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arXiv · 2610.04157

Mitigating Over-squashing without Rewiring: A Sheaf Effective Resistance Perspective

André Ribeiro·Germano Barcelos·Amauri H. Souza·Diego Mesquita·Ana Luiza Tenório
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Abstract

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.

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André Ribeiro, Germano Barcelos, Amauri H. Souza, Diego Mesquita, Ana Luiza Tenório. 2026-10-03. Mitigating Over-squashing without Rewiring: A Sheaf Effective Resistance Perspective. https://arxiv.org/abs/2610.04157

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