# Integrating Local and Global Entropy for Uncertainty Quantification in LLMs Source: [Integrating Local and Global Entropy for Uncertainty Quantification in LLMs]() Collection index: [llms.txt]() Data updated: 2026-06-11T05:00:05.512Z Authors: Johanne Medina, Tianyi Zhou, Keivin Isufaj, Aristides Gionis, Sanjay Chawla Published: 2026-06-02T20:57:14.000Z ## Abstract Large language models hallucinate confidently, making uncertainty quantification (UQ) essential for reliable deployment. Existing methods rely predominantly on token-level signals, leaving the geometric structure of intermediate hidden states underused. In this paper, we take the geometric complexity of hidden-state matrices as a measure of the global uncertainty of LLMs, while treating token-level uncertainty estimation as a local metric. We show that hidden-state geometric entropy (global uncertainty) and token-level entropy (local uncertainty) are statistically near-orthogonal, capturing distinct failure regimes for reliability prediction. In particular, global geometry recovers the confident-but-wrong failure mode that local signals systematically miss. Building on this, we propose Global-Local Uncertainty (GLU), an unsupervised, single-pass score that fuses the two signals via a multiplicative gate. Across three model families and six benchmarks, GLU matches or outperforms all unsupervised baselines while requiring only a single forward pass and remaining length-normalized and architecture-agnostic. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Reliability Estimation on TriviaQA](): Reliability Estimation; TriviaQA; AUROC: 83.4. - [Uncertainty Quantification on Longform](): Uncertainty Quantification; LongForm; AUROC: 65.9. - [Uncertainty Quantification on Multiturn](): Uncertainty Quantification; Multiturn; AUROC: 83.1. - [Uncertainty Quantification on MATH (PRR)](): Uncertainty Quantification; MATH; PRR: 70. - [Uncertainty Quantification on Longform (PRR)](): Uncertainty Quantification; LongForm; PRR: 0.221. - [Response Reliability Estimation on ArabicaQA](): Response reliability estimation; ArabicaQA; AUROC: 0.647. - [Response reliability estimation on Longform](): Response reliability estimation; LongForm; AUROC: 0.654. - [Response reliability estimation on Multiturn](): Response reliability estimation; Multiturn; AUROC: 0.831. - [Uncertainty Quantification on TruthfulQA](): Uncertainty Quantification; TruthfulQA; AUROC: 68. - [Response reliability estimation on MATH](): Response reliability estimation; MATH; AUROC: 0.799. - [Uncertainty Quantification on ArabicaQA](): Uncertainty Quantification; ArabicaQA; AUROC: 0.65. - [Uncertainty Quantification on Multiturn (PRR)](): Uncertainty Quantification; Multiturn; PRR: 0.691. - [Response Reliability Estimation on TruthfulQA](): Response reliability estimation; TruthfulQA; AUROC: 0.641. - [Uncertainty Quantification on MATH](): Uncertainty Quantification; MATH; AUROC: 80.1. - [Uncertainty Estimation on TriviaQA](): Uncertainty Estimation; TriviaQA; AUROC: 83.7. - [Uncertainty Quantification on TriviaQA](): Uncertainty Quantification; TriviaQA; PRR: 69.8. - [Uncertainty Estimation on TruthfulQA](): Uncertainty Estimation; TruthfulQA; PRR: 0.392. ## Original sources and implementation [Original paper]() [PDF]()