解释大模型推理中熵变化为何与正确答案相关。
The Stepwise Informativeness Assumption: Why are Entropy Dynamics and Reasoning Correlated in LLMs?
- 提出逐步信息性假设，说明模型通过有意义前缀积累答案信息。
- 实验证明正确推理路径有特定的条件熵演变模式。
- 适合研究大模型推理机制或可解释性的读者。
近期研究利用多层级表示中的熵信号来分析大语言模型的推理过程，但该领域仍以经验性发现为主。核心未解之谜在于：为何模型内部熵动态（基于预测分布定义）会与真实答案的外部正确性表现出如此强的相关性？本文认为，这种相关性源于自回归模型在生成过程中通过答案相关信息的前缀逐步累积信息。我们提出了逐步信息性假设（SIA），即随着生成推进，推理前缀在期望上不断积累与答案相关的信息。我们证明SIA可自然从人类推理轨迹的最大似然优化中产生，并在标准微调和强化学习流程中得到加强。进一步推导出可观察的SIA特征，将条件答案熵动态与正确性联系起来。在GSM8K、ARC、SVAMP等多个推理基准及多种开源大模型（Gemma-2、LLaMA-3.2、Qwen-2.5、DeepSeek、Olmo变体）上进行实证测试，结果表明训练能诱导出SIA，且正确推理路径展现出特定的条件熵模式。
原文摘要 · Abstract (English)
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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