger.error("Incorrect bound prediction")
# return False
except Exception as e:
logger.info(f"Exception {e} in top_test")
return False
return True
def idx_to_infix(env, idx, input=True):
"""
Convert an indexed prefix expression to SymPy.
"""
prefix = [env.id2word[wid] for wid in idx]
infix = env.input_to_infix(prefix) if input else env.output_to_infix(prefix)
return infix
def compare_gramians(env, tgt, hyp, tolerance, norm1=False):
nr_lines = tgt.count(env.line_separator)
nr_cols = tgt.count(env.list_separator)
nr_cols = nr_cols // nr_lines
# read hypothesis
h = hyp
h_gramian = np.zeros((nr_lines, nr_cols), dtype=float)
for i in range(nr_lines):
for j in range(nr_cols):
val, pos = env.parse_float(h)
if np.isnan(val):
return False
if len(h) <= pos or h[pos] != env.list_separator:
return False
h_gramian[i][j] = val
h = h[pos + 1 :]
if len(h) == 0 or h[0] != env.line_separator:
return False
h = h[1:]
# read target
t = tgt
t_gramian = np.zeros((nr_lines, nr_cols), dtype=float)
for i in range(nr_lines):
for j in range(nr_cols):
val, pos = env.parse_float(t)
t_gramian[i][j] = val
t = t[pos + 1 :]
t = t[1:]
# compare
if norm1:
tot = 0
nb = 0
for i in range(nr_lines):
for j in range(nr_cols):
if t_gramian[i][j] != h_gramian[i][j]:
den = h_gramian[i][j] if t_gramian[i][j] == 0 else t_gramian[i][j]
delta = abs((t_gramian[i][j] - h_gramian[i][j]) / den)
tot += delta
nb += 1
return tot <= tolerance * nb
else:
for i in range(nr_lines):
for j in range(nr_cols):
if t_gramian[i][j] != h_gramian[i][j]:
den = h_gramian[i][j] if t_gramian[i][j] == 0 else t_gramian[i][j]
delta = abs((t_gramian[i][j] - h_gramian[i][j]) / den)
if delta > tolerance:
return False
return True
def check_gramian(env, src, tgt, hyp):
# Read src
try:
degree, pos = env.parse_int(src)
nx = src[
pos:
] # retourne src sans le degree et le séparateur qui va avec si j'ai bien suivi
system = []
while len(nx) > 0:
b, nx = env.prefix_to_infix(nx[1:])
# convertit en sympy, on en aura besoin de toutes facons
s = sp.S(b)
system.append(s)
# get expected shape of solution (from tgt)
nr_lines = tgt.count(env.line_separator)
nr_cols = tgt.count(env.list_separator)
if nr_cols % nr_lines != 0 or nr_cols // nr_lines != degree:
logger.error("Incorrect target gramian in check_gramian")
return False
nr_cols = nr_cols // nr_lines
for i in range(degree):
valA, valB = env.compute_gradient_control(
system[i], env.eval_point, degree, nr_lines
)
if i == 0:
A = valA
B = valB
else:
A = np.vstack((A, valA))
B = np.vstack((B, valB))
A = A / np.linalg.norm(A)
B = B / np.linalg.norm(A)
# read hyp, check correct shape
h = hyp
K0 = np.zeros((nr_lines, nr_cols))
for i in range(nr_lines):
for j in range(nr_cols):
val, pos = env.parse_float(h)
if np.isnan(val):
return False
if len(h) <= pos or h[pos] != env.list_separator:
return False
K0[i][j] = val
h = h[pos + 1 :]
if len(h) == 0 or h[0] != env.line_separator:
return False
h = h[1:]
V = A + B @ K0
return max(np.linalg.eigvals(V).real) < 0
except TimeoutError:
return False
except Exception as e:
logger.info(f"{e} in check_gramian")
return False
def check_hypothesis(eq):
"""
Check a hypothesis for a given equation and its solution.
"""
env = Evaluator.ENV
src = [env.id2word[wid] for wid in eq["src"]]
tgt = [env.id2word[wid] for wid in eq["tgt"]]
hyp = [env.id2word[wid] for wid in eq["hyp"]]
if eq["task"] == "ode_convergence_speed":
try:
tgt, _ = env.parse_float(tgt)
l1 = len(hyp)
hyp, l2 = env.parse_float(hyp)
if hyp == np.nan or l2 != l1:
is_valid = False
elif hyp == tgt:
is_valid = True
else:
den = hyp if tgt == 0 else tgt
is_valid = abs((tgt - hyp) / den) < TOLERANCE_THRESHOLD
except Exception:
is_valid = False
tgt = 0
hyp = 0
elif eq["task"] == "ode_control":
if env.predict_gramian:
try:
d, l1 = env.parse_int(hyp)
t, l2 = env.parse_int(tgt)
if d == 0 and t == 0 and not env.auxiliary_task:
if env.euclidian_metric:
is_valid = compare_gramians(
env,
tgt[l2 + 1 :],
hyp[l1 + 1 :],
env.gramian_tolerance,
env.gramian_norm1,
)
else:
is_valid = check_gramian(env, src, tgt, hyp[l1 + 1 :])
else:
is_valid = d == t
except Exception:
is_valid = False
else:
try:
tgt, _ = env.parse_int(tgt)
l1 = len(hyp)
hyp, l2 = env.parse_int(hyp)
if hyp == np.nan or l2 != l1:
is_valid = False
else:
is_valid = hyp == tgt
except Exception:
is_valid = False
elif eq["task"] == "fourier_cond_init":
try:
is_valid = check_fourier_cond_init(env, src, tgt, hyp)
except Exception:
is_valid = False
else:
is_valid = hyp == tgt
# update hypothesis
eq["src"] = env.input_to_infix(src)
eq["tgt"] = tgt
eq["hyp"] = hyp
eq["is_valid"] = is_valid
return eq
class Evaluator(object):
ENV = None
def __init__(self, trainer):
"""
Initialize evaluator.
"""
self.trainer = trainer
self.modules = trainer.modules
self.params = trainer.params
self.env = trainer.env
Evaluator.ENV = trainer.env
def run_all_evals(self):
"""
Run all evaluations.
"""
params = self.params
scores = OrderedDict({"epoch": self.trainer.epoch})
# save statistics about generated data
if params.export_data:
scores["total"] = sum(self.trainer.EQUATIONS.values())
scores["unique"] = len(self.trainer.EQUATIONS)
scores["unique_prop"] = 100.0 * scores["unique"] / scores["total"]
return scores
with torch.no_grad():
# for data_type in ['valid', 'test']: FC save time
for data_type in ["valid"]:
for task in params.tasks:
if params.beam_eval:
self.enc_dec_step_beam_fast(data_type, task, scores)
else:
self.enc_dec_step(data_type, task, scores)
return scores
def truncate_at(self, x, xlen):
pattern = self.env.word2id[self.env.func_separator]
bs = len(xlen)
eos = self.env.eos_index
assert x.shape[1] == bs
new_seqs = []
new_lengths = []
for i in range(bs):
s = x[: xlen[i], i].tolist()
assert s[0] == s[-1] == eos
ns = second_index(s, pattern)
if ns != len(s):
s = s[:ns]
s.append(eos)
new_seqs.append(s)
new_lengths.append(len(s))
# batch sequence
lengths = torch.LongTensor(new_lengths)
seqs = torch.LongTensor(lengths.max().item(), bs).fill_(self.env.pad_index)
for i, s in enumerate(new_seqs):
seqs[: lengths[i], i].copy_(torch.LongTensor(s))
return seqs, lengths
def enc_dec_step(self, data_type, task, scores):
"""
Encoding / decoding step.
"""
params = self.params
env = self.env
encoder = (
self.modules["encoder"].module
if params.multi_gpu
else self.modules["encoder"]
)
decoder = (
self.modules["decoder"].module
if params.multi_gpu
else self.modules["decoder"]
)
encoder.eval()
decoder.eval()
assert params.eval_verbose in [0, 1]
assert params.eval_verbose_print is False or params.eval_verbose > 0
assert task in [
"ode_convergence_speed",
"ode_control",
"fourier_cond_init",
]
# stats
xe_loss = 0
n_valid = torch.zeros(1000, dtype=torch.long)
n_total = torch.zeros(1000, dtype=torch.long)
# evaluation details
if params.eval_verbose:
eval_path = os.path.join(
params.dump_path, f"eval.{data_type}.{task}.{scores['epoch']}"
)
f_export = open(eval_path, "w")
logger.info(f"Writing evaluation results in {eval_path} ...")
