Revisiting the Uniform Information Density Hypothesis in LLM Reasoning Traces
Minju Gwak
Abstract
Step-level uniformity in information density, measured using entropy-based metrics, improves reasoning accuracy in large language models across various benchmarks.
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.
Community
How do strong thinkers — and strong LLMs — pace their reasoning?
1️⃣
When people reason, we don’t unload every idea at once.
We build thoughts step by step, balancing clarity with just enough surprise to keep things compelling.
2️⃣
In our new paper, “Revisiting the Uniform Information Density Hypothesis in LLM Reasoning Traces,” we ask:
A. Do language models show a similar rhythm?
B. And can we actually measure how information flows through their reasoning?
3️⃣
Our findings: effective reasoning traces aren’t evenly flat.
They show both:
🟢 Local uniformity — each step adds a steady amount of new information
🔵 Global non-uniformity — bursts of insight that drive progress
4️⃣
This parallels a well-known principle in psycholinguistics:
Humans prefer sentences and thoughts that maintain smooth information density.
Too flat is dull. Too jagged is confusing.
The best reasoning has a natural rhythm.
5️⃣
We introduce entropy-based metrics to capture this flow — and show they predict reasoning quality.
Using them to select LLM traces boosts accuracy by 10–32% across benchmarks.
6️⃣
The bigger idea: good reasoning, whether human or machine, is about pacing.
Not too fast. Not too slow. The right cadence of surprise.
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