{"ID":2920984,"CreatedAt":"2026-06-02T02:42:49.606572591Z","UpdatedAt":"2026-06-04T07:41:34.29888543Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.02020","arxiv_id":"2606.02020","title":"Unveiling the Entropy Dynamics of Chain-of-Thought Reasoning","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.","short_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 -- answ...","url_abs":"https://arxiv.org/abs/2606.02020","url_pdf":"https://arxiv.org/pdf/2606.02020v1","authors":"[\"Ting Xu\",\"Xu He\",\"Yupu Lu\",\"Jiankai Sun\",\"Dong Li\",\"Wai Lam\",\"Jianye Hao\"]","published":"2026-06-01T10:11:14Z","proceeding":"cs.CL","tasks":"[\"cs.CL\",\"cs.LG\"]","methods":"[\"LoRA\"]","has_code":false}