Revisiting the Uniform Information Density Hypothesis in LLM Reasoning Traces
Minju Gwak, Guijin Son, Jaehyung Kim
2025-10-09
Summary
This paper investigates how consistently information is presented during the step-by-step reasoning process of large language models, and whether that consistency relates to how well the model actually reasons.
What's the problem?
Large language models are getting better at complex tasks, but it's hard to know *why* they get the right or wrong answer. We don't have a good way to look 'inside' their reasoning process to understand what makes a good reasoning trace versus a bad one. The paper asks if a smooth, consistent flow of information during reasoning – meaning not jumping around too much in terms of how much new information is presented at each step – is a sign of better reasoning.
What's the solution?
The researchers developed a way to measure how evenly information is distributed throughout each step of a language model's reasoning. They used a concept called 'information density' and calculated both a 'local' score (looking at each step individually) and a 'global' score (looking at the overall reasoning trace). They then tested whether these scores could predict the accuracy of the model's answers on several different reasoning tasks. They found that reasoning traces with more consistent information density were more likely to be correct, and they could even improve accuracy by selecting for these more uniform traces.
Why it matters?
This work provides a new tool for evaluating and improving the reasoning abilities of large language models. By focusing on the *process* of reasoning, rather than just the final answer, it helps us understand what makes a model think effectively. This could lead to building more reliable and accurate AI systems, and it offers a way to automatically select the best reasoning paths generated by a model.
Abstract
The Uniform Information Density (UID) hypothesis suggests that effective communication maintains a stable flow of information. In this work, we revisit this principle in the context of large language model (LLM) reasoning traces, asking whether step-level uniformity reflects reasoning quality. To this end, we propose an entropy-based stepwise information density metric and introduce two complementary measures of uniformity, local and global uniformity scores. Across the experiments on six different reasoning benchmarks, we find that step-level uniformity not only provides a strong theoretical lens but also yields practical performance benefits; for example, selecting reasoning traces with more uniform information density at the step-level improves accuracy by 10-32\% relative gains over baselines at AIME2025. Our analysis further reveals that correct reasoning traces tend to avoid sharp information density spikes, while incorrect traces exhibit irregular information bursts. These results demonstrate that UID-inspired information density measures outperform alternative internal signals as predictors of reasoning quality. Results highlight the uniformity of the information density as a robust diagnostic and selection criterion for building more reliable and accurate reasoning systems.