# iterator
iterator = self.env.create_test_iterator(
data_type,
task,
data_path=self.trainer.data_path,
batch_size=params.batch_size_eval,
params=params,
size=params.eval_size,
)
eval_size = len(iterator.dataset)
for (x1, len1), (x2, len2), nb_ops in iterator:
# print status
if n_total.sum().item() % 500 < params.batch_size_eval:
logger.info(f"{n_total.sum().item()}/{eval_size}")
# target words to predict
alen = torch.arange(len2.max(), dtype=torch.long, device=len2.device)
pred_mask = (
alen[:, None] < len2[None] - 1
) # do not predict anything given the last target word
y = x2[1:].masked_select(pred_mask[:-1])
assert len(y) == (len2 - 1).sum().item()
# optionally truncate input
x1_, len1_ = x1, len1
# cuda
x1_, len1_, x2, len2, y = to_cuda(x1_, len1_, x2, len2, y)
# forward / loss
encoded = encoder("fwd", x=x1_, lengths=len1_, causal=False)
decoded = decoder(
"fwd",
x=x2,
lengths=len2,
causal=True,
src_enc=encoded.transpose(0, 1),
src_len=len1_,
)
word_scores, loss = decoder(
"predict", tensor=decoded, pred_mask=pred_mask, y=y, get_scores=True
)
# correct outputs per sequence / valid top-1 predictions
t = torch.zeros_like(pred_mask, device=y.device)
t[pred_mask] += word_scores.max(1)[1] == y
valid = (t.sum(0) == len2 - 1).cpu().long()
# export evaluation details
if params.eval_verbose:
for i in range(len(len1)):
src = idx_to_infix(env, x1[1 : len1[i] - 1, i].tolist(), True)
tgt = idx_to_infix(env, x2[1 : len2[i] - 1, i].tolist(), False)
s = (
f"Equation {n_total.sum().item() + i} "
f"({'Valid' if valid[i] else 'Invalid'})\n"
f"src={src}\ntgt={tgt}\n"
)
if params.eval_verbose_print:
logger.info(s)
f_export.write(s + "\n")
f_export.flush()
# stats
xe_loss += loss.item() * len(y)
n_valid.index_add_(-1, nb_ops, valid)
n_total.index_add_(-1, nb_ops, torch.ones_like(nb_ops))
# evaluation details
if params.eval_verbose:
f_export.close()
# log
_n_valid = n_valid.sum().item()
_n_total = n_total.sum().item()
logger.info(
f"{_n_valid}/{_n_total} ({100. * _n_valid / _n_total}%) "
"equations were evaluated correctly."
)
# compute perplexity and prediction accuracy
assert _n_total == eval_size
scores[f"{data_type}_{task}_xe_loss"] = xe_loss / _n_total
scores[f"{data_type}_{task}_acc"] = 100.0 * _n_valid / _n_total
# per class perplexity and prediction accuracy
for i in range(len(n_total)):
if n_total[i].item() == 0:
continue
scores[f"{data_type}_{task}_acc_{i}"] = (
100.0 * n_valid[i].item() / max(n_total[i].item(), 1)
)
def enc_dec_step_beam_fast(self, data_type, task, scores, size=None):
"""
Encoding / decoding step with beam generation and SymPy check.
"""
params = self.params
env = self.env
encoder = (
self.modules["encoder"].module
if params.multi_gpu
else self.modules["encoder"]
)
decoder = (
self.modules["decoder"].module
if params.multi_gpu
else self.modules["decoder"]
)
encoder.eval()
decoder.eval()
assert params.eval_verbose in [0, 1, 2]
assert params.eval_verbose_print is False or params.eval_verbose > 0
assert task in [
"ode_convergence_speed",
"ode_control",
"fourier_cond_init",
]
# stats
xe_loss = 0
n_valid = torch.zeros(1000, dtype=torch.long)
n_total = torch.zeros(1000, dtype=torch.long)
# iterator
iterator = env.create_test_iterator(
data_type,
task,
data_path=self.trainer.data_path,
batch_size=params.batch_size_eval,
params=params,
size=params.eval_size,
)
eval_size = len(iterator.dataset)
# save beam results
beam_log = {}
hyps_to_eval = []
for (x1, len1), (x2, len2), nb_ops in iterator:
# update logs
for i in range(len(len1)):
beam_log[i + n_total.sum().item()] = {
"src": x1[1 : len1[i] - 1, i].tolist(),
"tgt": x2[1 : len2[i] - 1, i].tolist(),
"nb_ops": nb_ops[i].item(),
"hyps": [],
}
# target words to predict
alen = torch.arange(len2.max(), dtype=torch.long, device=len2.device)
pred_mask = (
alen[:, None] < len2[None] - 1
) # do not predict anything given the last target word
y = x2[1:].masked_select(pred_mask[:-1])
assert len(y) == (len2 - 1).sum().item()
# optionally truncate input
x1_, len1_ = x1, len1
# cuda
x1_, len1_, x2, len2, y = to_cuda(x1_, len1_, x2, len2, y)
bs = len(len1)
# forward
encoded = encoder("fwd", x=x1_, lengths=len1_, causal=False)
decoded = decoder(
"fwd",
x=x2,
lengths=len2,
causal=True,
src_enc=encoded.transpose(0, 1),
src_len=len1_,
)
word_scores, loss = decoder(
"predict", tensor=decoded, pred_mask=pred_mask, y=y, get_scores=True
)
# correct outputs per sequence / valid top-1 predictions
t = torch.zeros_like(pred_mask, device=y.device)
t[pred_mask] += word_scores.max(1)[1] == y
valid = (t.sum(0) == len2 - 1).cpu().long()
# update stats
xe_loss += loss.item() * len(y)
n_valid.index_add_(-1, nb_ops, valid)
n_total.index_add_(-1, nb_ops, torch.ones_like(nb_ops))
# update equations that were solved greedily
for i in range(len(len1)):
if valid[i]:
beam_log[i + n_total.sum().item() - bs]["hyps"].append(
(None, None, True)
)
# continue if everything is correct. if eval_verbose, perform
# a full beam search, even on correct greedy generations
if valid.sum() == len(valid) and params.eval_verbose < 2:
continue
# invalid top-1 predictions - check if there is a solution in the beam
invalid_idx = (1 - valid).nonzero().view(-1)
logger.info(
f"({n_total.sum().item()}/{eval_size}) Found "
f"{bs - len(invalid_idx)}/{bs} valid top-1 predictions. "
"Generating solutions ..."
)
# generate with beam search
_, _, generations = decoder.generate_beam(
encoded.transpose(0, 1),
len1_,
beam_size=params.beam_size,
length_penalty=params.beam_length_penalty,
early_stopping=params.beam_early_stopping,
max_len=params.max_len,
)
# prepare inputs / hypotheses to check
# if eval_verbose < 2, no beam search on equations solved greedily
for i in range(len(generations)):
if valid[i] and params.eval_verbose < 2:
continue
for j, (score, hyp) in enumerate(
sorted(generations[i].hyp, key=lambda x: x[0], reverse=True)
):
hyps_to_eval.append(
{
"i": i + n_total.sum().item() - bs,
"j": j,
"score": score,
"src": x1[1 : len1[i] - 1, i].tolist(),
"tgt": x2[1 : len2[i] - 1, i].tolist(),
"hyp": hyp[1:].tolist(),
"task": task,
}
)
# if the Jacobian is also predicted, only look at the eigenvalue
if task == "ode_convergence_speed":
sep_id = env.word2id[env.mtrx_separator]
for x in hyps_to_eval:
x["tgt"] = (
x["tgt"][x["tgt"].index(sep_id) + 1 :]
if sep_id in x["tgt"]
else x["tgt"]
)
x["hyp"] = (
x["hyp"][x["hyp"].index(sep_id) + 1 :]
if sep_id in x["hyp"]
else x["hyp"]
)
# solutions that perfectly match the reference with greedy decoding
assert all(
len(v["hyps"]) == 0
or len(v["hyps"]) == 1
and v["hyps"][0] == (None, None, True)
for v in beam_log.values()
)
init_valid = sum(
int(len(v["hyps"]) == 1 and v["hyps"][0][2] is True)
for v in beam_log.values()
)
logger.info(
f"Found {init_valid} solutions with greedy decoding "
"(perfect reference match)."
)
# check hypotheses with multiprocessing
eval_hyps = []
start = time.time()
logger.info(
f"Checking {len(hyps_to_eval)} hypotheses for "
f"{len(set(h['i'] for h in hyps_to_eval))} equations ..."
)
with ProcessPoolExecutor(max_workers=20) as executor:
for output in executor.map(check_hypothesis, hyps_to_eval, chunksize=1):
eval_hyps.append(output)
logger.info(f"Evaluation done in {time.time() - start:.2f} seconds.")
# update beam logs
for hyp in eval_hyps:
beam_log[hyp["i"]]["hyps"].append(
(hyp["hyp"], hyp["score"], hyp["is_valid"])
)
# print beam results
beam_valid = sum(
int(any(h[2] for h in v["hyps"]) and v["hyps"][0][1] is not None)
for v in beam_log.values()
)
all_valid = sum(int(any(h[2] for h in v["hyps"])) for v in beam_log.values())
assert init_valid + beam_valid == all_valid
assert len(beam_log) == n_total.sum().item()
logger.info(
f"Found {all_valid} valid solutions ({init_valid} with greedy decoding "
f"(perfect reference match), {beam_valid} with beam search)."
)
# update valid equation statistics
n_valid = torch.zeros(1000, dtype=torch.long)
for i, v in beam_log.items():
if any(h[2] for h in v["hyps"]):
n_valid[v["nb_ops"]] += 1
assert n_valid.sum().item() == all_valid
# export evaluation details
if params.eval_verbose:
eval_path = os.path.join(
params.dump_path, f"eval.beam.{data_type}.{task}.{scores['epoch']}"
)
with open(eval_path, "w") as f:
# for each equation
for i, res in sorted(beam_log.items()):
n_eq_valid = sum([int(v) for _, _, v in res["hyps"]])
src = idx_to_infix(env, res["src"], input=True).replace("|", " | ")
tgt = " ".join(env.id2word[wid] for wid in res["tgt"])
s = (
f"Equation {i} ({n_eq_valid}/{len(res['hyps'])})\n"
f"src={src}\ntgt={tgt}\n"
)
for hyp, score, valid in res["hyps"]:
if score is None:
assert hyp is None
s += f"{int(valid)} GREEDY\n"
else:
try:
hyp = " ".join(hyp)
except Exception:
hyp = f"INVALID OUTPUT {hyp}"
s += f"{int(valid)} {score :.3e} {hyp}\n"
if params.eval_verbose_print:
logger.info(s)
f.write(s + "\n")
f.flush()
logger.info(f"Evaluation results written in {eval_path}")
# log
_n_valid = n_valid.sum().item()
_n_total = n_total.sum().item()
logger.info(
f"{_n_valid}/{_n_total} ({100. * _n_valid / _n_total}%) equations "
"were evaluated correctly."
