Schreier-Coset Graph Rewiring

2026-07-29

AI Summary

Graph neural networks often suffer from structural bottlenecks that cause over-squashing, impeding the propagation of long-range information. This work proposes a group-theoretic graph rewiring approach that, for the first time, leverages the special linear group to construct Schreier–coset graphs. The method introduces low-resistance pathways with guaranteed spectral gaps and bounded effective resistance while preserving key properties of the original graph. Theoretically, this ensures efficient information propagation across the network. Empirically, the approach reduces effective resistance by 5%–40% across various tasks, substantially alleviating connectivity bottlenecks without compromising predictive accuracy, thereby maintaining competitive performance.

Abstract

The information flow in the graph neural networks (GNNs) is fundamentally constrained by over-squashing, where structural bottlenecks impede long range information propagation. Graph-rewiring methods, which modify graph topology, have been extensively used to alleviate this. However, existing approaches often introduce prohibitive structural and computational bottlenecks, fail to preserve the critical properties of original graphs, and increase the edge counts massively. We introduce a novel method Schreier-Coset Graph Rewiring , a group-theoretic rewiring method that augments the input graph with a Schreier-Coset graph derived from a special linear group. Our method provides theoretical guarantees, a graph that exhibits spectral gap and a bounded effective resistance, creating a low-resistance bypass for long-range communication. Empirical evaluations demonstrate that SCGR reduces effective resistance by 5-40% across various learning tasks, effectively mitigating connectivity bottlenecks while maintaining competitive accuracy.

Problem

• over-squashing
• graph neural networks
• long-range communication
• graph rewiring
• structural bottlenecks

Innovation

• Schreier-Coset Graph Rewiring
• over-squashing
• graph neural networks
• spectral gap
• effective resistance