发表机构
School of Mathematics, Sun Yat-sen University（中山大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出以对为中心的图重连框架PairAlign，结合结构需求与传播支持，引入最优传输引导的重连机制，在图基准实验中提升了消息传递骨干网络缓解过压缩的性能。
AI 中文摘要
消息传递神经网络（MPNNs）在任务相关信息分布在图的远端区域时常常表现不佳，因为局部传播必须通过有限的结构接口压缩远程信号。图重连为缓解过压缩问题提供了结构层面的解决方案。现有大多数方法依赖于边级瓶颈分数或图级连通性替代指标。在有限的重连预算下，关键问题在于哪些成对通信最需要结构支持。本文提出PairAlign，这是一个以对为中心的图重连框架，通过需求-支持缺口明确提出该问题。具体而言，PairAlign结合了原始图的结构需求与当前图的有限跳传播支持；两者的比值突出了那些通信需求未得到拓扑充分支持的交互，且我们的理论表明，该分数提供了基于雅可比矩阵的对应缺口的可计算代理，具有对过压缩的成对层面解释。我们的理论揭示了边插入的双向效应：新边可创建有用的游走，同时会稀释现有的归一化转移质量。基于这一观察，PairAlign优化缺口以倾向于添加能缓解过压缩的边。除了选择有用的添加边之外，PairAlign还进一步引入了最优传输引导的重连机制，以协调有限的边预算，实现成对层面的结构兼容性和缺口目标覆盖。该机制将候选边预算与缺口目标之间的通信对齐，且理论表明，这种分配方式比贪心局部分配能更广泛、更有效地覆盖缺口目标。在标准图基准上的实验显示，PairAlign在各类消息传递骨干网络上均实现了性能提升，验证了成对层面的修复是缓解过压缩的有效途径。
英文摘要
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.
