Are High-Degree Representations Really Unnecessary in Equivarinat Graph Neural Networks? (NeurIPS 2024)

Jiacheng Cen, Anyi Li, Ning Lin, Yuxiang Ren, Zihe Wang, Wenbing Huang

[OpenReview] [paper] [poster] [arXiv]

Common symmetric graphs. Equivariant GNNs on symmetric graphs will degenerate to a zero function if the degree of their representations is fixed as 1.

Key Requirements

dgl==1.1.3+cu118
e3nn==0.5.1
matplotlib==3.7.2
numpy==1.26.4
scipy==1.8.1
sympy==1.12
torch==2.1.0+cu118
torch_geometric==2.6.1
torch_scatter==2.1.2+pt21cu118
torch_sparse==0.6.18+pt21cu118

A more detailed Python environments is depicted in requirements.txt.

Expressivity on Symmetric Graphs

The /expressivity directory contains the notebooks with rot-3D-test.ipynb and reg-poly-test.ipynb, which respectively the expressivity evaulation on $k$-fold structure and five regular polyhedra.

Physical Dynamics Simulation

$N$-body System Dataset

Data Preparation

To generate datasets containing multiple isolated particles, please use the following command.

python -u ./datasets/nbody/datagen/generate_dataset.py --num-train 5000 --seed 43 --n_isolated 5 --n_stick 0 --n_hinge 0 --n_workers 50

Run Experiments

python ./main_nbody.py --model HEGNN --ell 3 --data_directory <your_dir> --dataset_name "5_0_0"

MD17 Dataset

Data Preparation

The MD17 dataset can be downloaded from MD17.

Run Experiments

python -u ./main_md17.py --model HEGNN --ell 3 --batch_size 100 --epochs 500 --data_dir <your_dir> --delta_frame 3000 --mol "aspirin" --device --outf "md17-logs" 

Perturbation Experiment

To run the experiment, please open /expressivity/perturbation-test.ipynb.

Acknowledgements

This project is based on the work from the Geometric GNN Dojo repository. We would like to express our gratitude to the original authors for their contributions to the field of geometric deep learning.

Citation

If you find this work useful in your research, please consider citing:

@inproceedings{cen2024high,
  title={Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?},
  author={Cen, Jiacheng and Li, Anyi and Lin, Ning and Ren, Yuxiang and Wang, Zihe and Huang, Wenbing},
  booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
  year={2024},
  url={https://openreview.net/forum?id=M0ncNVuGYN}
}