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Multimodal-Symbolic-Regression

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[ICLR 2024 Spotlight] SNIP on Symbolic Regression: Deep Symbolic Regression with Multimodal Pretraining

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# Symbolic Regression with SNIP Multi-modal Pretraining & Latent Space Optimization

Official Implementation of Using SNIP for Symbolic Regression in the paper [SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training](https://arxiv.org/abs/2310.02227) (**ICLR 2024 Spotlight**).

## Overview
**SNIP** stands for **Symbolic-Numeric Integrated Pretraining**, referring to the multi-modal transformer model pretrained betwen symbolic equation of math functions and their numeric data obervations. Here, we show the benefits of SNIP representations for the complex task of Symbolic Regression, a numeric-to-symbolic generation task of uncovering symbolic math equations from data observations.

There are two main steps to using SNIP for Symbolic Regression:
- **Training:** Train an Expression Generation Decoder to the SNIP Numeric Encoder.
- **Inference:** Look for better equations by exploring SNIP's latent space.

<img src="./images/SNIP-Symbolic-Regression.png" width="80%" /> 
 
Using SNIP Numeric Encoder for Symbolic Regression.

## Installation
Follow the installation steps from the SNIP repository **[Multimodal-Math-Pretraining](https://github.com/deep-symbolic-mathematics/Multimodal-Math-Pretraining)**. To install, use:
```
conda env create -f environment.yml
```
Note: Requires `python>3.7`.

## Training
To train your model for Symbolic Regression using the SNIP Numeric Encoder, follow these steps:

Download the required model weights:
* **SNIP Weights:** Get them from [here](https://drive.google.com/file/d/1jfkQdTvGibGwVqWHVIjQ_fxyBtV4EcoY/view?usp=share_link)
* **E2E Weights:** Available [here](https://dl.fbaipublicfiles.com/symbolicregression/model1.pt)

Place both in the `weights/` directory of the project. Then, run the following command to start training.
```
python train.py --reload_model_snipenc ./weights/snip-10dmax.pth \
                --reload_model_e2edec ./weights/e2e.pth \
                --freeze_encoder True \
                --batch_size 128 \
                --dump_path ./dump \
                --max_input_dimension 10 \
                --exp_name snipe2e \
                --exp_id run-train \
                --lr 4e-5 \
                --latent_dim 512 \
                --save_periodic 10
```
This command includes various parameters to customize your training, like batch size, learning rate, and maximum epochs. If you want to freeze the SNIP encoder during training, use `--freeze_encoder True`. For a deeper understanding of how training is set up, including how the model selects specific modules from the weights, take a look at the `train.py` file.

## Encoder-Decoder Model
Download the **Encoder-Decoder Symbolic Regression model weights** **[here](https://drive.google.com/drive/folders/1YAQSpZnuEFJa1osBGrcGTsEmir6zjwUd?usp=share_link)**. Save it in `weights/snip-e2e-sr.pth`. To use this model, simply activate the `--reload_model` parameter with the model path.

## SR Benchmark Datasets
* **Feynman** equations are [here](https://space.mit.edu/home/tegmark/aifeynman.html)
* **PMLB** datasets are also [here](https://github.com/EpistasisLab/pmlb/tree/master/datasets). Data points of PMLB datasets are used in the [SRBench (A Living Benchmark for Symbolic Regression)](https://github.com/cavalab/srbench), containing three data groups: **Feynman**, **Strogatz**, and **Black-box**.
      
Extract the datasets to this directory, Feynman datasets should be in `datasets/feynman/`, and PMLB datasets should be in `datasets/pmlb/`.

## Latent Space Optimization
As SNIP representations have strong pretrained information about potential mutual symbolic-numeric similarities, Latent Space Optimization (LSO) significantly boosts the quality of decoded equations. To run LSO for your problem, check `run_lso.sh` file.

Example of LSO run with default optimizer: 
```
python LSO_eval.py --reload_model ./weights/snip-e2e-sr.pth \
                    --eval_lso_on_pmlb True \
                    --pmlb_data_type strogatz \
                    --target_noise 0.0 \
                    --max_input_points 200 \
                    --lso_optimizer gwo \
                    --lso_pop_size 50 \
                    --lso_max_iteration 80 \
                    --lso_stop_r2 0.99 \
                    --beam_size 2
```

Here, LSO is performed on the representations of the pretrained model `./weights/snip-e2e-sr.pth`. To test LSO on other data groups, you can simply change `--pmlb_data_type` parameter to `feynman` or `blackbox`. LSO algorithm is designed with the [GWO](https://www.sciencedirect.com/science/article/abs/pii/S0965997813001853) optimizer by default. However, if you're interested, you can also try other gradient-free optimizers from the **[nevergrad](https://github.com/facebookresearch/nevergrad)** library by just changing the `--lso_optimizer` parameter.

## Final Results on SRBench 
Our experimental results of SNIP on SRBench datasets for symbolic regression are provided in the [srbench_results/](https://github.com/deep-symbolic-mathematics/Multimodal-Symbolic-Regression/tree/main/srbench_results) directory. These results are shared to help the research community reproduce our paper's findings and serve as reference benchmarks. Each result file contains detailed performance metrics and experimental configurations used in our evaluations.

## Citation
If you find the paper or the repo helpful, please cite it with
<pre>
@inproceedings{
meidani2024snip,
title={{SNIP}: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training},
author={Kazem Meidani and Parshin Shojaee and Chandan K. Reddy and Amir Barati Farimani},
booktitle={The Twelfth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=KZSEgJGPxu}
}
</pre>

## License 
This repository is licensed under MIT licence.

## Contact Us
For any questions or issues, you are welcome to open an issue in this repo, or contact us at mmeidani@andrew.cmu.edu, and parshinshojaee@vt.edu.

Multimodal-Symbolic-Regression

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