{
  "abstract": "In this paper we study the behavior of transformer networks generating text over long periods of time. We show that even a three-token, single-layer attention-only transformer can fail to converge. We then study a rich class of transformers with arbitrary finite depth, layer normalization, MLPs, RoPE encodings, and an arbitrary mix of local and global layers. Every transformer in this class has a softmax temperature threshold above which its empirical cache distribution converges to a unique limit, independent of initial conditions. We show further that, while each transformer has a temperature threshold, the supremum of this set is infinite, so there is no global minimal temperature that forces all transformers to converge.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19358",
  "author_total": 6,
  "authors": [
    {
      "name": "Katy Blumer"
    },
    {
      "name": "Da-Cheng Juan"
    },
    {
      "name": "Jon Kleinberg"
    },
    {
      "name": "Ravi Kumar"
    },
    {
      "name": "Cyrus Rashtchian"
    },
    {
      "name": "Andrew Tomkins"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4dhbjhz7aq7d4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19358",
  "fulltext_url": null,
  "id": "4dhbjhz7aq7d4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19358",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Topic Modeling"
    ]
  ],
  "openalex": "W7222093125",
  "pdf_url": "https://arxiv.org/pdf/2610.19358",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4dhbjhz7aq7d4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19358",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19358"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Asymptotic Behavior of Transformers",
  "title_text": "Asymptotic Behavior of Transformers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/4dhbjhz7aq7d4",
  "venue": "arXiv",
  "versions": []
}