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PreprintCC BY 4.0arXiv

Multiple Importance Sampling for Guided Speculative Inference

  • Joseph Rowan
  • Ashish J. Khisti
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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.

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Cite

BibTeXRIS
BibTeX
@misc{rowan2026multiple,
  title = {{Multiple Importance Sampling for Guided Speculative Inference}},
  author = {Joseph Rowan and Ashish J. Khisti},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33368},
  eprint = {2610.33368},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33368},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Multiple Importance Sampling for Guided Speculative Inference
AU  - Joseph Rowan
AU  - Ashish J. Khisti
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.33368
UR  - https://arxiv.org/abs/2610.33368
AB  - 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.
ER  -