)
# compute perplexity and prediction accuracy
assert _n_total == eval_size
scores[f'{data_type}_{task}_xe_loss'] = xe_loss / _n_total
scores[f"{data_type}_{task}_beam_acc"] = 100.0 * _n_valid / _n_total
# per class perplexity and prediction accuracy
for i in range(len(n_total)):
if n_total[i].item() == 0:
continue
logger.info(
f"{i}: {n_valid[i].sum().item()} / {n_total[i].item()} "
f"({100. * n_valid[i].sum().item() / max(n_total[i].item(), 1)}%)"
)
scores[f"{data_type}_{task}_beam_acc_{i}"] = (
100.0 * n_valid[i].sum().item() / max(n_total[i].item(), 1)
)
def convert_to_text(batch, lengths, id2word, params):
"""
Convert a batch of sequences to a list of text sequences.
"""
batch = batch.cpu().numpy()
lengths = lengths.cpu().numpy()
slen, bs = batch.shape
assert lengths.max() == slen and lengths.shape[0] == bs
assert (batch[0] == params.eos_index).sum() == bs
assert (batch == params.eos_index).sum() == 2 * bs
sequences = []
for j in range(bs):
words = []
for k in range(1, lengths[j]):
if batch[k, j] == params.eos_index:
break
words.append(id2word[batch[k, j]])
sequences.append(" ".join(words))
return sequences
================================================
FILE: src/logger.py
================================================
# Copyright (c) 2020-present, Facebook, Inc.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
#
import logging
import time
from datetime import timedelta
class LogFormatter:
def __init__(self):
self.start_time = time.time()
def format(self, record):
elapsed_seconds = round(record.created - self.start_time)
prefix = "%s - %s - %s" % (
record.levelname,
time.strftime("%x %X"),
timedelta(seconds=elapsed_seconds),
)
message = record.getMessage()
message = message.replace("\n", "\n" + " " * (len(prefix) + 3))
return "%s - %s" % (prefix, message) if message else ""
def create_logger(filepath, rank):
"""
Create a logger.
Use a different log file for each process.
"""
# create log formatter
log_formatter = LogFormatter()
# create file handler and set level to debug
if filepath is not None:
if rank > 0:
filepath = "%s-%i" % (filepath, rank)
file_handler = logging.FileHandler(filepath, "a")
file_handler.setLevel(logging.DEBUG)
file_handler.setFormatter(log_formatter)
# create console handler and set level to info
console_handler = logging.StreamHandler()
console_handler.setLevel(logging.INFO)
console_handler.setFormatter(log_formatter)
# create logger and set level to debug
logger = logging.getLogger()
logger.handlers = []
logger.setLevel(logging.DEBUG)
logger.propagate = False
if filepath is not None:
logger.addHandler(file_handler)
logger.addHandler(console_handler)
# reset logger elapsed time
def reset_time():
log_formatter.start_time = time.time()
logger.reset_time = reset_time
return logger
================================================
FILE: src/model/__init__.py
================================================
# Copyright (c) 2020-present, Facebook, Inc.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
#
from logging import getLogger
import os
import torch
from .transformer import TransformerModel
logger = getLogger()
def check_model_params(params):
"""
Check models parameters.
"""
# model dimensions
assert params.emb_dim % params.n_heads == 0
# reload a pretrained model
if params.reload_model != '':
assert os.path.isfile(params.reload_model)
def build_modules(env, params):
"""
Build modules.
"""
modules = {}
modules['encoder'] = TransformerModel(params, env.id2word, is_encoder=True, with_output=False)
modules['decoder'] = TransformerModel(params, env.id2word, is_encoder=False, with_output=True)
# reload pretrained modules
if params.reload_model != '':
logger.info(f"Reloading modules from {params.reload_model} ...")
reloaded = torch.load(params.reload_model)
for k, v in modules.items():
assert k in reloaded
if all([k2.startswith('module.') for k2 in reloaded[k].keys()]):
reloaded[k] = {k2[len('module.'):]: v2 for k2, v2 in reloaded[k].items()}
v.load_state_dict(reloaded[k])
# log
for k, v in modules.items():
logger.debug(f"{v}: {v}")
for k, v in modules.items():
logger.info(f"Number of parameters ({k}): {sum([p.numel() for p in v.parameters() if p.requires_grad])}")
# cuda
if not params.cpu:
for v in modules.values():
v.cuda()
return modules
================================================
FILE: src/model/transformer.py
================================================
# Copyright (c) 2020-present, Facebook, Inc.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
#
from logging import getLogger
import math
import itertools
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
N_MAX_POSITIONS = 4096 # maximum input sequence length
logger = getLogger()
def Embedding(num_embeddings, embedding_dim, padding_idx=None):
m = nn.Embedding(num_embeddings, embedding_dim, padding_idx=padding_idx)
nn.init.normal_(m.weight, mean=0, std=embedding_dim ** -0.5)
if padding_idx is not None:
nn.init.constant_(m.weight[padding_idx], 0)
return m
def create_sinusoidal_embeddings(n_pos, dim, out):
position_enc = np.array([
[pos / np.power(10000, 2 * (j // 2) / dim) for j in range(dim)]
for pos in range(n_pos)
])
out[:, 0::2] = torch.FloatTensor(np.sin(position_enc[:, 0::2]))
out[:, 1::2] = torch.FloatTensor(np.cos(position_enc[:, 1::2]))
out.detach_()
out.requires_grad = False
def get_masks(slen, lengths, causal):
"""
Generate hidden states mask, and optionally an attention mask.
"""
assert lengths.max().item() <= slen
bs = lengths.size(0)
alen = torch.arange(slen, dtype=torch.long, device=lengths.device)
mask = alen < lengths[:, None]
# attention mask is the same as mask, or triangular inferior attention (causal)
if causal:
attn_mask = alen[None, None, :].repeat(bs, slen, 1) <= alen[None, :, None]
else:
attn_mask = mask
# sanity check
assert mask.size() == (bs, slen)
assert causal is False or attn_mask.size() == (bs, slen, slen)
return mask, attn_mask
class MultiHeadAttention(nn.Module):
NEW_ID = itertools.count()
def __init__(self, n_heads, dim, dropout):
super().__init__()
self.layer_id = next(MultiHeadAttention.NEW_ID)
self.dim = dim
self.n_heads = n_heads
self.dropout = dropout
assert self.dim % self.n_heads == 0
self.q_lin = nn.Linear(dim, dim)
self.k_lin = nn.Linear(dim, dim)
self.v_lin = nn.Linear(dim, dim)
self.out_lin = nn.Linear(dim, dim)
def forward(self, input, mask, kv=None, use_cache=False):
"""
Self-attention (if kv is None) or attention over source sentence (provided by kv).
Input is (bs, qlen, dim)
Mask is (bs, klen) (non-causal) or (bs, klen, klen)
"""
assert not (use_cache and self.cache is None)
bs, qlen, dim = input.size()
if kv is None:
klen = qlen if not use_cache else self.cache['slen'] + qlen
else:
klen = kv.size(1)
assert dim == self.dim, 'Dimensions do not match: %s input vs %s configured' % (dim, self.dim)
n_heads = self.n_heads
dim_per_head = dim // n_heads
mask_reshape = (bs, 1, qlen, klen) if mask.dim() == 3 else (bs, 1, 1, klen)
def shape(x):
""" projection """
return x.view(bs, -1, self.n_heads, dim_per_head).transpose(1, 2)
def unshape(x):
""" compute context """
return x.transpose(1, 2).contiguous().view(bs, -1, self.n_heads * dim_per_head)
q = shape(self.q_lin(input)) # (bs, n_heads, qlen, dim_per_head)
if kv is None:
k = shape(self.k_lin(input)) # (bs, n_heads, qlen, dim_per_head)
v = shape(self.v_lin(input)) # (bs, n_heads, qlen, dim_per_head)
elif not use_cache or self.layer_id not in self.cache:
k = v = kv
k = shape(self.k_lin(k)) # (bs, n_heads, qlen, dim_per_head)
v = shape(self.v_lin(v)) # (bs, n_heads, qlen, dim_per_head)
if use_cache:
if self.layer_id in self.cache:
if kv is None:
k_, v_ = self.cache[self.layer_id]
k = torch.cat([k_, k], dim=2) # (bs, n_heads, klen, dim_per_head)
v = torch.cat([v_, v], dim=2) # (bs, n_heads, klen, dim_per_head)
else:
k, v = self.cache[self.layer_id]
self.cache[self.layer_id] = (k, v)
q = q / math.sqrt(dim_per_head) # (bs, n_heads, qlen, dim_per_head)
scores = torch.matmul(q, k.transpose(2, 3)) # (bs, n_heads, qlen, klen)
mask = (mask == 0).view(mask_reshape).expand_as(scores) # (bs, n_heads, qlen, klen)
scores.masked_fill_(mask, -float('inf')) # (bs, n_heads, qlen, klen)
weights = F.softmax(scores.float(), dim=-1).type_as(scores) # (bs, n_heads, qlen, klen)
weights = F.dropout(weights, p=self.dropout, training=self.training) # (bs, n_heads, qlen, klen)
context = torch.matmul(weights, v) # (bs, n_heads, qlen, dim_per_head)
context = unshape(context) # (bs, qlen, dim)
if TransformerModel.STORE_OUTPUTS and not self.training:
self.outputs = weights.detach().cpu()
return self.out_lin(context)
class TransformerFFN(nn.Module):
def __init__(self, in_dim, dim_hidden, out_dim, dropout):
super().__init__()
self.dropout = dropout
self.lin1 = nn.Linear(in_dim, dim_hidden)
self.lin2 = nn.Linear(dim_hidden, out_dim)
def forward(self, input):
x = self.lin1(input)
x = F.relu(x)
x = self.lin2(x)
x = F.dropout(x, p=self.dropout, training=self.training)
return x
class TransformerModel(nn.Module):
STORE_OUTPUTS = False
def __init__(self, params, id2word, is_encoder, with_output):
"""
Transformer model (encoder or decoder).
