Entropy trajectory shape predicts LLM reasoning reliability: A diagnostic study of uncertainty dynamics in chain-of-thought
Xinghao Zhao · Mar 19, 2026 · Citations: 0
How to use this page
Moderate trustUse this for comparison and orientation, not as your only source.
Best use
Background context only
What to verify
Validate the exact study setup in the full paper before operational use.
Evidence quality
Moderate
Derived from extracted protocol signals and abstract evidence.
Abstract
Chain-of-thought (CoT) reasoning improves LLM accuracy, yet detecting failures cheaply remains elusive. We study whether the shape of uncertainty dynamics across reasoning steps--captured by sampling a few answer completions per step--predicts correctness. We introduce entropy-trajectory monotonicity: a chain is monotone if its per-step answer-distribution entropy decreases at every step. On GSM8K (n=300) with Qwen2.5-7B-Instruct, monotone chains achieve 68.8% accuracy vs. 46.8% for non-monotone chains (+21.9 pp; Fisher's p=0.0005; OR=2.50). Critically, total entropy reduction is not predictive ($ρ$=-0.06, p=0.31), revealing a shape-over-magnitude dissociation: whether entropy decreases at every step matters, not how much. Violation count 0/1/2 gives 68.8%/50.8%/28.6% accuracy. Token log-probability confidence worsens in calibration with step depth (ECE: 0.186->0.312), and monotonicity achieves +5.8 pp at 73.7% coverage, outperforming scalar baselines at approx 1,500 tokens/question--1/8 the cost of 40-chain self-consistency. Results replicate on Mistral-7B (n=300): monotone chains reach 72.3% vs. 37.6% (+34.7 pp; OR=4.33). Structural properties of uncertainty trajectories are thus more informative than aggregate measures.