这篇论文揭示了CoT推理中隐藏的熵动力学规律，做推理加速和模型效率优化的研究者可以直接用CUSUM方法实现无训练早退，比现有方法更优。
这篇论文研究了链式推理（CoT）过程中的熵变化，发现了一个一致的两阶段结构：先是不确定性探索阶段，然后突然过渡到置信收敛阶段。置信阶段具有高可靠性和高冗余性两个关键特性，模型在得出正确答案后仍会生成大量无用token。基于此，作者提出了两种更高效的推理策略：早退机制（Early Exit）和测试时缩放（Test-Time Scaling）。他们使用累积和（CUSUM）算法进行实时推理控制，无需额外训练。实验表明，CUSUM早退在准确率63.06%时实现了11.1%的token缩减，优于DEER和Dynasor。
Unveiling the Entropy Dynamics of Chain-of-Thought Reasoning
This paper investigates the entropy dynamics of Chain-of-Thought (CoT) and uncovers a consistent two-phase structure: an Uncertainty Region of exploration transitioning sharply to a Confidence Region of convergence. We demonstrate that the Confidence Region possesses two critical properties: 1) High Reliability -- answers in the confidence region become highly accurate and stable, and 2) High Redundancy -- models generate unnecessary tokens long after reaching the correct answer. These properties unlock more efficient and reliable inference strategies: 1) Early Exit leverages reliability and redundancy to terminate computation safely when returns diminish, and 2)Test-Time Scaling uses the Confidence Region signal to prioritize converged trajectories. To operationalize these insights, we formulate Confidence Region detection as a sequential change-point detection problem, being the first to apply classical change-point methods to monitor CoT reasoning. Using the Cumulative Sum (CUSUM) algorithm, a statistically optimal change-point detector, we develop a training-free framework for real-time inference control. Experiments show our approach establishes a superior Pareto-frontier for early exit. CUSUM achieves 63.06% accuracy with 11.1% token reduction, outperforming DEER and Dynasor by 3.28% and 4.36% in accuracy respectively. For test-time scaling, CUSUM-weighted voting consistently outperforms self-consistency.