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

• URL: http://arxiv.org/abs/2604.06192v1
• Date: Wed, 11 Mar 2026 18:00:18 GMT
• Title: The Stepwise Informativeness Assumption: Why are Entropy Dynamics and Reasoning Correlated in LLMs?
• Abstract summary: We show that reasoning prefixes accumulate answer-relevant information in expectation as generation progresses.<n>We derive observable signatures of SIA linking conditional answer entropy dynamics to correctness.
• Score: 14.977096886054142
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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