A new perspective on building efficient and expressive 3D equivariant graph neural networks
This work addresses the problem of designing more expressive and efficient geometric GNNs for researchers in molecular modeling, though it appears incremental as it builds on existing equivariant GNN frameworks.
The paper tackled the lack of comprehensive evaluation for 3D equivariant graph neural networks by proposing a local hierarchy of 3D isomorphism to analyze expressiveness, leading to LEFTNet which achieved state-of-the-art performance on molecular property prediction tasks.
Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these networks through a local-to-global analysis lacks today. In this paper, we propose a local hierarchy of 3D isomorphism to evaluate the expressive power of equivariant GNNs and investigate the process of representing global geometric information from local patches. Our work leads to two crucial modules for designing expressive and efficient geometric GNNs; namely local substructure encoding (LSE) and frame transition encoding (FTE). To demonstrate the applicability of our theory, we propose LEFTNet which effectively implements these modules and achieves state-of-the-art performance on both scalar-valued and vector-valued molecular property prediction tasks. We further point out the design space for future developments of equivariant graph neural networks. Our codes are available at \url{https://github.com/yuanqidu/LeftNet}.