The Stepwise Informativeness Assumption: When Do Entropy Dynamics Track Reasoning Correctness in LLMs?

Recent work uses entropy-based signals at multiple representation levels to study reasoning in large language models, but the field remains largely empirical. From a theoretical perspective, reductions in model uncertainty do not necessarily reflect progress toward correctness. In this work, we characterize when such alignment can be expected through the Stepwise Informativeness Assumption (SIA), which requires entropy-reducing reasoning-prefix extensions increase the probability assigned to valid answers in expectation. We show that next-token prediction can transfer answer-relevant information from training data to the model, but does not, by itself, guarantee alignment with correctness. Instead, we propose that this alignment depends on how the training regime couples reasoning traces to correct answers. Furthermore, we hypothesize observable signatures of this phenomenon and characterize its expected failure regimes. We empirically investigate how entropy dynamics relate to correctness across four reasoning benchmarks (GSM8K, ARC, SVAMP, MATH) and diverse open-weight language models spanning base, instruction-tuned, and RL-trained regimes. Our results show that entropy-correctness alignment strengthens with post-training but can weaken when task difficulty exceeds model capabilities.