CoT-Kinetics: A Theoretical Modeling Assessing LRM Reasoning Process

TL;DR

This paper introduces CoT-Kinetics, a theoretical model inspired by classical mechanics, to evaluate the reasoning process in large reasoning models by quantifying the soundness of reasoning trajectories, leading to more accurate quality assessment.

Contribution

The paper proposes a novel CoT-Kinetics energy equation that models reasoning as a particle dynamics process, improving the assessment of reasoning soundness in large reasoning models.

Findings

CoT-Kinetics effectively evaluates reasoning soundness.

The model provides a scalar score correlating with answer confidence.

It enhances overall output quality measurement.

Abstract

Recent Large Reasoning Models significantly improve the reasoning ability of Large Language Models by learning to reason, exhibiting the promising performance in solving complex tasks. LRMs solve tasks that require complex reasoning by explicitly generating reasoning trajectories together with answers. Nevertheless, judging the quality of such an output answer is not easy because only considering the correctness of the answer is not enough and the soundness of the reasoning trajectory part matters as well. Logically, if the soundness of the reasoning part is poor, even if the answer is correct, the confidence of the derived answer should be low. Existing methods did consider jointly assessing the overall output answer by taking into account the reasoning part, however, their capability is still not satisfactory as the causal relationship of the reasoning to the concluded answer cannot properly reflected. In this paper, inspired by classical mechanics, we present a novel approach towards establishing a CoT-Kinetics energy equation. Specifically, our CoT-Kinetics energy equation formulates the token state transformation process, which is regulated by LRM internal transformer layers, as like a particle kinetics dynamics governed in a mechanical field. Our CoT-Kinetics energy assigns a scalar score to evaluate specifically the soundness of the reasoning phase, telling how confident the derived answer could be given the evaluated reasoning. As such, the LRM's overall output quality can be accurately measured, rather than a coarse judgment (e.g., correct or incorrect) anymore.