← 研踪 PaperTrailarXiv:2611.14171 · v1
BARS: Budget-Aware Sequential Sampling with Refusal for Majority Identification under Unknown Distributions
首次提交 2026-11-10 23:00
版本更新 2026-11-10 23:00
雷达观测 2026-11-11 13:08
摘要
Repeated sampling with majority selection is an effective means of enforcing self-consistency in large language models. Recently, a variant has also been introduced that terminates early to save costs when the output distribution is favorable. But it still cannot yield a correct confidence estimate from the answer distribution. For this issue, we formalize this as majority identification under an unknown distribution with a budget and a target error rate, and propose BARS, a sequential rule certifying the top-two gap and returning an early stop, a budgeted majority vote, or a refusal when feasibility cannot be established. A refusal is a statement about the rule and its budget, not a claim that a question is unanswerable, and it tells practitioners when to widen the budget or switch models. A certified mode carries proven bounds on the joint answering error and on refusing an instance the budget could handle, while a practical mode, used in our experiments, replaces them with empirical calibration. On synthetic instances drawn from known distributions over thousands of seeds, the difficulty-driven behavior is recovered and the price of the certified mode is measured.On GSM8K the practical mode draws 22.3\% fewer samples than fixed-8 sampling over the same pool, refused questions included, at the cost of declining 18.8\% of the questions. On MATH, it greatly improves the accuracy of its output answers into 82.5\% at the cost of honestly refusing to answer half of the difficult questions that the model itself is unable to solve.
作者备注：23 pages (17 pages without appendix), 7 tables, 8 figures
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v1 · 2026-11-10 23:00 · 最新观测版本
BARS: Budget-Aware Sequential Sampling with Refusal for Majority Identification under Unknown Distributions
Repeated sampling with majority selection is an effective means of enforcing self-consistency in large language models. Recently, a variant has also been introduced that terminates early to save costs when the output distribution is favorable. But it still cannot yield a correct confidence estimate from the answer distribution. For this issue, we formalize this as majority identification under an unknown distribution with a budget and a target error rate, and propose BARS, a sequential rule certifying the top-two gap and returning an early stop, a budgeted majority vote, or a refusal when feasibility cannot be established. A refusal is a statement about the rule and its budget, not a claim that a question is unanswerable, and it tells practitioners when to widen the budget or switch models. A certified mode carries proven bounds on the joint answering error and on refusing an instance the budget could handle, while a practical mode, used in our experiments, replaces them with empirical calibration. On synthetic instances drawn from known distributions over thousands of seeds, the difficulty-driven behavior is recovered and the price of the certified mode is measured.On GSM8K the practical mode draws 22.3\% fewer samples than fixed-8 sampling over the same pool, refused questions included, at the cost of declining 18.8\% of the questions. On MATH, it greatly improves the accuracy of its output answers into 82.5\% at the cost of honestly refusing to answer half of the difficult questions that the model itself is unable to solve.
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