EquiHGNN: Scalable Rotationally Equivariant Hypergraph Neural Networks

Published at Journal of Chemical Physics: https://pubs.aip.org/aip/jcp/article/164/14/144101/3386416/EquiHGNN-Scalable-rotationally-equivariant

Presented at workshops of NeurIPS 2025:

• New Perspectives in Advancing Graph Machine Learning Workshop: https://openreview.net/forum?id=2YIhVthm0F
• AI for Science: https://openreview.net/forum?id=McZIwV1dva
• Machine Learning and the Physical Sciences: https://ml4physicalsciences.github.io/2025/files/NeurIPS_ML4PS_2025_118.pdf

Preprint: https://arxiv.org/pdf/2505.05650.pdf

Abstract

Molecular interactions often involve high-order relationships that cannot be fully captured by traditional graph-based models limited to pairwise connections. Hypergraphs naturally extend graphs by enabling multi-way interactions, making them well-suited for modeling complex molecular systems. In this work, we introduce EquiHGNN, an Equivariant Hypergraph Neural Network framework that integrates symmetry-aware representations to improve molecular modeling. By enforcing equivariance under relevant transformation groups, our approach preserves geometric and topological properties, leading to more robust and physically meaningful representations. We examine a range of equivariant architectures and demonstrate that integrating symmetry constraints leads to notable performance gains on large-scale molecular datasets. Experiments on both small and large molecules show that high-order interactions offer limited benefits for small molecules but consistently outperform 2D graphs on larger ones. Adding geometric features to these high-order structures further improves performance, emphasizing the value of spatial information in molecular learning.

Overview of the Equivariant Hypergraph Neural Network framework (EquiHGNN).

Datasets

This project currently utilizes four main datasets:

• OPV: The Organic Photovoltaic (OPV) dataset contains molecular structures and their corresponding photovoltaic properties.
• QM9: The QM9 dataset consists of small molecules with geometric, energetic, electronic, and thermodynamic properties.
• PCQM4Mv2: From the PubChemQC project, this dataset of ~3.7M molecules supports quantum chemistry tasks like predicting HOMO–LUMO gaps from SMILES; useful for materials discovery and drug design.
• Molecule3D: Also based on PubChemQC, this benchmark includes ~3.9M molecular graphs for predicting 3D structures and quantum properties from 2D inputs, supporting applications in molecular modeling and property prediction.

Setup

First, create and activate a Conda environment:

conda create --name equihgnn python=3.10
conda activate equihgnn
make

Train the Model

Training parameters, including model type, dataset selection, and hyperparameters, are configurable within the ./scripts directory. A flexible interface allows easy model selection using the --method flag. The following models are supported:

• gin, gat: 2D Graph Neural Network.
• mhnnm: Molecular Hypergraph Neural Network (baseline).
• egnn_equihnns: Equivariant Graph Neural Network (EGNN) integration for geometric feature extraction.
• equiformer_equihnns: Equiformer integration for geometric feature extraction.
• faformer_equihnns: Frame Averaging Transformer (FAFormer) integration for geometric feature extraction.

OPV

OPV dataset task IDs:

• Molecular: 0-gap, 1-homo, 2-lumo, 3-spectral_overlap
• Polymer: 4-homo, 5-lumo, 6-gap, 7-optical_lumo

# Without geometric:
bash scripts/run_opv.sh $TASK_ID

# With geometric:
bash scripts/run_opv_3d.sh $TASK_ID

QM9

QM9 dataset task IDs: 0-mu, 1-alpha, 2-homo, 3-lumo, 4-epsilon, 5-$R^2$

# Without geometric:
bash scripts/run_qm9.sh $TASK_ID

# With geometric:
bash scripts/run_qm9_3d.sh $TASK_ID

PCQM4Mv2

# Without geometric:
bash scripts/run_pcqm.sh

# With geometric:
bash scripts/run_pcqm_3d.sh

Molecule3D

Molecule3D dataset task IDs 0-dipole x, 1-dipole y, 2-dipole z, 3-homo, 4-lumo, 5-homolumogap, 6-scf-energy

# Without geometric:
bash scripts/run_molecule.sh $TASK_ID

# With geometric:
bash scripts/run_molecule_3d.sh $TASK_ID

Training with Docker

Build the Docker image:

docker build -t equihgnn .

Run training inside a Docker container:

docker run \
  --gpus all \
  -v ./datasets:/module/datasets \
  -v ./logs:/module/logs \
  -v ./scripts:/module/scripts \
  -e COMET_API_KEY=$(COMET_API_KEY) \
  equihgnn bash scripts/*.sh $TASK_ID

Acknowledgements

This project utilizes code and inspiration from the following open-source repositories:

• MHNN Baseline: schwallergroup/mhnn
• EGNNs: lucidrains/egnn-pytorch
• SE(3) Transformers: lucidrains/se3-transformer-pytorch
• Equiformer: lucidrains/equiformer-pytorch
• Frame Averaging Transformer: Graph-and-Geometric-Learning/Frame-Averaging-Transformer
• VisNet: pyg-team/pytorch_geometric

Please cite our work!

@article{10.1063/5.0317966,
    author = {Dang, Tien and Hy, Truong-Son},
    title = {EquiHGNN: Scalable rotationally equivariant hypergraph neural networks},
    journal = {The Journal of Chemical Physics},
    volume = {164},
    number = {14},
    pages = {144101},
    year = {2026},
    month = {04},
    abstract = {Molecular interactions often involve higher-order relationships that cannot be fully captured by traditional graph-based models limited to pairwise connections. Hypergraphs naturally extend graphs by enabling multi-way interactions, making them well-suited for modeling complex molecular systems. In this work, we introduce EquiHGNN, an equivariant hypergraph neural network framework that integrates symmetry-aware representations to improve molecular modeling. By enforcing the equivariance under relevant transformation groups, our approach preserves geometric and topological properties, leading to more robust and physically meaningful representations. We examine a range of equivariant architectures and demonstrate that integrating symmetry constraints leads to notable performance gains on large-scale molecular datasets. Experiments across small and large molecules indicate that while higher-order interactions provide marginal gains for small systems, they surpass 2D graphs on larger ones. Incorporating geometric features into these higher-order structures further enhances performance, underscoring the critical role of spatial information in molecular representation learning. Our source code is available at https://github.com/HySonLab/EquiHGNN/.},
    issn = {0021-9606},
    doi = {10.1063/5.0317966},
    url = {https://doi.org/10.1063/5.0317966},
    eprint = {https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/5.0317966/20968155/144101_1_5.0317966.pdf},
}

@misc{dang2025equihgnnscalablerotationallyequivariant,
      title={EquiHGNN: Scalable Rotationally Equivariant Hypergraph Neural Networks},
      author={Tien Dang and Truong-Son Hy},
      year={2025},
      eprint={2505.05650},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2505.05650},
}