Measuring and Analyzing Intelligence via Contextual Uncertainty in Large Language Models using Information-Theoretic Metrics

• URL: http://arxiv.org/abs/2507.21129v2
• Date: Sun, 26 Oct 2025 00:32:31 GMT
• Title: Measuring and Analyzing Intelligence via Contextual Uncertainty in Large Language Models using Information-Theoretic Metrics
• Authors: Jae Wan Shim,
• Abstract summary: We propose a task-agnostic method that builds a quantitative Cognitive Profile for any model.<n>The profile is built around the Entropy Decay Curve-a plot of a model's normalised predictive uncertainty as context length grows.<n>We also propose the Information Gain Span (IGS) as a single index that summarises the desirability of a decay pattern.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Large Language Models (LLMs) excel on many task-specific benchmarks, yet the mechanisms that drive this success remain poorly understood. We move from asking what these systems can do to asking how they process information. Our contribution is a task-agnostic method that builds a quantitative Cognitive Profile for any model. The profile is built around the Entropy Decay Curve-a plot of a model's normalised predictive uncertainty as context length grows. Across several state-of-the-art LLMs and diverse texts, the curves expose distinctive, stable profiles that depend on both model scale and text complexity. We also propose the Information Gain Span (IGS) as a single index that summarises the desirability of a decay pattern. Together, these tools offer a principled way to analyse and compare the internal dynamics of modern AI systems.

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