Revisiting the Uniform Information Density Hypothesis in LLM Reasoning Traces

2025-10-08

AI Summary

This work investigates whether step-level information density uniformity in large language model (LLM) reasoning trajectories serves as an effective predictor of reasoning quality, testing the Uniform Information Density (UID) hypothesis. Method: We propose an entropy-based, layer-wise information density metric that jointly models local abruptness suppression and global distribution uniformity, yielding a differentiable, unsupervised UID scoring mechanism. Contribution/Results: Experiments show that correct reasoning paths significantly avoid information density spikes, and UID strongly correlates with answer correctness. Our method achieves 10–32% relative accuracy gains across six major reasoning benchmarks and substantially outperforms baselines on AIME2025. This is the first systematic demonstration that information density uniformity constitutes a critical implicit indicator of LLM reasoning robustness—establishing a novel, annotation-free paradigm for reasoning quality assessment and trajectory selection.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• Evaluating whether step-level information uniformity reflects reasoning quality in LLMs
• Developing entropy-based metrics to measure local and global uniformity in reasoning traces
• Using information density uniformity as predictor for reliable reasoning system selection

Innovation

• Proposed entropy-based stepwise information density metric
• Introduced local and global uniformity scores
• Used uniformity to select high-quality reasoning traces