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

View PDF HTML (experimental) 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. Comments: 21 pages, 5 figures, 3 tables Subjects: Computation and Language (cs.CL); Artificial Intelligence (cs.AI); Information Theory (cs.IT); Machine Learning (cs.LG) Cite as: arXiv:2604.06192 [cs.CL] (or arXiv:2604.06192v1 [cs.CL] for this version) https://doi.org/10.48550/arXiv.2604.06192 arXiv-issued DOI via DataCite Submission history From: Mar Gonzàlez I Català [view email] [v1] Wed, 11 Mar 2026 18:00:18 UTC (757 KB)