# Measuring Reasoning Utility in LLMs via Conditional Entropy Reduction

arXiv: https://arxiv.org/abs/2508.20395 · HTML: https://mlsanity.com/paper/2508.20395/

## Key facts

- Cited by 6 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 13 of its 20 references that are in the map.
- First posted on arXiv 28 Aug 2025.

## 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, 13 of 13)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Large Language Model based Multi-Agents: A Survey of Progress and Challenges](https://mlsanity.com/paper/2402.01680/) (2024)
- [Confidence Improves Self-Consistency in LLMs](https://mlsanity.com/paper/2502.06233/) (2025)
- [Sampling-Efficient Test-Time Scaling: Self-Estimating the Best-of-N Sampling in Early Decoding](https://mlsanity.com/paper/2503.01422/) (2025)
- [SoftCoT++: Test-Time Scaling with Soft Chain-of-Thought Reasoning](https://mlsanity.com/paper/2505.11484/) (2025)
- [Bridging Internal Probability and Self-Consistency for Effective and Efficient LLM Reasoning](https://mlsanity.com/paper/2502.00511/) (2025)
- [Path-Consistency with Prefix Enhancement for Efficient Inference in LLMs](https://mlsanity.com/paper/2409.01281/) (2024)

## Built on by (most cited first, 6 of 6)

- [Slim-SC: Thought Pruning for Efficient Scaling with Self-Consistency](https://mlsanity.com/paper/2509.13990/) (2025)
- [The Stepwise Informativeness Assumption: Why are Entropy Dynamics and Reasoning Correlated in LLMs?](https://mlsanity.com/paper/2604.06192/) (2026)
- [When Retrieval Succeeds and Fails: Rethinking Retrieval-Augmented Generation for LLMs](https://mlsanity.com/paper/2510.09106/) (2025)
- [InfoDensity: Rewarding Information-Dense Traces for Efficient Reasoning](https://mlsanity.com/paper/2603.17310/) (2026)
- [Towards a Science of Collective AI: LLM-based Multi-Agent Systems Need a Transition from Blind Trial-and-Error to Rigorous Science](https://mlsanity.com/paper/2602.05289/) (2026)
- [Advancing Entropy-Level Credit Assignment in RLVR via Proximal Entropy Policy Optimization](https://mlsanity.com/paper/2609.39402/) (2026)

## Abstract (arXiv)

Recent advancements in large language models (LLMs) often rely on generating intermediate reasoning steps to enhance accuracy. However, little work has examined how reasoning utility contributes to the final answer's correctness. Due to the stochastic nature of autoregressive generation, generating more context does not guarantee increased confidence in the answer. If we could predict, during generation, whether a reasoning step will be useful, we could stop early or prune ineffective steps, avoiding distractions in the final decision. We present an oracle study on MATH dataset, using Qwen2.5-32B and GPT-4o to generate reasoning chains, and then employing a separate model (Qwen3-8B) to quantify the utility of these chains for final accuracy. Specifically, we measure the model's uncertainty on the answer span Y at each reasoning step using conditional entropy (expected negative log-likelihood over the vocabulary) with context expanding step by step. Our results show a clear pattern: conditional entropy that decreases over steps is strongly associated with correct answers, whereas flat or increasing entropy often results in wrong answers. We also corroborate that incorrect reasoning paths tend to be longer than correct ones, suggesting that longer reasoning does not necessarily yield better outcomes. These findings serve as a foundation to inspire future work on designing efficient reasoning pipelines that detect and avoid unproductive reasoning early.