"""
super().__init__()
# encoder / decoder, output layer
self.dtype = torch.half if params.fp16 else torch.float
self.is_encoder = is_encoder
self.is_decoder = not is_encoder
self.with_output = with_output
# dictionary
self.n_words = params.n_words
self.eos_index = params.eos_index
self.pad_index = params.pad_index
self.id2word = id2word
assert len(self.id2word) == self.n_words
# model parameters
self.dim = params.emb_dim # 512 by default
self.hidden_dim = self.dim * 4 # 2048 by default
self.n_heads = params.n_heads # 8 by default
self.n_layers = params.n_enc_layers if is_encoder else params.n_dec_layers
self.dropout = params.dropout
self.attention_dropout = params.attention_dropout
assert self.dim % self.n_heads == 0, 'transformer dim must be a multiple of n_heads'
# embeddings
self.position_embeddings = Embedding(N_MAX_POSITIONS, self.dim)
if params.sinusoidal_embeddings:
create_sinusoidal_embeddings(N_MAX_POSITIONS, self.dim, out=self.position_embeddings.weight)
self.embeddings = Embedding(self.n_words, self.dim, padding_idx=self.pad_index)
self.layer_norm_emb = nn.LayerNorm(self.dim, eps=1e-12)
# transformer layers
self.attentions = nn.ModuleList()
self.layer_norm1 = nn.ModuleList()
self.ffns = nn.ModuleList()
self.layer_norm2 = nn.ModuleList()
if self.is_decoder:
self.layer_norm15 = nn.ModuleList()
self.encoder_attn = nn.ModuleList()
for layer_id in range(self.n_layers):
self.attentions.append(MultiHeadAttention(self.n_heads, self.dim, dropout=self.attention_dropout))
self.layer_norm1.append(nn.LayerNorm(self.dim, eps=1e-12))
if self.is_decoder:
self.layer_norm15.append(nn.LayerNorm(self.dim, eps=1e-12))
self.encoder_attn.append(MultiHeadAttention(self.n_heads, self.dim, dropout=self.attention_dropout))
self.ffns.append(TransformerFFN(self.dim, self.hidden_dim, self.dim, dropout=self.dropout))
self.layer_norm2.append(nn.LayerNorm(self.dim, eps=1e-12))
self.cache = None
# output layer
if self.with_output:
self.proj = nn.Linear(self.dim, params.n_words, bias=True)
if params.share_inout_emb:
self.proj.weight = self.embeddings.weight
def forward(self, mode, **kwargs):
"""
Forward function with different forward modes.
### Small hack to handle PyTorch distributed.
"""
if mode == 'fwd':
return self.fwd(**kwargs)
elif mode == 'predict':
return self.predict(**kwargs)
else:
raise Exception("Unknown mode: %s" % mode)
def fwd(self, x, lengths, causal, src_enc=None, src_len=None, positions=None, use_cache=False):
"""
Inputs:
`x` LongTensor(slen, bs), containing word indices
`lengths` LongTensor(bs), containing the length of each sentence
`causal` Boolean, if True, the attention is only done over previous hidden states
`positions` LongTensor(slen, bs), containing word positions
"""
# lengths = (x != self.pad_index).float().sum(dim=1)
# mask = x != self.pad_index
# check inputs
slen, bs = x.size()
assert lengths.size(0) == bs
assert lengths.max().item() <= slen
x = x.transpose(0, 1) # batch size as dimension 0
assert (src_enc is None) == (src_len is None)
if src_enc is not None:
assert self.is_decoder
assert src_enc.size(0) == bs
assert not (use_cache and self.cache is None)
# generate masks
mask, attn_mask = get_masks(slen, lengths, causal)
if self.is_decoder and src_enc is not None:
src_mask = torch.arange(src_len.max(), dtype=torch.long, device=lengths.device) < src_len[:, None]
# positions
if positions is None:
positions = x.new(slen).long()
positions = torch.arange(slen, out=positions).unsqueeze(0)
else:
assert positions.size() == (slen, bs)
positions = positions.transpose(0, 1)
# do not recompute cached elements
if use_cache:
_slen = slen - self.cache['slen']
x = x[:, -_slen:]
positions = positions[:, -_slen:]
mask = mask[:, -_slen:]
attn_mask = attn_mask[:, -_slen:]
# all layer outputs
if TransformerModel.STORE_OUTPUTS and not self.training:
self.outputs = []
# embeddings
tensor = self.embeddings(x)
tensor = tensor + self.position_embeddings(positions).expand_as(tensor)
tensor = self.layer_norm_emb(tensor)
tensor = F.dropout(tensor, p=self.dropout, training=self.training)
tensor *= mask.unsqueeze(-1).to(tensor.dtype)
if TransformerModel.STORE_OUTPUTS and not self.training:
self.outputs.append(tensor.detach().cpu())
# transformer layers
for i in range(self.n_layers):
# self attention
self.attentions[i].cache = self.cache
attn = self.attentions[i](tensor, attn_mask, use_cache=use_cache)
attn = F.dropout(attn, p=self.dropout, training=self.training)
tensor = tensor + attn
tensor = self.layer_norm1[i](tensor)
# encoder attention (for decoder only)
if self.is_decoder and src_enc is not None:
self.encoder_attn[i].cache = self.cache
attn = self.encoder_attn[i](tensor, src_mask, kv=src_enc, use_cache=use_cache)
attn = F.dropout(attn, p=self.dropout, training=self.training)
tensor = tensor + attn
tensor = self.layer_norm15[i](tensor)
# FFN
tensor = tensor + self.ffns[i](tensor)
tensor = self.layer_norm2[i](tensor)
tensor *= mask.unsqueeze(-1).to(tensor.dtype)
if TransformerModel.STORE_OUTPUTS and not self.training:
self.outputs.append(tensor.detach().cpu())
# update cache length
if use_cache:
self.cache['slen'] += tensor.size(1)
# move back sequence length to dimension 0
tensor = tensor.transpose(0, 1)
return tensor
def predict(self, tensor, pred_mask, y, get_scores):
"""
Given the last hidden state, compute word scores and/or the loss.
`pred_mask` is a ByteTensor of shape (slen, bs), filled with 1 when
we need to predict a word
`y` is a LongTensor of shape (pred_mask.sum(),)
`get_scores` is a boolean specifying whether we need to return scores
"""
x = tensor[pred_mask.unsqueeze(-1).expand_as(tensor)].view(-1, self.dim)
assert (y == self.pad_index).sum().item() == 0
scores = self.proj(x).view(-1, self.n_words)
loss = F.cross_entropy(scores.float(), y, reduction='mean')
return scores, loss
def generate(self, src_enc, src_len, max_len=200, sample_temperature=None):
"""
Decode a sentence given initial start.
`x`:
- LongTensor(bs, slen)
<EOS> W1 W2 W3 <EOS> <PAD>
<EOS> W1 W2 W3 W4 <EOS>
`lengths`:
- LongTensor(bs) [5, 6]
`positions`:
- False, for regular "arange" positions (LM)
- True, to reset positions from the new generation (MT)
"""
# input batch
bs = len(src_len)
assert src_enc.size(0) == bs
# generated sentences
generated = src_len.new(max_len, bs) # upcoming output
generated.fill_(self.pad_index) # fill upcoming ouput with <PAD>
generated[0].fill_(self.eos_index) # we use <EOS> for <BOS> everywhere
# positions
positions = src_len.new(max_len).long()
positions = torch.arange(max_len, out=positions).unsqueeze(1).expand(max_len, bs)
# current position / max lengths / length of generated sentences / unfinished sentences
cur_len = 1
gen_len = src_len.clone().fill_(1)
unfinished_sents = src_len.clone().fill_(1)
# cache compute states
self.cache = {'slen': 0}
while cur_len < max_len:
# compute word scores
tensor = self.forward(
'fwd',
x=generated[:cur_len],
lengths=gen_len,
positions=positions[:cur_len],
causal=True,
src_enc=src_enc,
src_len=src_len,
use_cache=True
)
assert tensor.size() == (1, bs, self.dim)
tensor = tensor.data[-1, :, :].to(self.dtype) # (bs, dim)
scores = self.proj(tensor) # (bs, n_words)
# select next words: sample or greedy
if sample_temperature is None:
next_words = torch.topk(scores, 1)[1].squeeze(1)
else:
next_words = torch.multinomial(F.softmax(scores.float() / sample_temperature, dim=1), 1).squeeze(1)
assert next_words.size() == (bs,)
# update generations / lengths / finished sentences / current length
generated[cur_len] = next_words * unfinished_sents + self.pad_index * (1 - unfinished_sents)
gen_len.add_(unfinished_sents)
unfinished_sents.mul_(next_words.ne(self.eos_index).long())
cur_len = cur_len + 1
# stop when there is a </s> in each sentence, or if we exceed the maximul length
if unfinished_sents.max() == 0:
break
# add <EOS> to unfinished sentences
if cur_len == max_len:
generated[-1].masked_fill_(unfinished_sents.byte(), self.eos_index)
# sanity check
assert (generated == self.eos_index).sum() == 2 * bs
return generated[:cur_len], gen_len
def generate_beam(self, src_enc, src_len, beam_size, length_penalty, early_stopping, max_len=200):
"""
Decode a sentence given initial start.
