Expander Graph Propagation
This work addresses scalability and performance issues in GNNs for whole-graph classification tasks, offering a novel approach to counter oversquashing, though it appears incremental in the context of existing GNN research.
The paper tackles the challenge of designing graph neural networks (GNNs) that balance local and global graph information while avoiding bottlenecks like oversquashing, proposing the EGP model based on expander graph propagation. It shows EGP addresses these concerns with minimal setup and demonstrates empirical utility on Open Graph Benchmark datasets, theoretically proving that negatively curved edges are likely necessary for scalable message passing without bottlenecks.
Deploying graph neural networks (GNNs) on whole-graph classification or regression tasks is known to be challenging: it often requires computing node features that are mindful of both local interactions in their neighbourhood and the global context of the graph structure. GNN architectures that navigate this space need to avoid pathological behaviours, such as bottlenecks and oversquashing, while ideally having linear time and space complexity requirements. In this work, we propose an elegant approach based on propagating information over expander graphs. We leverage an efficient method for constructing expander graphs of a given size, and use this insight to propose the EGP model. We show that EGP is able to address all of the above concerns, while requiring minimal effort to set up, and provide evidence of its empirical utility on relevant graph classification datasets and baselines in the Open Graph Benchmark. Importantly, using expander graphs as a template for message passing necessarily gives rise to negative curvature. While this appears to be counterintuitive in light of recent related work on oversquashing, we theoretically demonstrate that negatively curved edges are likely to be required to obtain scalable message passing without bottlenecks. To the best of our knowledge, this is a previously unstudied result in the context of graph representation learning, and we believe our analysis paves the way to a novel class of scalable methods to counter oversquashing in GNNs.