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SE3Set: Harnessing equivariant hypergraph neural networks for molecular representation learning (2405.16511v1)

Published 26 May 2024 in cs.LG, cs.AI, and physics.comp-ph

Abstract: In this paper, we develop SE3Set, an SE(3) equivariant hypergraph neural network architecture tailored for advanced molecular representation learning. Hypergraphs are not merely an extension of traditional graphs; they are pivotal for modeling high-order relationships, a capability that conventional equivariant graph-based methods lack due to their inherent limitations in representing intricate many-body interactions. To achieve this, we first construct hypergraphs via proposing a new fragmentation method that considers both chemical and three-dimensional spatial information of molecular system. We then design SE3Set, which incorporates equivariance into the hypergragh neural network. This ensures that the learned molecular representations are invariant to spatial transformations, thereby providing robustness essential for accurate prediction of molecular properties. SE3Set has shown performance on par with state-of-the-art (SOTA) models for small molecule datasets like QM9 and MD17. It excels on the MD22 dataset, achieving a notable improvement of approximately 20% in accuracy across all molecules, which highlights the prevalence of complex many-body interactions in larger molecules. This exceptional performance of SE3Set across diverse molecular structures underscores its transformative potential in computational chemistry, offering a route to more accurate and physically nuanced modeling.

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Summary

  • The paper introduces SE3Set, leveraging SE(3) equivariance to accurately model high-order many-body interactions in molecular systems.
  • It employs a novel hypergraph fragmentation technique combining 2D chemical structure and 3D spatial information for robust hyperedge construction.
  • Evaluation on datasets like QM9 and MD22 shows a ~20% reduction in error, highlighting significant improvements in molecular property prediction.

SE3Set: Harnessing Equivariant Hypergraph Neural Networks for Molecular Representation Learning

Introduction

The paper, "SE3Set: Harnessing equivariant hypergraph neural networks for molecular representation learning," presents SE3Set, an SE(3) equivariant hypergraph neural network architecture designed for molecular representation learning. SE3Set addresses the inadequacies of traditional graph-based methods that fall short in modeling the high-order relationships prevalent in molecular systems. By leveraging hypergraphs and embedding SE(3) equivariance into a novel architecture, SE3Set models complex many-body interactions, crucial for accurately predicting molecular properties. Figure 1

Figure 1: Folic acid fragmentation illustrated with CID 135398658 from PubChem.

Equivariant Hypergraph Neural Networks

SE3Set is rooted in the principle of equivariance, ensuring model outputs are invariant to spatial transformations such as rotation and translation. The architecture comprises three main components: node embeddings, hyperedge embeddings, and attention mechanisms. Node and hyperedge embeddings are initially generated by integrating atomic numbers and position vectors, transforming these into higher-dimensional representations that capture both chemical and spatial information.

The architecture incorporates SE(3) equivariant transformations between nodes and hyperedges, ensuring that molecular representations are consistent regardless of orientation. This design principle is pivotal as it retains rotational and translational symmetry, thereby accurately reflecting physical reality in molecular systems.

Fragmentation Algorithm

A key innovation is the fragmentation method for hypergraph construction. This process uses both 2D chemical structure and 3D spatial information to define hyperedges, each representing a subset of atoms with functional group integrity. The fragmentation approach follows four steps: identifying cleavable bonds, forming initial fragments, merging fragments to satisfy size criteria, and expanding fragments to maintain connectivity. This methodology is visually captured in Figure 1.

Implementation and Performance

Figure 2

Figure 2: Overall architecture of SE3Set.

Figure 2 illustrates the core architecture. SE3Set effectively integrates Vertex-to-Edge (V2E) and Edge-to-Vertex (E2V) attention mechanisms. These mechanisms compute attention weights that are dynamically adjusted using DTP with irreps, thereby enhancing the model's ability to capture complex molecular interactions. The SE3 equivariance ensures that these calculations maintain symmetry, contributing to accurate molecular property predictions.

SE3Set was evaluated against state-of-the-art models on small-molecule datasets like QM9 and MD17, exhibiting competitive performance. Notably, SE3Set excels on the MD22 dataset, reducing mean absolute errors by approximately 20%. These numerical results underscore the efficacy of incorporating higher-order interactions in larger molecular systems.

Implications and Future Directions

SE3Set's capacity to model complex interactions robustly positions it for extensive applications in computational chemistry, drug discovery, and materials science. Its approach could be expanded to accommodate even more complex molecular interactions, potentially integrating quantum effects or dynamic simulations. Future developments could focus on further reducing computational overhead and enhancing scalability to accommodate even larger datasets and higher-dimensional systems.

Conclusion

SE3Set significantly advances the field of molecular representation learning by combining equivariant hypergraph neural networks with innovative fragmentation techniques. Its ability to model high-order many-body interactions with SE3 equivariance presents a powerful tool for accurate molecular property prediction. This work lays a foundation for future explorations into more complex molecular systems, enhancing our understanding and computational handling of molecular interaction dynamics.

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