The Stepwise Informativeness Assumption: Why are Entropy Dynamics and Reasoning Correlated in LLMs?
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| Format: | Preprint |
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2026
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| author | Català, Mar Gonzàlez I Borde, Haitz Sáez de Ocáriz Montañez, George D. Liò, Pietro |
| author_facet | Català, Mar Gonzàlez I Borde, Haitz Sáez de Ocáriz Montañez, George D. Liò, Pietro |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_06192 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Stepwise Informativeness Assumption: Why are Entropy Dynamics and Reasoning Correlated in LLMs? Català, Mar Gonzàlez I Borde, Haitz Sáez de Ocáriz Montañez, George D. Liò, Pietro Computation and Language Artificial Intelligence Information Theory Machine Learning 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. |
| title | The Stepwise Informativeness Assumption: Why are Entropy Dynamics and Reasoning Correlated in LLMs? |
| topic | Computation and Language Artificial Intelligence Information Theory Machine Learning |
| url | https://arxiv.org/abs/2604.06192 |