{
  "abstract": "Large language models (LLMs) are trained and evaluated as though perfect reliability is achievable for any task given sufficient scale. We show that this assumption is information-theoretically unjustified. Every generative task has a reliability ceiling that no model can exceed, determined by how much output uncertainty is resolvable from observable context. The gap decomposes into a resolvable component closable with additional context and a subjective component inherent to task ambiguity. Autoregressive generation further degrades this ceiling at a rate governed by the task's dependency kernel, which quantifies inter-token correlations in the output. From these two primitives, we derive a first-principles scaling law where LLM performance is bottlenecked by the scarcer resource: training data or model capacity. This law recovers the Chinchilla scaling law as a special case and provides a structural account of when scaling improves reliability. Beyond scaling, our framework unifies diverse practical phenomena, such as the benefits of retrieval-augmentation and the spectral mechanics of catastrophic forgetting. Our work formalizes the resource-complexity tradeoffs that govern model performance across domains, offering a unified theory of performance limits in generative language models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.14112",
  "author_total": 1,
  "authors": [
    {
      "name": "Subhabrata Majumdar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b2g3dat7ecxh0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.14112",
  "fulltext_url": null,
  "id": "b2g3dat7ecxh0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.14112",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.CL"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Topic Modeling"
    ]
  ],
  "openalex": "W7169498256",
  "pdf_url": "https://arxiv.org/pdf/2607.14112",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b2g3dat7ecxh0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2607.14112",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.14112"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Limits of Reliability and Scaling in Language Models",
  "title_text": "Limits of Reliability and Scaling in Language Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/b2g3dat7ecxh0",
  "venue": "arXiv",
  "versions": []
}