`x`:
- LongTensor(bs, slen)
<EOS> W1 W2 W3 <EOS> <PAD>
<EOS> W1 W2 W3 W4 <EOS>
`lengths`:
- LongTensor(bs) [5, 6]
`positions`:
- False, for regular "arange" positions (LM)
- True, to reset positions from the new generation (MT)
"""
# check inputs
assert src_enc.size(0) == src_len.size(0)
assert beam_size >= 1
# batch size / number of words
bs = len(src_len)
n_words = self.n_words
# expand to beam size the source latent representations / source lengths
src_enc = src_enc.unsqueeze(1).expand((bs, beam_size) + src_enc.shape[1:]).contiguous().view((bs * beam_size,) + src_enc.shape[1:])
src_len = src_len.unsqueeze(1).expand(bs, beam_size).contiguous().view(-1)
# generated sentences (batch with beam current hypotheses)
generated = src_len.new(max_len, bs * beam_size) # upcoming output
generated.fill_(self.pad_index) # fill upcoming ouput with <PAD>
generated[0].fill_(self.eos_index) # we use <EOS> for <BOS> everywhere
# generated hypotheses
generated_hyps = [BeamHypotheses(beam_size, max_len, length_penalty, early_stopping) for _ in range(bs)]
# positions
positions = src_len.new(max_len).long()
positions = torch.arange(max_len, out=positions).unsqueeze(1).expand_as(generated)
# scores for each sentence in the beam
beam_scores = src_enc.new(bs, beam_size).float().fill_(0)
beam_scores[:, 1:] = -1e9
beam_scores = beam_scores.view(-1)
# current position
cur_len = 1
# cache compute states
self.cache = {'slen': 0}
# done sentences
done = [False for _ in range(bs)]
while cur_len < max_len:
# compute word scores
tensor = self.forward(
'fwd',
x=generated[:cur_len],
lengths=src_len.new(bs * beam_size).fill_(cur_len),
positions=positions[:cur_len],
causal=True,
src_enc=src_enc,
src_len=src_len,
use_cache=True
)
assert tensor.size() == (1, bs * beam_size, self.dim)
tensor = tensor.data[-1, :, :].to(self.dtype) # (bs * beam_size, dim)
scores = self.proj(tensor) # (bs * beam_size, n_words)
scores = F.log_softmax(scores.float(), dim=-1) # (bs * beam_size, n_words)
assert scores.size() == (bs * beam_size, n_words)
# select next words with scores
_scores = scores + beam_scores[:, None].expand_as(scores) # (bs * beam_size, n_words)
_scores = _scores.view(bs, beam_size * n_words) # (bs, beam_size * n_words)
next_scores, next_words = torch.topk(_scores, 2 * beam_size, dim=1, largest=True, sorted=True)
assert next_scores.size() == next_words.size() == (bs, 2 * beam_size)
# next batch beam content
# list of (bs * beam_size) tuple(next hypothesis score, next word, current position in the batch)
next_batch_beam = []
# for each sentence
for sent_id in range(bs):
# if we are done with this sentence
done[sent_id] = done[sent_id] or generated_hyps[sent_id].is_done(next_scores[sent_id].max().item())
if done[sent_id]:
next_batch_beam.extend([(0, self.pad_index, 0)] * beam_size) # pad the batch
continue
# next sentence beam content
next_sent_beam = []
# next words for this sentence
for idx, value in zip(next_words[sent_id], next_scores[sent_id]):
# get beam and word IDs
beam_id = idx // n_words
word_id = idx % n_words
# end of sentence, or next word
if word_id == self.eos_index or cur_len + 1 == max_len:
generated_hyps[sent_id].add(generated[:cur_len, sent_id * beam_size + beam_id].clone().cpu(), value.item())
else:
next_sent_beam.append((value, word_id, sent_id * beam_size + beam_id))
# the beam for next step is full
if len(next_sent_beam) == beam_size:
break
# update next beam content
assert len(next_sent_beam) == 0 if cur_len + 1 == max_len else beam_size
if len(next_sent_beam) == 0:
next_sent_beam = [(0, self.pad_index, 0)] * beam_size # pad the batch
next_batch_beam.extend(next_sent_beam)
assert len(next_batch_beam) == beam_size * (sent_id + 1)
# sanity check / prepare next batch
assert len(next_batch_beam) == bs * beam_size
beam_scores = beam_scores.new([x[0] for x in next_batch_beam])
beam_words = generated.new([x[1] for x in next_batch_beam])
beam_idx = src_len.new([x[2] for x in next_batch_beam])
# re-order batch and internal states
generated = generated[:, beam_idx]
generated[cur_len] = beam_words
for k in self.cache.keys():
if k != 'slen':
self.cache[k] = (self.cache[k][0][beam_idx], self.cache[k][1][beam_idx])
# update current length
cur_len = cur_len + 1
# stop when we are done with each sentence
if all(done):
break
# def get_coeffs(s):
# roots = [int(s[i + 2]) for i, c in enumerate(s) if c == 'x']
# poly = np.poly1d(roots, r=True)
# coeffs = list(poly.coefficients.astype(np.int64))
# return [c % 10 for c in coeffs], coeffs
# visualize hypotheses
# print([len(x) for x in generated_hyps], cur_len)
# globals().update( locals() );
# !import code; code.interact(local=vars())
# for ii in range(bs):
# for ss, ww in sorted(generated_hyps[ii].hyp, key=lambda x: x[0], reverse=True):
# hh = " ".join(self.id2word[x] for x in ww.tolist())
# print(f"{ss:+.4f} {hh}")
# # cc = get_coeffs(hh[4:])
# # print(f"{ss:+.4f} {hh} || {cc[0]} || {cc[1]}")
# print("")
# select the best hypotheses
tgt_len = src_len.new(bs)
best = []
for i, hypotheses in enumerate(generated_hyps):
best_hyp = max(hypotheses.hyp, key=lambda x: x[0])[1]
tgt_len[i] = len(best_hyp) + 1 # +1 for the <EOS> symbol
best.append(best_hyp)
# generate target batch
decoded = src_len.new(tgt_len.max().item(), bs).fill_(self.pad_index)
for i, hypo in enumerate(best):
decoded[:tgt_len[i] - 1, i] = hypo
decoded[tgt_len[i] - 1, i] = self.eos_index
# sanity check
assert (decoded == self.eos_index).sum() == 2 * bs
return decoded, tgt_len, generated_hyps
class BeamHypotheses(object):
def __init__(self, n_hyp, max_len, length_penalty, early_stopping):
"""
Initialize n-best list of hypotheses.
"""
self.max_len = max_len - 1 # ignoring <BOS>
self.length_penalty = length_penalty
self.early_stopping = early_stopping
self.n_hyp = n_hyp
self.hyp = []
self.worst_score = 1e9
def __len__(self):
"""
Number of hypotheses in the list.
"""
return len(self.hyp)
def add(self, hyp, sum_logprobs):
"""
Add a new hypothesis to the list.
"""
score = sum_logprobs / len(hyp) ** self.length_penalty
if len(self) < self.n_hyp or score > self.worst_score:
self.hyp.append((score, hyp))
if len(self) > self.n_hyp:
sorted_scores = sorted([(s, idx) for idx, (s, _) in enumerate(self.hyp)])
del self.hyp[sorted_scores[0][1]]
self.worst_score = sorted_scores[1][0]
else:
self.worst_score = min(score, self.worst_score)
def is_done(self, best_sum_logprobs):
"""
If there are enough hypotheses and that none of the hypotheses being generated
can become better than the worst one in the heap, then we are done with this sentence.
"""
if len(self) < self.n_hyp:
return False
elif self.early_stopping:
return True
else:
return self.worst_score >= best_sum_logprobs / self.max_len ** self.length_penalty
================================================
FILE: src/optim.py
================================================
# Copyright (c) 2020-present, Facebook, Inc.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
#
import re
import math
import inspect
import torch
from torch import optim
class Adam(optim.Optimizer):
"""
Same as https://github.com/pytorch/pytorch/blob/master/torch/optim/adam.py,
without amsgrad, with step in a tensor, and states initialization in __init__.
It was important to add `.item()` in `state['step'].item()`.
"""
def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8, weight_decay=0):
if not 0.0 <= lr:
raise ValueError("Invalid learning rate: {}".format(lr))
if not 0.0 <= eps:
raise ValueError("Invalid epsilon value: {}".format(eps))
if not 0.0 <= betas[0] < 1.0:
raise ValueError("Invalid beta parameter at index 0: {}".format(betas[0]))
if not 0.0 <= betas[1] < 1.0:
raise ValueError("Invalid beta parameter at index 1: {}".format(betas[1]))
defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay)
super().__init__(params, defaults)
for group in self.param_groups:
for p in group["params"]:
state = self.state[p]
state["step"] = 0 # torch.zeros(1)
state["exp_avg"] = torch.zeros_like(p.data)
state["exp_avg_sq"] = torch.zeros_like(p.data)
def __setstate__(self, state):
super().__setstate__(state)
def step(self, closure=None):
"""
Step.
