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Unveiling the Entropy Dynamics of Chain-of-Thought Reasoning

ICML 2026 · Large language models › Reasoning and chain of thought · approach: Long CoT dynamics and efficiency · 0 citations (OpenAlex)

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Shows CoT entropy dynamics follow a two-phase (uncertainty to confidence) structure and uses training-free CUSUM change-point detection for early exit and CUSUM-weighted test-time voting.

Problem

Understanding how CoT reasoning evolves globally from exploration to convergence, and detecting when reasoning has converged so that computation can be cut or trajectories weighted at inference time.

Approach

Model per-step intermediate-answer predictive entropy as switching between two regimes and apply CUSUM sequential change-point detection online to trigger early exit and weight voting, with no training.

Key results

• CUSUM averages 63.06% accuracy with 11.1% token reduction across three models and three benchmarks, versus DEER 59.78% and Dynasor 58.70%.
• On AIME25 with Qwen3-4B-Thinking-2507, CUSUM-weighted voting leads self-consistency by 3.33% at N=64.
• On AMC23 with DeepSeek-R1-Distill-Qwen-7B, CUSUM reduces tokens by 9.7% with accuracy 89.36% vs 89.69% vanilla.

Surprising findings

• Early exit with CUSUM keeps accuracy on correctly converged trajectories while also cutting tokens on incorrectly converged ones, indicating the method detects convergence independent of correctness.
• Problem difficulty shifts transition timing: easy problems enter the Confidence Region at 30-34% of trajectory, hard ones at 52-56%.

Limitations

• Trajectories often oscillate between regions (63% in the AIME25 analysis), and the i.i.d. CUSUM assumption is only approximately satisfied given temporal dependence in entropy.
• Hyperparameter h is chosen per model using a calibration set, and distributions f0 and f1 are estimated from Bespoke-Stratos-17k.
• Gains are modest, about 3 points over baselines on average, and the reported code release is only promised upon acceptance.

Experimental setup

Datasets: Bespoke-Stratos-17k AIME24 AIME25 GPQA-Diamond HotpotQA LiveCodeBench AMC23

Benchmarks: AIME24 AIME25 GPQA-Diamond HotpotQA LiveCodeBench AMC23

Metrics: accuracy token count token reduction exact match

Baselines: Vanilla DEER Dynasor Self-Consistency

Builds on: self-consistency DEER Dynasor CUSUM

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