{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04157",
  "author_total": 5,
  "authors": [
    {
      "name": "André Ribeiro"
    },
    {
      "name": "Germano Barcelos"
    },
    {
      "name": "Amauri H. Souza"
    },
    {
      "name": "Diego Mesquita"
    },
    {
      "name": "Ana Luiza Tenório"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/06t9qvy9g3yp0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04157",
  "fulltext_url": null,
  "id": "06t9qvy9g3yp0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04157",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Advanced Graph Neural Networks"
    ]
  ],
  "openalex": "W7220727489",
  "pdf_url": "https://arxiv.org/pdf/2610.04157",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/06t9qvy9g3yp0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:16Z",
      "native_id": "2610.04157",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04157"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Mitigating Over-squashing without Rewiring: A Sheaf Effective Resistance Perspective",
  "title_text": "Mitigating Over-squashing without Rewiring: A Sheaf Effective Resistance Perspective",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/06t9qvy9g3yp0",
  "venue": "arXiv",
  "versions": []
}