{
  "abstract": "Sampling temperature can substantially reshape autoregressive generation, but it is unclear when temperature changes in long-range correlations reflect a genuine phase transition rather than a smooth change in statistics. We study this question in a controlled analogue of temperature sampling: a finite-depth probabilistic context-free grammar on a fixed hierarchical tree, where exact next-token conditionals are computed by belief propagation and then rescaled by a softmax temperature before autoregressive sampling. We measure two-point mutual information between tokens as a function of separation. Across the tested temperatures and grammar ensembles, mutual information remains well described by a power-law envelope. Temperature changes the correlation magnitude and fitted exponent, but within the accessible system sizes we find no long-distance plateau characteristic of an ordered phase and no clear crossover to short-range exponential decay. An approximate mapping to an Ising model on a tree explains how exponential decay in tree distance becomes a power law in token distance, allowing power laws to persist without tuning to a special decoding temperature. This controlled baseline clarifies which temperature effects can arise from hierarchical structure alone, before adding training, approximation error, or neural architecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24334",
  "author_total": 2,
  "authors": [
    {
      "name": "Marcel Kühn"
    },
    {
      "name": "Bernd Rosenow"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9tckvqj9kefmq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24334",
  "fulltext_url": null,
  "id": "9tckvqj9kefmq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24334",
  "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",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7223005423",
  "pdf_url": "https://arxiv.org/pdf/2610.24334",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9tckvqj9kefmq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.24334",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24334"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Power-Law Correlations Without Apparent Temperature-Tuned Criticality in Fixed-Tree Hierarchical Languages",
  "title_text": "Power-Law Correlations Without Apparent Temperature-Tuned Criticality in Fixed-Tree Hierarchical Languages",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/9tckvqj9kefmq",
  "venue": "arXiv",
  "versions": []
}