Symmetry Discovery for Different Data Types

This repository is the official implementation of the paper Symmetry Discovery for Different Data Types (Neural Networks, 2025).

Requirements

To install requirements:

pip install -r requirements.txt

To install Adan:

git clone https://github.com/sail-sg/Adan.git
cd Adan
python3 setup.py install --unfused

To download the top quark tagging dataset:

wget -P ./data/top-quark-tagging https://zenodo.org/records/2603256/files/train.h5

Experiments

Two-body problem

To use LieSD for symmetry discovery in the two-body problem on the uniform dataset, run this command:

python main_liesd.py --dataset 2body --num_epochs 10 --D 1 --gpu [gpu] --seed [seed]

To use LieSD ($k$-NN) for symmetry discovery in the two-body problem on the uniform dataset, run this command:

python main_liesd_knn.py --dataset 2body --n_neighbors -1 --D 1

To use LieGAN (baseline) for symmetry discovery in the two-body problem on the uniform dataset, run this command:

cd baseline && python main_baseline.py --g_init 2*2_factorization --lamda 1 --sigma_init 1 --num_epochs 100 --gpu [gpu] --seed [seed]

To use LieSD for symmetry discovery in the two-body problem on the non-uniform dataset, run this command:

python main_liesd.py --dataset 2body --num_epochs 10 --D 1 --non_uniform --gpu [gpu] --seed [seed]

To use LieGAN (baseline) for symmetry discovery in the two-body problem on the non-uniform dataset, run this command:

cd baseline && python main_baseline.py --g_init 2*2_factorization --lamda 1 --sigma_init 1 --num_epochs 100 --non_uniform --gpu [gpu] --seed [seed]

The moment of inertia matrix prediction

To use the tensor form of LieSD for symmetry discovery in predicting the moment of inertia matrix (w/o noise), run this command:

python main_liesd.py --dataset inertia --N 100000 --k 3 --num_epochs 100 --D 5 --tensor --gpu [gpu] --seed [seed]

To use the tensor form of LieSD ($k$-NN) for symmetry discovery in predicting the moment of inertia matrix (w/o noise), run this command:

python main_liesd_knn.py --dataset inertia --N 100000 --k 3 --n_neighbors -1 --D 5 --tensor

To use the vector form of LieSD (baseline) for symmetry discovery in predicting the moment of inertia matrix (w/o noise), run this command:

python main_liesd.py --dataset inertia --N 100000 --k 3 --num_epochs 100 --D 5 --gpu [gpu] --seed [seed]

To use the tensor form of LieSD for symmetry discovery in predicting the moment of inertia matrix (w/ noise), run this command:

python main_liesd.py --dataset inertia --N 100000 --k 3 --num_epochs 100 --D 5 --tensor --noise 0.1 --gpu [gpu] --seed [seed]

To use the tensor form of LieSD ($k$-NN) for symmetry discovery in predicting the moment of inertia matrix (w/ noise), run this command:

python main_liesd_knn.py --dataset inertia --N 100000 --k 3 --n_neighbors -1 --D 5 --tensor --noise 0.1

To use the vector form of LieSD (baseline) for symmetry discovery in predicting the moment of inertia matrix (w/ noise), run this command:

python main_liesd.py --dataset inertia --N 100000 --k 3 --num_epochs 100 --D 5 --noise 0.1 --gpu [gpu] --seed [seed]

Top quark tagging

To use LieSD for symmetry discovery in top quark tagging (w/o noise), run this command:

python main_liesd.py --dataset top_quark_tagging --n_component 20 --num_epochs 100 --D 9 --gpu [gpu] --seed [seed]

To use LieGAN (baseline) with 7 channels for symmetry discovery in top quark tagging (w/o noise), run this command:

cd baseline && python main_baseline.py --task top_tagging --lamda 1 --g_init random --n_channel 7 --y_type scalar --sigma_init 1 --eta 0.1 --n_component 200 --num_epochs 100 --gpu [gpu] --seed [seed]

To use LieGAN (baseline) with 9 channels for symmetry discovery in top quark tagging (w/o noise), run this command:

cd baseline && python main_baseline.py --task top_tagging --lamda 1 --g_init random --n_channel 9 --y_type scalar --sigma_init 1 --eta 0.1 --n_component 200 --num_epochs 100 --gpu [gpu] --seed [seed]

To use LieSD for symmetry discovery in top quark tagging (w/ noise), run this command:

python main_liesd.py --dataset top_quark_tagging --n_component 20 --num_epochs 100 --D 9 --noise 0.1 --gpu [gpu] --seed [seed]

To use LieGAN (baseline) with 7 channels for symmetry discovery in top quark tagging (w/ noise), run this command:

cd baseline && python main_baseline.py --task top_tagging --lamda 1 --g_init random --n_channel 7 --y_type scalar --sigma_init 1 --eta 0.1 --n_component 200 --num_epochs 100 --noise 0.1 --gpu [gpu] --seed [seed]

To use LieGAN (baseline) with 9 channels for symmetry discovery in top quark tagging (w/ noise), run this command:

cd baseline && python main_baseline.py --task top_tagging --lamda 1 --g_init random --n_channel 9 --y_type scalar --sigma_init 1 --eta 0.1 --n_component 200 --num_epochs 100 --noise 0.1 --gpu [gpu] --seed [seed]

Rotated MNIST

To use LieSD for symmetry discovery in rotated MNIST, run this command:

python main_liesd.py --dataset mnist --num_epochs [num_epochs] --D 1 --degree [degree] --gpu [gpu] --seed [seed]

To use LieGAN (baseline) for symmetry discovery in rotated MNIST, run this command:

cd baseline && python main_baseline.py --task mnist --lamda 1 --g_init random --n_channel 1 --x_type image --y_type scalar --sigma_init 1 --eta 0.1 --num_epochs [num_epochs] --degree [degree] --gpu [gpu] --seed [seed]

Citation

@article{hu2025symmetry,
  title={Symmetry discovery for different data types},
  author={Hu, Lexiang and Li, Yikang and Lin, Zhouchen},
  journal={Neural Networks},
  pages={107481},
  year={2025},
  publisher={Elsevier}
}