Geometrically Equivariant Graph Neural Networks: A Survey

TL;DR

This survey reviews the development of geometrically equivariant Graph Neural Networks, categorizing methods, summarizing benchmarks, and discussing future research directions to advance understanding of geometric graph processing.

Contribution

It provides a comprehensive classification and analysis of existing equivariant GNN methods, along with benchmarks and datasets, to guide future research in the field.

Findings

Methods are categorized into three groups based on message passing and aggregation.

Summaries of benchmarks and datasets facilitate future methodology development.

Future directions for equivariant GNN research are discussed.

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.