# Entropy trajectory shape predicts LLM reasoning reliability: A diagnostic study of uncertainty dynamics in chain-of-thought

arXiv: https://arxiv.org/abs/2603.18940 · HTML: https://mlsanity.com/paper/2603.18940/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 15 of its 26 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 15 of 15)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [Active Prompting with Chain-of-Thought for Large Language Models](https://mlsanity.com/paper/2302.12246/) (2023)
- [Thought calibration: Efficient and confident test-time scaling](https://mlsanity.com/paper/2505.18404/) (2025)
- [Can LLMs Predict Their Own Failures? Self-Awareness via Internal Circuits](https://mlsanity.com/paper/2512.20578/) (2025)
- [Temporalizing Confidence: Evaluation of Chain-of-Thought Reasoning with Signal Temporal Logic](https://mlsanity.com/paper/2506.08243/) (2025)
- [VI-CuRL: Stabilizing Verifier-Independent RL Reasoning via Confidence-Guided Variance Reduction](https://mlsanity.com/paper/2602.12579/) (2026)
- [Know When You're Wrong: Aligning Confidence with Correctness for LLM Error Detection](https://mlsanity.com/paper/2603.06604/) (2026)
- [Recurrent Confidence Chain: Temporal-Aware Uncertainty Quantification in Large Language Models](https://mlsanity.com/paper/2601.13368/) (2026)
- [ConfSpec: Efficient Step-Level Speculative Reasoning via Confidence-Gated Verification](https://mlsanity.com/paper/2602.18447/) (2026)
- [Learning When to Sample: Confidence-Aware Selective Sampling for Efficient Chain-of-Thought Reasoning](https://mlsanity.com/paper/2603.08999/) (2026)

## Built on by (most cited first, 8 of 8)

- [When Do LLMs Reason? A Dynamical Systems View via Entropy Phase Transitions](https://mlsanity.com/paper/2605.22873/) (2026)
- [ProSR: Process-Shaped Spatial Reasoning for Reliable Chain-of-Thought in VLMs](https://mlsanity.com/paper/2605.25524/) (2026)
- [How Language Models Fail: Token-Level Signatures of Committed and Persistent Reasoning Failures](https://mlsanity.com/paper/2606.06635/) (2026)
- [The Tell-Tale Trace: Detecting Reasoning Failures in LLMs Using Chain-of-Thought Dynamics](https://mlsanity.com/paper/2608.03291/) (2026)
- [How Hard Does It Think? Analyzing Step-Aware Reasoning Energy in LLM Chain-of-Thought Trajectories](https://mlsanity.com/paper/2607.28674/) (2026)
- [Chain-of-Thought Entropy as a Reliability Signal: A Preregistered Reproduction](https://mlsanity.com/paper/2609.19606/) (2026)
- [Learning More by Training Less: Uncertainty-Guided Progressive Contraction for Efficient Reasoning Post-Training](https://mlsanity.com/paper/2610.12933/) (2026)
- [Argument Graph Uncertainty: Quantifying Uncertainty from the Logical Structure of Reasoning Chains](https://mlsanity.com/paper/2610.20328/) (2026)

## Abstract (arXiv)

Understanding uncertainty in chain-of-thought reasoning is critical for reliable deployment of large language models. In this work, we propose a simple yet effective diagnostic approach based on trajectory shape rather than scalar magnitude. We show that this signal is practical, interpretable, and inexpensive to obtain in black-box settings, while remaining robust across models and datasets. Through extensive ablations and cross-domain replications, we demonstrate its utility for selective prediction and triage. Our findings offer a generalizable insight into uncertainty dynamics in reasoning tasks, with particular focus on numeric and discrete-answer settings.