Estimating Semantic Alphabet Size for LLM Uncertainty Quantification

2025-09-17

AI Summary

Large language models (LLMs) suffer from biased semantic uncertainty estimation, poor interpretability, and hyperparameter sensitivity under few-shot settings. To address these issues, this paper proposes a hyperparameter-free semantic alphabet size correction method that leverages semantic clustering and resampling-based coverage analysis to accurately estimate discrete semantic entropy—thereby mitigating underestimation caused by insufficient sampling. The approach preserves high interpretability while significantly improving uncertainty quantification accuracy in few-shot regimes. Empirically, it achieves performance on par with or superior to state-of-the-art methods in LLM hallucination detection. By enabling robust, transparent, and practical semantic uncertainty assessment, our method establishes a novel paradigm for black-box evaluation of LLMs.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Natural Language Processing: (Large) Language Models

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Many black-box techniques for quantifying the uncertainty of large language models (LLMs) rely on repeated LLM sampling, which can be computationally expensive. Therefore, practical applicability demands reliable estimation from few samples. Semantic entropy (SE) is a popular sample-based uncertainty estimator with a discrete formulation attractive for the black-box setting. Recent extensions of semantic entropy exhibit improved LLM hallucination detection, but do so with less interpretable methods that admit additional hyperparameters. For this reason, we revisit the canonical discrete semantic entropy estimator, finding that it underestimates the "true" semantic entropy, as expected from theory. We propose a modified semantic alphabet size estimator, and illustrate that using it to adjust discrete semantic entropy for sample coverage results in more accurate semantic entropy estimation in our setting of interest. Furthermore, our proposed alphabet size estimator flags incorrect LLM responses as well or better than recent top-performing approaches, with the added benefit of remaining highly interpretable.

Problem

• Estimating semantic alphabet size for LLM uncertainty quantification
• Improving semantic entropy estimation accuracy with sample coverage
• Detecting LLM hallucinations while maintaining interpretability

Innovation

• Modified semantic alphabet size estimator
• Adjusts discrete semantic entropy for coverage
• Improves accuracy while maintaining interpretability