Title: Deciphering the Entropy Patterns in Chain-of-Thought Reasoning

Original: arXiv:2606.02020v1 Announce Type: cross Abstract: 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.

Rewritten: Title: Analyzing Entropy Fluctuations in Chain-of-Thought Logic

Original: arXiv:2606.02020v1 Announce Type: cross Abstract: This study explores the entropy behaviors inherent in Chain-of-Thought (CoT) processes, revealing a distinct bipartite architecture: an initial phase characterized by an Uncertainty Region focused on exploration, which abruptly shifts into a Confidence Region defined by convergence. Our analysis identifies two pivotal attributes within this Confidence Region: first, High Reliability, wherein responses achieve significant precision and stability; and second, High Redundancy, where models continue producing superfluous tokens well past the point of identifying the correct solution. These characteristics enable the development of optimized inference protocols, specifically: 1) Early Exit, which capitalizes on reliability and redundancy to halt processing efficiently once marginal gains plateau, and 2) Test-Time Scaling, which employs Confidence Region indicators to favor trajectories that have reached convergence. To implement these findings, we frame the identification of the Confidence Region as a sequential change-point detection task, marking the inaugural application of traditional change-point techniques to CoT monitoring. By utilizing the Cumulative Sum (CUSUM) algorithm—recognized for its statistical optimality in change-point detection—we created a training-free system for managing inference in real time. Our experimental results demonstrate that this method defines a superior Pareto frontier for early exit mechanisms. Specifically, CUSUM attained an accuracy of 63.06% while reducing token usage by 11.1%, surpassing DEER and Dynasor in accuracy by 3.28% and 4.36%, respectively. In the context of test-time scaling, voting mechanisms weighted by CUSUM consistently exceeded the performance of self-consistency methods.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC