{
  "abstract": "Frontier reasoning models are produced by post-training base language models with reinforcement learning. Recent work has challenged this by showing that sampling from a sharpened version of the base model's distribution, a so-called power distribution, elicits comparable reasoning without additional training, curated datasets, or verifiers. However, making this method practical requires efficiently sampling from the power distribution. A sampler needs to \"mix\" to the power distribution, which necessitates moving between modes of the target distribution; intuitively, e.g., trying different reasoning strategies. The samplers proposed in prior works repeatedly select a \"cut\" position in the current reasoning trace uniformly at random and resample the suffix from that position onward. However, reasoning traces typically contain a few consequential decisions (e.g., the choice of proof strategy or algorithm), and we observe that a uniformly chosen cut tends to rewrite local details rather than revisit decision points. We introduce an algorithm (Entropy-Cut Metropolis-Hastings) that uses the base model's next-token entropy as a proxy to identify key decision points and resample from those positions. We empirically verify that entropy jumps are a useful proxy for decision points and, in a stylized model of reasoning, prove that our method's mixing time scales with the number of decisions in a trace rather than with the number of tokens, which can be much larger. Across MATH500, HumanEval, GPQA Diamond, and AIME26, our method consistently improves over baselines and RL-trained models, including best-of-N at the same token budget.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.30327",
  "author_total": 3,
  "authors": [
    {
      "name": "Felix Zhou"
    },
    {
      "name": "Anay Mehrotra"
    },
    {
      "name": "Quanquan C. Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/23wmen8kvs01f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.30327",
  "fulltext_url": null,
  "id": "23wmen8kvs01f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.30327",
  "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.LG"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Topic Modeling"
    ]
  ],
  "openalex": "W7162751592",
  "pdf_url": "https://arxiv.org/pdf/2605.30327",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/23wmen8kvs01f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2605.30327",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.30327"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Reasoning with Sampling: Cutting at Decision Points",
  "title_text": "Reasoning with Sampling: Cutting at Decision Points",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:41Z",
  "url": "https://research.draconitic.com/paper/23wmen8kvs01f",
  "venue": "arXiv",
  "versions": []
}