Quantifying and Understanding Uncertainty in Large Reasoning Models

Large Reasoning Models (LRMs) have recently demonstrated significant improvements in complex reasoning. While quantifying generation uncertainty in LRMs is crucial, traditional methods are often insufficient because they do not provide finite-sample guarantees for reasoning-answer generation. Conformal prediction (CP) stands out as a distribution-free and model-agnostic methodology that constructs statistically rigorous uncertainty sets. However, existing CP methods ignore the logical connection between the reasoning trace and the final answer. Additionally, prior studies fail to interpret the origins of uncertainty coverage for LRMs as they typically overlook the specific training factors driving valid reasoning. Notably, it is challenging to disentangle reasoning quality from answer correctness when quantifying uncertainty, while simultaneously establishing theoretical guarantees for computationally efficient explanation methods. To address these challenges, we first propose a novel methodology that quantifies uncertainty in the reasoning-answer structure with statistical guarantees. Subsequently, we develop a unified example-to-step explanation framework using Shapley values that identifies a provably sufficient subset of training examples and their key reasoning steps to preserve the guarantees. We also provide theoretical analyses of our proposed methods. Extensive experiments on challenging reasoning datasets verify the effectiveness of the proposed methods.