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.
@article{arxiv.2507.21129,
title = {Measuring and Analyzing Intelligence via Contextual Uncertainty in Large Language Models using Information-Theoretic Metrics},
author = {Jae Wan Shim},
journal= {arXiv preprint arXiv:2507.21129},
year = {2026}
}