{
  "abstract": "Many applications of language models require estimating the expectation of a test functional under the model. Obtaining precise estimates can be computationally expensive. We show how to improve estimation precision by exploiting next-token conditional probabilities available as a by-product of sampling. Our approach uses potentials: real-valued functions of prefixes that induce an additive decomposition of the test functional. We construct a family of estimators parameterized by these potentials and derive conditions for variance reduction. Across applications including entropy estimation, watermark detection, and rare-event probability estimation, our estimators achieve substantial variance reductions relative to Monte Carlo and importance sampling baselines at comparable computational cost.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11399",
  "author_total": 4,
  "authors": [
    {
      "name": "Francesco I. Re"
    },
    {
      "name": "Shubhangi Ghosh"
    },
    {
      "name": "Tim Vieira"
    },
    {
      "name": "Ryan Cotterell"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/89c9gvmmdrqrz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11399",
  "fulltext_url": null,
  "id": "89c9gvmmdrqrz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11399",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "1702|Topic Modeling"
    ]
  ],
  "openalex": "W7221146835",
  "pdf_url": "https://arxiv.org/pdf/2610.11399",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/89c9gvmmdrqrz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:29Z",
      "native_id": "2610.11399",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11399"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Estimating Great Expectations Under Autoregressive Language Models with Potentials",
  "title_text": "Estimating Great Expectations Under Autoregressive Language Models with Potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:29Z",
  "url": "https://research.draconitic.com/paper/89c9gvmmdrqrz",
  "venue": "arXiv",
  "versions": []
}