Entropy trajectory shape predicts LLM reasoning reliability: A diagnostic study of uncertainty dynamics in chain-of-thought
This provides a low-cost diagnostic tool for improving LLM reasoning reliability, though it is incremental as it builds on existing chain-of-thought methods.
The study tackled the problem of cheaply detecting failures in chain-of-thought reasoning for LLMs by analyzing uncertainty dynamics, finding that monotone entropy trajectories (where entropy decreases at every step) predict correctness with accuracy improvements of up to 34.7 percentage points over non-monotone chains.
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 ($Ï$=-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.