用推理和答案的联合概率选最优解，无需训练即可显著提升大模型推理准确率。
PiCSAR: Probabilistic Confidence Selection And Ranking for Reasoning Chains
- 通过联合概率评估推理链与答案，无需训练即可生成可信度分数。
- 在MATH500和AIME2025上分别提升10.18和9.81分，且用更少样本优于基线。
- 适合追求高效、低成本提升推理模型性能的研究者和应用开发者。
最佳- n 采样通过生成多个候选解并选择奖励最高的一个，提升了大语言模型（LLMs）和大推理模型（LRMs）的准确性。推理任务的关键挑战在于设计评分函数，以在无真实答案的情况下识别正确推理链。本文提出概率置信度选择与排序（PiCSAR）：一种无需训练的简单方法，利用推理过程与最终答案的联合对数似然对每个候选生成进行评分。该联合对数似然自然分解为推理置信度与答案置信度。PiCSAR在多种基准测试中取得显著提升（MATH500 +10.18，AIME2025 +9.81），且在20次对比中的16次中以至少两倍少的采样数超越基线。分析表明，正确推理链在推理与答案置信度上均显著更高，验证了PiCSAR的有效性。
原文摘要 · Abstract (English)
Best-of-n sampling improves the accuracy of large language models (LLMs) and large reasoning models (LRMs) by generating multiple candidate solutions and selecting the one with the highest reward. The key challenge for reasoning tasks is designing a scoring function that can identify correct reasoning chains without access to ground-truth answers. We propose Probabilistic Confidence Selection And Ranking (PiCSAR): a simple, training-free method that scores each candidate generation using the joint log-likelihood of the reasoning and final answer. The joint log-likelihood of the reasoning and final answer naturally decomposes into reasoning confidence and answer confidence. PiCSAR achieves substantial gains across diverse benchmarks (+10.18 on MATH500, +9.81 on AIME2025), outperforming baselines with at least 2x fewer samples in 16 out of 20 comparisons. Our analysis reveals that correct reasoning chains exhibit significantly higher reasoning and answer confidence, justifying the effectiveness of PiCSAR.
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