# The Stepwise Informativeness Assumption: Why are Entropy Dynamics and Reasoning Correlated in LLMs?

arXiv: https://arxiv.org/abs/2604.06192 · HTML: https://mlsanity.com/paper/2604.06192/

## Key facts

- Cited by 3 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 23 of its 31 references that are in the map.
- First posted on arXiv 11 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, 23 of 23)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [Olmo 3](https://mlsanity.com/paper/2512.13961/) (2025)
- [Demystifying Reasoning Dynamics with Mutual Information: Thinking Tokens are Information Peaks in LLM Reasoning](https://mlsanity.com/paper/2506.02867/) (2025)
- [Making Slow Thinking Faster: Compressing LLM Chain-of-Thought via Step Entropy](https://mlsanity.com/paper/2508.03346/) (2025)
- [Understanding Chain-of-Thought in LLMs through Information Theory](https://mlsanity.com/paper/2411.11984/) (2024)
- [Position: Stop Anthropomorphizing Intermediate Tokens as Reasoning/Thinking Traces!](https://mlsanity.com/paper/2504.09762/) (2025)
- [Entropy-based Exploration Conduction for Multi-step Reasoning](https://mlsanity.com/paper/2503.15848/) (2025)
- [Think Just Enough: Sequence-Level Entropy as a Confidence Signal for LLM Reasoning](https://mlsanity.com/paper/2510.08146/) (2025)
- [Performative Thinking? The Brittle Correlation Between CoT Length and Problem Complexity](https://mlsanity.com/paper/2509.07339/) (2025)
- [Entropy-Lens: Uncovering Decision Strategies in LLMs](https://mlsanity.com/paper/2502.16570/) (2025)
- [Measuring Reasoning Utility in LLMs via Conditional Entropy Reduction](https://mlsanity.com/paper/2508.20395/) (2025)
- [Token Signature: Predicting Chain-of-Thought Gains with Token Decoding Feature in Large Language Models](https://mlsanity.com/paper/2506.06008/) (2025)

## Built on by (most cited first, 3 of 3)

- [Adaptive Depth in Looped Transformers: Diagnosing Learned Halting Gates and Trajectory Readouts](https://mlsanity.com/paper/2607.20519/) (2026)
- [Answer-Distribution Trajectories: A Stochastic-Dynamics View of LLM Reasoning](https://mlsanity.com/paper/2609.09030/) (2026)
- [Predicting Task Difficulty Without Rollouts](https://mlsanity.com/paper/2608.05797/) (2026)

## Abstract (arXiv)

Recent work uses entropy-based signals at multiple representation levels to study reasoning in large language models, but the field remains largely empirical. A central unresolved puzzle is why internal entropy dynamics, defined under the predictive distribution of a model, correlate so robustly with external correctness given by the ground-truth answer. In this paper, we argue that this correlation arises because autoregressive models reason correctly when they accumulate information about the true answer via answer-informative prefixes. We formalize this intuition via the Stepwise Informativeness Assumption (SIA), which states that reasoning prefixes accumulate answer-relevant information in expectation as generation progresses. We show that SIA naturally emerges from maximum-likelihood optimization on human reasoning traces and is reinforced by standard fine-tuning and reinforcement-learning pipelines. We then derive observable signatures of SIA linking conditional answer entropy dynamics to correctness. We empirically test SIA across multiple reasoning benchmarks (GSM8K, ARC, SVAMP) and a diverse set of open-weight LLMs (Gemma-2, LLaMA-3.2, Qwen-2.5, DeepSeek and Olmo variants), showing that training induces it and that correct traces exhibit characteristic conditional answer entropy patterns.