"""
loss = None
if closure is not None:
loss = closure()
for group in self.param_groups:
for p in group["params"]:
if p.grad is None:
continue
grad = p.grad.data
if grad.is_sparse:
raise RuntimeError(
"Adam does not support sparse gradients, "
"please consider SparseAdam instead"
)
state = self.state[p]
exp_avg, exp_avg_sq = state["exp_avg"], state["exp_avg_sq"]
beta1, beta2 = group["betas"]
state["step"] += 1
# if group['weight_decay'] != 0:
# grad.add_(group['weight_decay'], p.data)
# Decay the first and second moment running average coefficient
exp_avg.mul_(beta1).add_(1 - beta1, grad)
exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
denom = exp_avg_sq.sqrt().add_(group["eps"])
# denom = exp_avg_sq.sqrt().clamp_(min=group['eps'])
bias_correction1 = 1 - beta1 ** state["step"] # .item()
bias_correction2 = 1 - beta2 ** state["step"] # .item()
step_size = group["lr"] * math.sqrt(bias_correction2) / bias_correction1
if group["weight_decay"] != 0:
p.data.add_(-group["weight_decay"] * group["lr"], p.data)
p.data.addcdiv_(-step_size, exp_avg, denom)
return loss
class AdamInverseSqrtWithWarmup(Adam):
"""
Decay the LR based on the inverse square root of the update number.
We also support a warmup phase where we linearly increase the learning rate
from some initial learning rate (`warmup-init-lr`) until the configured
learning rate (`lr`). Thereafter we decay proportional to the number of
updates, with a decay factor set to align with the configured learning rate.
During warmup:
lrs = torch.linspace(warmup_init_lr, lr, warmup_updates)
lr = lrs[update_num]
After warmup:
lr = decay_factor / sqrt(update_num)
where
decay_factor = lr * sqrt(warmup_updates)
"""
def __init__(
self,
params,
lr=1e-3,
betas=(0.9, 0.999),
eps=1e-8,
weight_decay=0,
warmup_updates=4000,
warmup_init_lr=1e-7,
exp_factor=0.5,
):
super().__init__(
params, lr=warmup_init_lr, betas=betas, eps=eps, weight_decay=weight_decay,
)
# linearly warmup for the first warmup_updates
self.warmup_updates = warmup_updates
self.warmup_init_lr = warmup_init_lr
warmup_end_lr = lr
self.lr_step = (warmup_end_lr - warmup_init_lr) / warmup_updates
# then, decay prop. to the inverse square root of the update number
self.exp_factor = exp_factor
self.decay_factor = warmup_end_lr * warmup_updates ** self.exp_factor
# total number of updates
for param_group in self.param_groups:
param_group["num_updates"] = 0
def get_lr_for_step(self, num_updates):
if num_updates < self.warmup_updates:
return self.warmup_init_lr + num_updates * self.lr_step
else:
return self.decay_factor * (num_updates ** -self.exp_factor)
def step(self, closure=None):
super().step(closure)
for param_group in self.param_groups:
param_group["num_updates"] += 1
param_group["lr"] = self.get_lr_for_step(param_group["num_updates"])
class AdamCosineWithWarmup(Adam):
"""
Assign LR based on a cyclical schedule that follows the cosine function.
See https://arxiv.org/pdf/1608.03983.pdf for details.
We also support a warmup phase where we linearly increase the learning rate
from some initial learning rate (``--warmup-init-lr``) until the configured
learning rate (``--lr``).
During warmup::
lrs = torch.linspace(args.warmup_init_lr, args.lr, args.warmup_updates)
lr = lrs[update_num]
After warmup::
lr = lr_min + 0.5*(lr_max - lr_min)*(1 + cos(t_curr / t_i))
where ``t_curr`` is current percentage of updates within the current period
range and ``t_i`` is the current period range, which is scaled by ``t_mul``
after every iteration.
"""
def __init__(
self,
params,
lr=1e-3,
betas=(0.9, 0.999),
eps=1e-8,
weight_decay=0,
warmup_updates=4000,
warmup_init_lr=1e-7,
min_lr=1e-9,
init_period=1000000,
period_mult=1,
lr_shrink=0.75,
):
super().__init__(
params, lr=warmup_init_lr, betas=betas, eps=eps, weight_decay=weight_decay,
)
# linearly warmup for the first warmup_updates
self.warmup_updates = warmup_updates
self.warmup_init_lr = warmup_init_lr
warmup_end_lr = lr
self.lr_step = (warmup_end_lr - warmup_init_lr) / warmup_updates
# then, apply cosine scheduler
self.min_lr = min_lr
self.max_lr = lr
self.period = init_period
self.period_mult = period_mult
self.lr_shrink = lr_shrink
# total number of updates
for param_group in self.param_groups:
param_group["num_updates"] = 0
def get_lr_for_step(self, num_updates):
if num_updates < self.warmup_updates:
return self.warmup_init_lr + num_updates * self.lr_step
else:
t = num_updates - self.warmup_updates
if self.period_mult == 1:
pid = math.floor(t / self.period)
t_i = self.period
t_curr = t - (self.period * pid)
else:
pid = math.floor(
math.log(
1 - t / self.period * (1 - self.period_mult), self.period_mult
)
)
t_i = self.period * (self.period_mult ** pid)
t_curr = (
t
- (1 - self.period_mult ** pid)
/ (1 - self.period_mult)
* self.period
)
lr_shrink = self.lr_shrink ** pid
min_lr = self.min_lr * lr_shrink
max_lr = self.max_lr * lr_shrink
return min_lr + 0.5 * (max_lr - min_lr) * (
1 + math.cos(math.pi * t_curr / t_i)
)
def step(self, closure=None):
super().step(closure)
for param_group in self.param_groups:
param_group["num_updates"] += 1
param_group["lr"] = self.get_lr_for_step(param_group["num_updates"])
def get_optimizer(parameters, s):
"""
Parse optimizer parameters.
Input should be of the form:
- "sgd,lr=0.01"
- "adagrad,lr=0.1,lr_decay=0.05"
"""
if "," in s:
method = s[: s.find(",")]
optim_params = {}
for x in s[s.find(",") + 1 :].split(","):
split = x.split("=")
assert len(split) == 2
assert re.match(r"^[+-]?(\d+(\.\d*)?|\.\d+)$", split[1]) is not None
optim_params[split[0]] = float(split[1])
else:
method = s
optim_params = {}
if method == "adadelta":
optim_fn = optim.Adadelta
elif method == "adagrad":
optim_fn = optim.Adagrad
elif method == "adam":
optim_fn = Adam
optim_params["betas"] = (
optim_params.get("beta1", 0.9),
optim_params.get("beta2", 0.999),
)
optim_params.pop("beta1", None)
optim_params.pop("beta2", None)
elif method == "adam_inverse_sqrt":
optim_fn = AdamInverseSqrtWithWarmup
optim_params["betas"] = (
optim_params.get("beta1", 0.9),
optim_params.get("beta2", 0.999),
)
optim_params.pop("beta1", None)
optim_params.pop("beta2", None)
elif method == "adam_cosine":
optim_fn = AdamCosineWithWarmup
optim_params["betas"] = (
optim_params.get("beta1", 0.9),
optim_params.get("beta2", 0.999),
)
optim_params.pop("beta1", None)
optim_params.pop("beta2", None)
elif method == "adamax":
optim_fn = optim.Adamax
elif method == "asgd":
optim_fn = optim.ASGD
elif method == "rmsprop":
optim_fn = optim.RMSprop
elif method == "rprop":
optim_fn = optim.Rprop
elif method == "sgd":
optim_fn = optim.SGD
assert "lr" in optim_params
else:
raise Exception('Unknown optimization method: "%s"' % method)
# check that we give good parameters to the optimizer
expected_args = inspect.getargspec(optim_fn.__init__)[0]
assert expected_args[:2] == ["self", "params"]
if not all(k in expected_args[2:] for k in optim_params.keys()):
raise Exception(
'Unexpected parameters: expected "%s", got "%s"'
% (str(expected_args[2:]), str(optim_params.keys()))
)
return optim_fn(parameters, **optim_params)
================================================
FILE: src/slurm.py
================================================
# Copyright (c) 2020-present, Facebook, Inc.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
#
from logging import getLogger
import os
import sys
import torch
import socket
import signal
import subprocess
logger = getLogger()
def sig_handler(signum, frame):
logger.warning("Signal handler called with signal " + str(signum))
prod_id = int(os.environ["SLURM_PROCID"])
logger.warning("Host: %s - Global rank: %i" % (socket.gethostname(), prod_id))
if prod_id == 0:
logger.warning("Requeuing job " + os.environ["SLURM_JOB_ID"])
os.system("scontrol requeue " + os.environ["SLURM_JOB_ID"])
else:
logger.warning("Not the master process, no need to requeue.")
sys.exit(-1)
def term_handler(signum, frame):
logger.warning("Signal handler called with signal " + str(signum))
logger.warning("Bypassing SIGTERM.")
def init_signal_handler():
"""
Handle signals sent by SLURM for time limit / pre-emption.
"""
signal.signal(signal.SIGUSR1, sig_handler)
signal.signal(signal.SIGTERM, term_handler)
logger.warning("Signal handler installed.")
def init_distributed_mode(params):
"""
Handle single and multi-GPU / multi-node / SLURM jobs.
