{
  "abstract": "The Dobrushin coefficient of each attention-rollout factor satisfies $κ(\\frac12(I+A))\\le\\frac12(1+κ(A))$, and multiplying these inequalities over layers bounds the coefficient of the whole rollout. We characterise exactly when the layerwise bound is tight: equality holds if and only if some token pair attaining $κ(A)$ is mutually self-dominant - each of the two attends to itself at least as strongly as the other attends to it. The condition is far from automatic: uniformly random stochastic matrices satisfy it only 24-30% of the time. When tested on the head-averaged attention of each individual input and restricted to content tokens - image patches, words or tabular features, excluding cls, register and separator tokens - the condition holds for essentially every input at every layer of DINOv2 (three model sizes), RoBERTa and DistilBERT. In the supervised models DeiT-B and ViT-B/16 it holds for 91% and 64% of input-layer pairs respectively, with all failures occurring late in depth. In FT-Transformer trained on two standard tabular benchmarks it holds for only 11-44% of input-layer pairs. The special tokens account for almost all failures in DINOv2 and the language models: when they are included, the condition holds for only 82-97% of input-layer pairs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05558",
  "author_total": 1,
  "authors": [
    {
      "name": "Przemysław Rola"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/98wesqvjvhqdg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05558",
  "fulltext_url": null,
  "id": "98wesqvjvhqdg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05558",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1702|Topic Modeling"
    ]
  ],
  "openalex": "W7220741030",
  "pdf_url": "https://arxiv.org/pdf/2610.05558",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/98wesqvjvhqdg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05558",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05558"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "An equality condition for the Dobrushin bound on attention rollout and how often it holds in trained transformers",
  "title_text": "An equality condition for the Dobrushin bound on attention rollout and how often it holds in trained transformers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/98wesqvjvhqdg",
  "venue": "arXiv",
  "versions": []
}