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EquiHGNN: Scalable Rotationally Equivariant Hypergraph Neural Networks

Tien Dang, Truong-Son Hy

TL;DR

EquiHGNN introduces a symmetry-aware hypergraph framework for molecular property prediction by combining AllSet-style hyperedge passing with equivariant geometric embeddings. The approach shows that high-order interactions confer limited benefits for small molecules but provide gains on large-scale datasets when augmented with 3D geometry, with Equiformer often achieving top QM9 performance. The results demonstrate scalability beyond 2D graphs and offer a simple, plug-and-play embedding strategy to inject geometric priors into HGNNs, with implications for drug discovery and materials science. Overall, EquiHGNN provides a principled, scalable path to leverage higher-order structure and geometry in molecular modeling.

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 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 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 the performance, emphasizing the value of spatial information in molecular learning. Our source code is available at https://github.com/HySonLab/EquiHGNN/

EquiHGNN: Scalable Rotationally Equivariant Hypergraph Neural Networks

TL;DR

EquiHGNN introduces a symmetry-aware hypergraph framework for molecular property prediction by combining AllSet-style hyperedge passing with equivariant geometric embeddings. The approach shows that high-order interactions confer limited benefits for small molecules but provide gains on large-scale datasets when augmented with 3D geometry, with Equiformer often achieving top QM9 performance. The results demonstrate scalability beyond 2D graphs and offer a simple, plug-and-play embedding strategy to inject geometric priors into HGNNs, with implications for drug discovery and materials science. Overall, EquiHGNN provides a principled, scalable path to leverage higher-order structure and geometry in molecular modeling.

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 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 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 the performance, emphasizing the value of spatial information in molecular learning. Our source code is available at https://github.com/HySonLab/EquiHGNN/
Paper Structure (22 sections, 6 equations, 2 figures, 6 tables)

This paper contains 22 sections, 6 equations, 2 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Graph Neural Network
  4. Geometric Graph Neural Networks
  5. Topological Deep Learning
  6. Method
  7. AllSet
  8. Equivariant Hypergraph Neural Network
  9. Experiment
  10. Dataset
  11. Training details
  12. Results
  13. QM9 dataset
  14. OPV dataset
  15. PCQM4Mv2
  16. ...and 7 more sections

Figures (2)

  • Figure 1: a) Illustration of a hypergraph constructed from a molecule, where vertices represent atoms and hyperedges represent conjugated bonds, highlighted in blue and orange. b) Hypergraph to Bipartite representations.
  • Figure 2: Overview of the Equivariant Hypergraph Neural Network framework.