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

arXiv: https://arxiv.org/abs/2507.21129 · HTML: https://mlsanity.com/paper/2507.21129/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 21 Jul 2025.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [How Can We Know What Language Models Know?](https://mlsanity.com/paper/1911.12543/) (2019)
- [Quantifying Memorization Across Neural Language Models](https://mlsanity.com/paper/2202.07646/) (2022)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)

## Abstract (arXiv)

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.