Title: PiCSAR: Probabilistic Confidence Selection And Ranking for Reasoning Chains
Primary area: foundation or frontier models, including LLMs
Keywords: Large Language Models, Large Reasoning Models, Probabilistic Confidence, Mathematical Reasoning

Abstract: 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 for Reasoning Chains (PiCSAR): a simple, training-free method that scores each candidate generation using the joint log-likelihood of the reasoning and final answer. This method utilises both the scores of the reasoning path (_reasoning confidence_) and the final answer (_answer confidence_). PiCSAR achieves substantial gains across diverse benchmarks ($+11.7$ on AIME2024, $+9.81$ on AIME2025), outperforming baselines with fewer than at least 2x samples in 20 out of 25 comparisons. Our analysis reveals that correct reasoning chains exhibit significantly higher reasoning and answer confidence, justifying the effectiveness of PiCSAR.