Integrating Local and Global Entropy for Uncertainty Quantification in LLMs

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.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML)

arXiv:2606.09875 [cs.LG]

(or arXiv:2606.09875v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.09875 Focus to learn more arXiv-issued DOI via DataCite

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