Adaptive Self-Consistency: From Black-Box Sampling to Distribution-Valued Feedback

Abstract:Self-consistency samples many reasoning trajectories and aggregates their final answers, treating the LLM as a black box that returns one answer per trajectory. Yet the final answer of each trajectory is sampled from a softmax vector that is available from the model's log-probabilities. We refer to this as the grey-box setting in which each trajectory reveals this answer distribution rather than a single draw from it. We formulate efficient inference in this setting as sequential mode identification with distribution-valued observations: sample trajectories one at a time and stop as soon as the LLM's modal answer is identified at a prescribed confidence level. We characterize the asymptotic stopping rate of mode identification with distribution-valued observations exactly and show that it is never worse than the black-box rate. We then propose the ASC-D algorithm, a betting stopping rule that attains this asymptotic stopping rate. On MMLU-Redux, ASC-D uses $46.4$--$95.6\%$ fewer trajectories than answer-only adaptive self-consistency baselines and achieves the highest fixed-budget correct-certification rate across three open-source models.

27 pages, 4 figures, 7 tables. The first two authors contributed equally

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2609.38931 [cs.LG]

(or arXiv:2609.38931v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.38931 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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