Initialize the following variables:
- n_nodes
- node_id
- local_rank
- global_rank
- world_size
"""
params.is_slurm_job = "SLURM_JOB_ID" in os.environ and not params.debug_slurm
print("SLURM job: %s" % str(params.is_slurm_job))
# SLURM job
if params.is_slurm_job:
assert params.local_rank == -1 # on the cluster, this is handled by SLURM
SLURM_VARIABLES = [
"SLURM_JOB_ID",
"SLURM_JOB_NODELIST",
"SLURM_JOB_NUM_NODES",
"SLURM_NTASKS",
"SLURM_TASKS_PER_NODE",
"SLURM_MEM_PER_NODE",
"SLURM_MEM_PER_CPU",
"SLURM_NODEID",
"SLURM_PROCID",
"SLURM_LOCALID",
"SLURM_TASK_PID",
]
PREFIX = "%i - " % int(os.environ["SLURM_PROCID"])
for name in SLURM_VARIABLES:
value = os.environ.get(name, None)
print(PREFIX + "%s: %s" % (name, str(value)))
# # job ID
# params.job_id = os.environ['SLURM_JOB_ID']
# number of nodes / node ID
params.n_nodes = int(os.environ["SLURM_JOB_NUM_NODES"])
params.node_id = int(os.environ["SLURM_NODEID"])
# local rank on the current node / global rank
params.local_rank = int(os.environ["SLURM_LOCALID"])
params.global_rank = int(os.environ["SLURM_PROCID"])
# number of processes / GPUs per node
params.world_size = int(os.environ["SLURM_NTASKS"])
params.n_gpu_per_node = params.world_size // params.n_nodes
# define master address and master port
hostnames = subprocess.check_output(
["scontrol", "show", "hostnames", os.environ["SLURM_JOB_NODELIST"]]
)
params.master_addr = hostnames.split()[0].decode("utf-8")
assert 10001 <= params.master_port <= 20000 or params.world_size == 1
print(PREFIX + "Master address: %s" % params.master_addr)
print(PREFIX + "Master port : %i" % params.master_port)
# set environment variables for 'env://'
os.environ["MASTER_ADDR"] = params.master_addr
os.environ["MASTER_PORT"] = str(params.master_port)
os.environ["WORLD_SIZE"] = str(params.world_size)
os.environ["RANK"] = str(params.global_rank)
# multi-GPU job (local or multi-node) - jobs started with torch.distributed.launch
elif params.local_rank != -1:
assert params.master_port == -1
# read environment variables
params.global_rank = int(os.environ["RANK"])
params.world_size = int(os.environ["WORLD_SIZE"])
params.n_gpu_per_node = int(os.environ["NGPU"])
# number of nodes / node ID
params.n_nodes = params.world_size // params.n_gpu_per_node
params.node_id = params.global_rank // params.n_gpu_per_node
# local job (single GPU)
else:
assert params.local_rank == -1
assert params.master_port == -1
params.n_nodes = 1
params.node_id = 0
params.local_rank = 0
params.global_rank = 0
params.world_size = 1
params.n_gpu_per_node = 1
# sanity checks
assert params.n_nodes >= 1
assert 0 <= params.node_id < params.n_nodes
assert 0 <= params.local_rank <= params.global_rank < params.world_size
assert params.world_size == params.n_nodes * params.n_gpu_per_node
# define whether this is the master process / if we are in distributed mode
params.is_master = params.node_id == 0 and params.local_rank == 0
params.multi_node = params.n_nodes > 1
params.multi_gpu = params.world_size > 1
# summary
PREFIX = "%i - " % params.global_rank
print(PREFIX + "Number of nodes: %i" % params.n_nodes)
print(PREFIX + "Node ID : %i" % params.node_id)
print(PREFIX + "Local rank : %i" % params.local_rank)
print(PREFIX + "Global rank : %i" % params.global_rank)
print(PREFIX + "World size : %i" % params.world_size)
print(PREFIX + "GPUs per node : %i" % params.n_gpu_per_node)
print(PREFIX + "Master : %s" % str(params.is_master))
print(PREFIX + "Multi-node : %s" % str(params.multi_node))
print(PREFIX + "Multi-GPU : %s" % str(params.multi_gpu))
print(PREFIX + "Hostname : %s" % socket.gethostname())
# set GPU device
if not params.cpu:
torch.cuda.set_device(params.local_rank)
# initialize multi-GPU
if params.multi_gpu:
# http://pytorch.apachecn.org/en/0.3.0/distributed.html#environment-variable-initialization
# 'env://' will read these environment variables:
# MASTER_PORT - required; has to be a free port on machine with rank 0
# MASTER_ADDR - required (except for rank 0); address of rank 0 node
# WORLD_SIZE - required; can be set either here, or in a call to init function
# RANK - required; can be set either here, or in a call to init function
print("Initializing PyTorch distributed ...")
torch.distributed.init_process_group(
init_method="env://", backend="nccl",
)
================================================
FILE: src/trainer.py
================================================
# Copyright (c) 2020-present, Facebook, Inc.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
#
import os
import io
import sys
import time
from logging import getLogger
from collections import OrderedDict
import numpy as np
import torch
from torch import nn
from torch.nn.utils import clip_grad_norm_
from .optim import get_optimizer
from .utils import to_cuda
if torch.cuda.is_available():
import apex
logger = getLogger()
class Trainer(object):
EQUATIONS = {}
def __init__(self, modules, env, params):
"""
Initialize trainer.
"""
# modules / params
self.modules = modules
self.params = params
self.env = env
# epoch / iteration size
self.epoch_size = params.epoch_size
if self.epoch_size == -1:
self.epoch_size = self.data
assert self.epoch_size > 0
# data iterators
self.iterators = {}
# set parameters
self.set_parameters()
# float16 / distributed (no AMP)
assert params.amp >= 1 or not params.fp16
assert params.amp >= 0 or params.accumulate_gradients == 1
if params.multi_gpu and params.amp == -1:
logger.info("Using nn.parallel.DistributedDataParallel ...")
for k in self.modules.keys():
self.modules[k] = nn.parallel.DistributedDataParallel(
self.modules[k],
device_ids=[params.local_rank],
output_device=params.local_rank,
broadcast_buffers=True,
)
# set optimizers
self.set_optimizers()
# float16 / distributed (AMP)
if params.amp >= 0:
self.init_amp()
if params.multi_gpu:
logger.info("Using apex.parallel.DistributedDataParallel ...")
for k in self.modules.keys():
self.modules[k] = apex.parallel.DistributedDataParallel(
self.modules[k], delay_allreduce=True
)
# stopping criterion used for early stopping
if params.stopping_criterion != "":
split = params.stopping_criterion.split(",")
assert len(split) == 2 and split[1].isdigit()
self.decrease_counts_max = int(split[1])
self.decrease_counts = 0
if split[0][0] == "_":
self.stopping_criterion = (split[0][1:], False)
else:
self.stopping_criterion = (split[0], True)
self.best_stopping_criterion = -1e12 if self.stopping_criterion[1] else 1e12
else:
self.stopping_criterion = None
self.best_stopping_criterion = None
# validation metrics
self.metrics = []
metrics = [m for m in params.validation_metrics.split(",") if m != ""]
for m in metrics:
m = (m[1:], False) if m[0] == "_" else (m, True)
self.metrics.append(m)
self.best_metrics = {
metric: (-1e12 if biggest else 1e12) for (metric, biggest) in self.metrics
}
# training statistics
self.epoch = 0
self.n_iter = 0
self.n_total_iter = 0
gitextract_0mmsfh5n/ ├── CODE_OF_CONDUCT.md ├── CONTRIBUTING.md ├── LICENSE ├── README.md ├── split_data.py ├── src/ │ ├── __init__.py │ ├── envs/ │ │ ├── __init__.py │ │ └── ode.py │ ├── evaluator.py │ ├── logger.py │ ├── model/ │ │ ├── __init__.py │ │ └── transformer.py │ ├── optim.py │ ├── slurm.py │ ├── trainer.py │ └── utils.py └── train.py
SYMBOL INDEX (142 symbols across 11 files)
FILE: src/envs/__init__.py
function build_env (line 21) | def build_env(params):
FILE: src/envs/ode.py
class UnknownSymPyOperator (line 37) | class UnknownSymPyOperator(Exception):
class InvalidPrefixExpression (line 41) | class InvalidPrefixExpression(Exception):
method __init__ (line 42) | def __init__(self, data):
method __str__ (line 45) | def __str__(self):
function has_inf_nan (line 49) | def has_inf_nan(*args):
function second_index (line 59) | def second_index(x, bal):
function simplify (line 69) | def simplify(f, seconds):
function expr_to_fun_real (line 93) | def expr_to_fun_real(x, fun, dimension):
class Node (line 105) | class Node:
method __init__ (line 106) | def __init__(self, value, children=None):
method push_child (line 110) | def push_child(self, child):
method prefix (line 113) | def prefix(self):
method qtree_prefix (line 120) | def qtree_prefix(self):
method infix (line 127) | def infix(self):
method __len__ (line 139) | def __len__(self):
method __str__ (line 145) | def __str__(self):
class ODEEnvironment (line 150) | class ODEEnvironment(object):
method __init__ (line 158) | def __init__(self, params):
method get_integer (line 333) | def get_integer(self, cplex=False):
method generate_leaf (line 356) | def generate_leaf(self, degree, index):
method generate_ops (line 364) | def generate_ops(self, arity):
method generate_dist (line 381) | def generate_dist(self, max_ops):
method sample_next_pos (line 405) | def sample_next_pos(self, nb_empty, nb_ops):
method generate_tree (line 425) | def generate_tree(self, nb_ops, degree, index=0):
method generate_polynomial (line 447) | def generate_polynomial(
method batch_sequences (line 489) | def batch_sequences(self, sequences):
method write_int (line 508) | def write_int(self, val):
method parse_int (line 524) | def parse_int(self, lst):
method write_float (line 542) | def write_float(self, value, precision=None):
method parse_float (line 554) | def parse_float(self, lst):
method write_complex (line 592) | def write_complex(self, value, precision=None):
method parse_complex (line 605) | def parse_complex(self, lst):
method input_to_infix (line 620) | def input_to_infix(self, lst):
method output_to_infix (line 637) | def output_to_infix(self, lst):
method prefix_to_infix (line 641) | def prefix_to_infix(self, expr):
method _sympy_to_prefix (line 672) | def _sympy_to_prefix(self, op, expr):
method sympy_to_prefix (line 703) | def sympy_to_prefix(self, expr):
method encode_expr (line 729) | def encode_expr(self, tree, cplx=False):
method compute_gradient (line 746) | def compute_gradient(self, expr, point, degree):
method gen_ode_system_convergence (line 758) | def gen_ode_system_convergence(self, return_system=False):
method compute_gradient_control (line 878) | def compute_gradient_control(self, expr, point, degree, p):
method gen_control (line 899) | def gen_control(self, return_system=False, skip_unstable=False):
method compute_gradient_control_t (line 1072) | def compute_gradient_control_t(self, expr, point, degree, p):
method compute_rank (line 1091) | def compute_rank(self, A, B, degree, p, val):
method gen_control_t (line 1111) | def gen_control_t(self):
method generate_cond_init (line 1218) | def generate_cond_init(self, max_delay, dimension, unariesexp, unaries...
