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A Survey of Uncertainty Estimation in LLMs: Theory Meets Practice

Hsiu-Yuan Huang, Yutong Yang, Zhaoxi Zhang, Sanwoo Lee, Yunfang Wu

TL;DR

This survey addresses uncertainty estimation in LLMs by integrating Bayesian, ensemble, information-theoretic, and language-expression perspectives to ground heuristic methods in theory. It discusses practical constraints posed by large-scale, commercial black-box models and outlines methods—BNNs with variational approximations, variance- and consistency-based ensembles, information-theoretic metrics, and verbal uncertainty prompts—that illuminate and mitigate model uncertainty. Key contributions include clarifying distinctions between uncertainty and confidence, mapping methods to black-box applicability, and outlining concrete applications in OOD detection, data annotation, and question clarification. The work aims to guide the development of more reliable uncertainty estimation techniques for real-world LLM deployments and to bridge theoretical foundations with practical deployment considerations.

Abstract

As large language models (LLMs) continue to evolve, understanding and quantifying the uncertainty in their predictions is critical for enhancing application credibility. However, the existing literature relevant to LLM uncertainty estimation often relies on heuristic approaches, lacking systematic classification of the methods. In this survey, we clarify the definitions of uncertainty and confidence, highlighting their distinctions and implications for model predictions. On this basis, we integrate theoretical perspectives, including Bayesian inference, information theory, and ensemble strategies, to categorize various classes of uncertainty estimation methods derived from heuristic approaches. Additionally, we address challenges that arise when applying these methods to LLMs. We also explore techniques for incorporating uncertainty into diverse applications, including out-of-distribution detection, data annotation, and question clarification. Our review provides insights into uncertainty estimation from both definitional and theoretical angles, contributing to a comprehensive understanding of this critical aspect in LLMs. We aim to inspire the development of more reliable and effective uncertainty estimation approaches for LLMs in real-world scenarios.

A Survey of Uncertainty Estimation in LLMs: Theory Meets Practice

TL;DR

This survey addresses uncertainty estimation in LLMs by integrating Bayesian, ensemble, information-theoretic, and language-expression perspectives to ground heuristic methods in theory. It discusses practical constraints posed by large-scale, commercial black-box models and outlines methods—BNNs with variational approximations, variance- and consistency-based ensembles, information-theoretic metrics, and verbal uncertainty prompts—that illuminate and mitigate model uncertainty. Key contributions include clarifying distinctions between uncertainty and confidence, mapping methods to black-box applicability, and outlining concrete applications in OOD detection, data annotation, and question clarification. The work aims to guide the development of more reliable uncertainty estimation techniques for real-world LLM deployments and to bridge theoretical foundations with practical deployment considerations.

Abstract

As large language models (LLMs) continue to evolve, understanding and quantifying the uncertainty in their predictions is critical for enhancing application credibility. However, the existing literature relevant to LLM uncertainty estimation often relies on heuristic approaches, lacking systematic classification of the methods. In this survey, we clarify the definitions of uncertainty and confidence, highlighting their distinctions and implications for model predictions. On this basis, we integrate theoretical perspectives, including Bayesian inference, information theory, and ensemble strategies, to categorize various classes of uncertainty estimation methods derived from heuristic approaches. Additionally, we address challenges that arise when applying these methods to LLMs. We also explore techniques for incorporating uncertainty into diverse applications, including out-of-distribution detection, data annotation, and question clarification. Our review provides insights into uncertainty estimation from both definitional and theoretical angles, contributing to a comprehensive understanding of this critical aspect in LLMs. We aim to inspire the development of more reliable and effective uncertainty estimation approaches for LLMs in real-world scenarios.

Paper Structure

This paper contains 36 sections, 11 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Uncertainty: Aleatoric vs. Epistemic
  4. Differences: Uncertainty vs. Confidence
  5. Uncertainty Estimation with Bayesian Inference
  6. Bayesian Neural Networks
  7. Approximate BNN Methods
  8. Variational Inference
  9. Deep Gaussian Processes
  10. Markov Chain Monte Carlo
  11. Takeaways
  12. Uncertainty Estimation with Ensemble Strategies
  13. Variance-Based Ensemble
  14. Monte Carlo Dropout
  15. Deep Ensemble
  16. ...and 21 more sections

Figures (1)

  • Figure 1: Taxonomy of uncertainty estimates. Blue nodes stand for white-box-LLMs-only methods, while green nodes stand for methods suitable for black-box LLMs as well.