arXiv:2608.10619cs.LG2026-08

通过最优传输对齐,精准修复图神经网络中远距离通信的过压缩问题。

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

论文配图:Pair-Centric Graph Rewiring for Over-Squashing via Optimal Transport-Guided Communication Alignment
图 1 · 摘自论文原文
  • 基于成对通信需求与支撑的缺口,定位亟需结构支持的远距离节点对。
  • 新边插入可增进建立有效路径,同时稀释原有传播质量,需权衡优化。
  • 适合解决图神经网络中远距离信息传递受阻的场景,尤其在小预算下有效。

消息传递神经网络(MPNN)在处理图中相距较远但任务相关的信息时表现不佳,因局部传播需通过有限的结构接口压缩远程信号。图重连是缓解过压缩的一种结构手段。现有方法多依赖边级瓶颈得分或图级连通性代理,但在有限重连预算下,关键问题是:哪些成对通信最需要结构支持?本文提出 PairAlign,一种以成对为中心的图重连框架,通过需求-支撑缺口显式回答此问题。PairAlign结合原图结构需求与当前图有限跳数传播支撑,其比值突出拓扑未能充分支持的通信交互;理论证明该得分可计算地逼近基于雅可比矩阵的缺口,具备成对层面的过压缩解释力。理论揭示边插入具有双重效应:新边可创造有效路径,同时稀释已有的归一化转移质量。基于此,PairAlign优化缺口以优先选择缓解过压缩的边添加。除筛选有效新增边外,还引入最优传输引导的重连机制,协调有限边预算实现成对结构兼容性与缺口目标覆盖。该分配策略比贪婪局部分配更广泛、有效地覆盖缺口目标。标准图基准测试显示,PairAlign在多种消息传递骨干网络上均有提升,验证了成对修复是缓解过压缩的有效路径。

原文摘要 · Abstract (English)

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.

图神经网络过压缩图重连最优传输

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