method gen_fourier_cond_init (line 1307) | def gen_fourier_cond_init(self):
method create_train_iterator (line 1402) | def create_train_iterator(self, task, data_path, params):
method create_test_iterator (line 1428) | def create_test_iterator(
method register_args (line 1459) | def register_args(parser):
class EnvDataset (line 1636) | class EnvDataset(Dataset):
method __init__ (line 1637) | def __init__(self, env, task, train, params, path, size=None):
method collate_fn (line 1709) | def collate_fn(self, elements):
method init_rng (line 1721) | def init_rng(self):
method get_worker_id (line 1741) | def get_worker_id(self):
method __len__ (line 1751) | def __len__(self):
method __getitem__ (line 1757) | def __getitem__(self, index):
method read_sample (line 1768) | def read_sample(self, index):
method generate_sample (line 1780) | def generate_sample(self):
FILE: src/evaluator.py
function check_fourier_cond_init (line 28) | def check_fourier_cond_init(env, src, tgt, hyp):
function idx_to_infix (line 143) | def idx_to_infix(env, idx, input=True):
function compare_gramians (line 152) | def compare_gramians(env, tgt, hyp, tolerance, norm1=False):
function check_gramian (line 204) | def check_gramian(env, src, tgt, hyp):
function check_hypothesis (line 266) | def check_hypothesis(eq):
class Evaluator (line 338) | class Evaluator(object):
method __init__ (line 342) | def __init__(self, trainer):
method run_all_evals (line 352) | def run_all_evals(self):
method truncate_at (line 377) | def truncate_at(self, x, xlen):
method enc_dec_step (line 402) | def enc_dec_step(self, data_type, task, scores):
method enc_dec_step_beam_fast (line 536) | def enc_dec_step_beam_fast(self, data_type, task, scores, size=None):
function convert_to_text (line 812) | def convert_to_text(batch, lengths, id2word, params):
FILE: src/logger.py
class LogFormatter (line 13) | class LogFormatter:
method __init__ (line 14) | def __init__(self):
method format (line 17) | def format(self, record):
function create_logger (line 30) | def create_logger(filepath, rank):
FILE: src/model/__init__.py
function check_model_params (line 18) | def check_model_params(params):
function build_modules (line 30) | def build_modules(env, params):
FILE: src/model/transformer.py
function Embedding (line 23) | def Embedding(num_embeddings, embedding_dim, padding_idx=None):
function create_sinusoidal_embeddings (line 31) | def create_sinusoidal_embeddings(n_pos, dim, out):
function get_masks (line 42) | def get_masks(slen, lengths, causal):
class MultiHeadAttention (line 64) | class MultiHeadAttention(nn.Module):
method __init__ (line 68) | def __init__(self, n_heads, dim, dropout):
method forward (line 81) | def forward(self, input, mask, kv=None, use_cache=False):
class TransformerFFN (line 141) | class TransformerFFN(nn.Module):
method __init__ (line 143) | def __init__(self, in_dim, dim_hidden, out_dim, dropout):
method forward (line 149) | def forward(self, input):
class TransformerModel (line 157) | class TransformerModel(nn.Module):
method __init__ (line 161) | def __init__(self, params, id2word, is_encoder, with_output):
method forward (line 222) | def forward(self, mode, **kwargs):
method fwd (line 234) | def fwd(self, x, lengths, causal, src_enc=None, src_len=None, position...
method predict (line 325) | def predict(self, tensor, pred_mask, y, get_scores):
method generate (line 339) | def generate(self, src_enc, src_len, max_len=200, sample_temperature=N...
method generate_beam (line 417) | def generate_beam(self, src_enc, src_len, beam_size, length_penalty, e...
class BeamHypotheses (line 594) | class BeamHypotheses(object):
method __init__ (line 596) | def __init__(self, n_hyp, max_len, length_penalty, early_stopping):
method __len__ (line 607) | def __len__(self):
method add (line 613) | def add(self, hyp, sum_logprobs):
method is_done (line 627) | def is_done(self, best_sum_logprobs):
FILE: src/optim.py
class Adam (line 16) | class Adam(optim.Optimizer):
method __init__ (line 23) | def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8, weig...
method __setstate__ (line 42) | def __setstate__(self, state):
method step (line 45) | def step(self, closure=None):
class AdamInverseSqrtWithWarmup (line 92) | class AdamInverseSqrtWithWarmup(Adam):
method __init__ (line 108) | def __init__(
method get_lr_for_step (line 137) | def get_lr_for_step(self, num_updates):
method step (line 143) | def step(self, closure=None):
class AdamCosineWithWarmup (line 150) | class AdamCosineWithWarmup(Adam):
method __init__ (line 167) | def __init__(
method get_lr_for_step (line 202) | def get_lr_for_step(self, num_updates):
method step (line 231) | def step(self, closure=None):
function get_optimizer (line 238) | def get_optimizer(parameters, s):
FILE: src/slurm.py
function sig_handler (line 20) | def sig_handler(signum, frame):
function term_handler (line 32) | def term_handler(signum, frame):
function init_signal_handler (line 37) | def init_signal_handler():
function init_distributed_mode (line 46) | def init_distributed_mode(params):
FILE: src/trainer.py
class Trainer (line 29) | class Trainer(object):
method __init__ (line 33) | def __init__(self, modules, env, params):
method set_parameters (line 164) | def set_parameters(self):
method set_optimizers (line 179) | def set_optimizers(self):
method init_amp (line 190) | def init_amp(self):
method optimize (line 211) | def optimize(self, loss):
method iter (line 257) | def iter(self):
method print_stats (line 265) | def print_stats(self):
method save_checkpoint (line 307) | def save_checkpoint(self, name, include_optimizers=True):
method reload_checkpoint (line 336) | def reload_checkpoint(self):
method save_periodic (line 390) | def save_periodic(self):
method save_best_model (line 402) | def save_best_model(self, scores):
method end_epoch (line 418) | def end_epoch(self, scores):
method get_batch (line 454) | def get_batch(self, task):
method export_data (line 478) | def export_data(self, task):
method enc_dec_step (line 502) | def enc_dec_step(self, task):
FILE: src/utils.py
class AttrDict (line 33) | class AttrDict(dict):
method __init__ (line 34) | def __init__(self, *args, **kwargs):
function bool_flag (line 39) | def bool_flag(s):
function initialize_exp (line 51) | def initialize_exp(params):
function get_dump_path (line 94) | def get_dump_path(params):
function to_cuda (line 130) | def to_cuda(*args):
class TimeoutError (line 139) | class TimeoutError(BaseException):
function timeout (line 143) | def timeout(seconds=10, error_message=os.strerror(errno.ETIME)):
FILE: train.py
function get_parser (line 26) | def get_parser():
function main (line 270) | def main(params):
Condensed preview — 17 files, each showing path, character count, and a content snippet. Download the .json file or copy for the full structured content (238K chars).
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{
"path": "CODE_OF_CONDUCT.md",
"chars": 244,
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},
{
"path": "CONTRIBUTING.md",
"chars": 572,
"preview": "# Contributing to this repo\n\n## Pull Requests\n\nIn order to accept your pull request, we need you to submit a CLA. You on"
},
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"path": "LICENSE",
"chars": 19332,
"preview": "Attribution-NonCommercial 4.0 International\n\n=======================================================================\n\nCr"
},
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"path": "README.md",
"chars": 32799,
"preview": "# Maths from examples - Learning advanced mathematical computations from examples\n\nThis is the source code and data set"
},
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"path": "split_data.py",
"chars": 2387,
"preview": "# Copyright (c) 2020-present, Facebook, Inc.\n# All rights reserved.\n#\n# This source code is licensed under the license f"
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"chars": 701,
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"chars": 29150,
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"chars": 1671,
"preview": "# Copyright (c) 2020-present, Facebook, Inc.\n# All rights reserved.\n#\n# This source code is licensed under the license f"
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"chars": 25410,
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}
]
About this extraction
This page contains the full source code of the facebookresearch/MathsFromExamples GitHub repository, extracted and formatted as plain text for AI agents and large language models (LLMs). The extraction includes 17 files (224.0 KB), approximately 54.7k tokens, and a symbol index with 142 extracted functions, classes, methods, constants, and types. Use this with OpenClaw, Claude, ChatGPT, Cursor, Windsurf, or any other AI tool that accepts text input. You can copy the full output to your clipboard or download it as a .txt file.
Extracted by GitExtract — free GitHub repo to text converter for AI. Built by Nikandr Surkov.