{
  "abstract": "We study an extension of the Guided Speculative Inference (GSI) algorithm for test-time-scaling of large language models (LLMs) to a novel setting where an ensemble of smaller LLMs proposes draft reasoning steps which are later verified by a larger base model and a process reward model. Using the established framework of multiple importance sampling (MIS), we introduce weighting schemes to aggregate samples from a diverse collection of proposal distributions. We provide new bounds on the KL divergence from the optimal reward-tilted target distribution and the expected reward degradation, then demonstrate that the well-known balance heuristic is optimal. Compared to GSI with a single well-tuned drafter, combining several diverse LLMs while retaining the same total number of samples maintains competitive pass-at-$N$ downstream performance while being mathematically robust to situations where the support of a single draft model does not cover that of the target, where GSI may fail.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33368",
  "author_total": 2,
  "authors": [
    {
      "name": "Joseph Rowan"
    },
    {
      "name": "Ashish J. Khisti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/44m23m929csmh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33368",
  "fulltext_url": null,
  "id": "44m23m929csmh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33368",
  "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.IT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Topic Modeling"
    ]
  ],
  "openalex": "W7223899403",
  "pdf_url": "https://arxiv.org/pdf/2610.33368",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/44m23m929csmh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33368",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33368"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Multiple Importance Sampling for Guided Speculative Inference",
  "title_text": "Multiple Importance Sampling for Guided Speculative Inference",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/44m23m929csmh",
  "venue": "arXiv",
  "versions": []
}