Pair-Centric Graph Rewiring for Over-Squashing via Optimal Transport-Guided Communication Alignment

2026-08-11

AI Summary

Message-passing neural networks often suffer from over-squashing when capturing long-range dependencies in graphs, which impedes effective propagation of distant information. This work proposes PairAlign, a novel framework that explicitly models, at the node-pair level, the gap between communication demand and the support provided by the current graph topology. It introduces a computable proxy metric—“demand-support deficit”—to identify critical interactions and leverages optimal transport theory to perform globally coordinated graph rewiring under a constrained edge budget. Integrating graph neural networks, Jacobian analysis, and bounded-hop propagation models, PairAlign drives structure optimization aligned with communication needs. Experiments demonstrate that PairAlign consistently enhances the performance of diverse backbone architectures on standard graph benchmarks, confirming the efficacy of node-pair-level topological refinement in mitigating over-squashing.

Abstract

Message-passing neural networks (MPNNs) often struggle when task-relevant information is distributed across distant regions of a graph, since local propagation must compress remote signals through limited structural interfaces. Graph rewiring provides a structural response to over-squashing. Most existing methods rely on edge-level bottleneck scores or graph-level connectivity surrogates. With a limited rewiring budget, the key question is which pairwise communications most need structural support. This paper proposes PairAlign, a pair-centric graph rewiring framework that makes this question explicit through demand-support shortage. Specifically, PairAlign combines original-graph structural demand with current-graph finite-hop propagation support; their ratio highlights interactions whose communication demand is poorly supported by topology, and our theory shows that this score provides a computable proxy for the corresponding Jacobian-based shortage with a pair-level interpretation of over-squashing. Our theory reveals a two-sided effect of edge insertion: a new edge can create useful walks and simultaneously dilute existing normalized transition mass. Guided by this observation, PairAlign optimizes shortage to favor edge additions that alleviate over-squashing. Beyond selecting useful additions, PairAlign further introduces an Optimal Transport-guided rewiring mechanism to coordinate the finite edge budget for pair-level structural compatibility and shortage-target coverage. It formulates communication alignment between the candidate edge budget and the shortage targets, and the theory shows that this allocation covers shortage targets more broadly and effectively than a greedy-local assignment. Experiments on standard graph benchmarks show PairAlign's improvement across message-passing backbones, validating pair-level repair as an effective route for alleviating over-squashing.

Problem

• over-squashing
• graph rewiring
• message-passing neural networks
• pairwise communication
• structural support

Innovation

• Pair-Centric Rewiring
• Over-Squashing
• Optimal Transport
• Communication Alignment
• Graph Neural Networks