Geometrically Equivariant Graph Neural Networks: A Survey
Jiaqi Han, Yu Rong, Tingyang Xu, Wenbing Huang
TL;DR
This survey consolidates geometrically equivariant GNNs for geometric graphs, introducing a taxonomy based on irreducible representations, regular representations, and scalarization to organize message-passing designs. It contextualizes methods within three application domains—physical dynamics, molecules, and point clouds—and catalogs representative datasets and benchmarks. The article also outlines practical challenges, notably theoretical completeness and scalability, and proposes directions such as hierarchical modeling and expanded real-world datasets. By providing concise mathematical preliminaries and a unified framework, the paper aims to accelerate entry, comparison, and advancement of equivariant GNNs in scientific domains.
Abstract
Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias and developed geometrically equivariant Graph Neural Networks (GNNs) to better characterize the geometry and topology of geometric graphs. Despite fruitful achievements, it still lacks a survey to depict how equivariant GNNs are progressed, which in turn hinders the further development of equivariant GNNs. To this end, based on the necessary but concise mathematical preliminaries, we analyze and classify existing methods into three groups regarding how the message passing and aggregation in GNNs are represented. We also summarize the benchmarks as well as the related datasets to facilitate later researches for methodology development and experimental evaluation. The prospect for future potential directions is also provided.