Curvature constrained MPNNs: Improving message passing with local structural properties

Abstract

Graph neural networks operate through an iterative process that involves updating node representations by aggregating information from neighboring nodes, a concept commonly referred to as the message passing paradigm. Despite their widespread usage, a recognized issue with these networks is the tendency to over-squash, leading to diminished efficiency. Recent studies have highlighted that this bottleneck phenomenon is often associated with specific regions within graphs, that can be identified through a measure of edge curvature. In this paper, we present a novel framework designed for any Message Passing Neural Network (MPNN) architecture, wherein information distribution is guided by the curvature of the graph’s edges. Our approach aims to address the over-squashing problem by strategically considering the geometric properties of the underlying graph. The experiments carried out show that our method demonstrates significant improvements in mitigating over-squashing, surpassing the performance of existing graph rewiring techniques across multiple node classification datasets.