Geometrically Equivariant Graph Neural Networks: A Survey
This survey addresses the lack of a comprehensive overview in the field, which hinders further development, but it is incremental as it synthesizes existing work rather than introducing new methods.
The paper surveys geometrically equivariant Graph Neural Networks (GNNs), which are designed to handle geometric graphs with symmetries like translations and rotations, and it analyzes existing methods, benchmarks, and datasets to aid future research.
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.