Rewiring Networks for Graph Neural Network Training Using Discrete Geometry

TL;DR

This paper explores using discrete geometric curvature measures to rewire networks, significantly improving graph neural network training efficiency and accuracy on real-world datasets.

Contribution

It introduces classical geometric notions of curvature as a novel, computationally efficient method for network rewiring to enhance GNN training.

Findings

Achieves state-of-the-art GNN accuracy on multiple datasets.

Provides a computationally faster rewiring method by several orders of magnitude.

Effectively mitigates information over-squashing in GNNs.

Abstract

Information over-squashing is a phenomenon of inefficient information propagation between distant nodes on networks. It is an important problem that is known to significantly impact the training of graph neural networks (GNNs), as the receptive field of a node grows exponentially. To mitigate this problem, a preprocessing procedure known as rewiring is often applied to the input network. In this paper, we investigate the use of discrete analogues of classical geometric notions of curvature to model information flow on networks and rewire them. We show that these classical notions achieve state-of-the-art performance in GNN training accuracy on a variety of real-world network datasets. Moreover, compared to the current state-of-the-art, these classical notions exhibit a clear advantage in computational runtime by several orders of magnitude.