CoT-Kinetics: A Theoretical Modeling Assessing LRM Reasoning Process

TL;DR

This work tackles the challenge of evaluating the soundness of chain-of-thought reasoning in LRMs by introducing CoT-Kinetics energy, a theory-grounded metric that treats internal reasoning token dynamics as a discrete kinetic process regulated by transformer layers. The energy combines semantic momentum, semantic curvature, and an entropy term derived from internal states to produce a scalar score reflecting reasoning soundness without external supervision. Extensive experiments across seven open-source LRMs and six benchmarks (including multilingual MGSM) demonstrate that CoT-Kinetics energy aligns more closely with answer correctness than existing baselines, and exhibits strong generalization across domains and languages. The framework offers a principled, training-free tool for assessing and potentially guiding LRM reasoning, with practical implications for reliability and interpretability in complex reasoning tasks.

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.

Figures (2)

• Figure 1: Illustration of the necessity to separately assess the reasoning trajectory part with fine-grained granularity. Given a query from a specific domain, an LRM generates both a final answer and a CoT reasoning trajectory. However, the final answer may still be correct even if the reasoning path contains flawed assumptions or unstable logic. As shown in Example 2, evaluating only the final output overlooks deficiencies in the reasoning process. A higher score (Example 1) reflects a more sound reasoning trajectory and a greater likelihood of correctness, whereas a lower score (Example 3) indicates flawed assumptions or unstable logic and a higher chance of error. It motivates that only considering the correctness of the final answer is inappropriate while an accurate assessment technique such as the proposed CoT-Kinetics energy is required.
• Figure 2: Left: Samples ranked by CoT-Kinetics energy $\mathcal{E}_\text{CoT}$, where higher scores align with correct outputs, reflecting the soundness of reasoning and logical causal relationship in terms of AUROC, AUPR, and FPR@95 metric. Right: ROC curves comparing CoT-Kinetics energy $\mathcal{E}_\text{CoT}$ with baselines, where the dashed line denotes the expected performance of a random scoring function as a lower bound.