发表机构
Getulio Vargas Foundation; Federal University of Viçosa; Federal Institute of Ceará; UFRRJ（热图利奥·瓦加斯基金会; 维索萨联邦大学; 塞阿拉联邦学院; 里约热内卢联邦农村大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出层化有效电阻视角，证明过压缩瓶颈可通过调整层化而非重连图来缓解，并实例化为FlatNSD，在不改拓扑下于过压缩基准上表现良好。
AI 中文摘要
图神经网络（GNNs）常常因过压缩现象而难以捕捉长程依赖——这是一种节点嵌入被反复压缩成有限大小消息导致表示坍缩的现象。过压缩通常被视为图拓扑的一种属性，有效电阻作为瓶颈的一种原则性度量。我们对此提供互补视角：基于细胞层化，我们引入层化有效电阻，这是有效电阻的一种推广，依赖于附着在图上的层化，并证明对于平坦向量丛，雅可比意义上的过压缩敏感性由与节点间层化有效电阻相关的量上界所限定。因此，瓶颈未必存在于图本身：它可以通过调整层化而被重新定位并减少。我们将这一思想实例化为FlatNSD，一种神经层化扩散的简单消息传递变体，并展示它隐式学习调节总层化有效电阻，在不改变原始图拓扑的情况下，在专为施压过压缩设计的基准上表现良好。
英文摘要
Graph Neural Networks (GNNs) often struggle to capture long-range dependencies due to over-squashing -- a phenomenon in which the repeated compression of node embeddings into finite-size messages causes representations to collapse. Over-squashing is most often diagnosed as a property of the graph topology, with effective resistance serving as a principled measure of the bottleneck. We provide a complementary view on the matter: building on cellular sheaves, we introduce sheaf effective resistance, a generalization of effective resistance that depends on the sheaf attached to the graph, and we prove that for flat vector bundles, the over-squashing sensitivity in the Jacobian sense is upper bounded by a quantity related to the sheaf effective resistance between the nodes. The bottleneck thus need not lie in the graph itself: it can be relocated, and reduced, by adjusting the sheaf. We instantiate this idea in FlatNSD, a simple message-passing variant of Neural Sheaf Diffusion, and show that it implicitly learns to modulate total sheaf effective resistance, performing well on benchmarks designed to stress over-squashing without altering the original graph topology.
CommentsAccepted to NeurIPS 2026
