# A Survey of Uncertainty Estimation in LLMs: Theory Meets Practice

arXiv: https://arxiv.org/abs/2410.15326 · HTML: https://mlsanity.com/paper/2410.15326/

## Key facts

- Cited by 55 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 66 references that are in the map.
- First posted on arXiv 20 Oct 2024.

## Builds on (most cited first, 30 of 39)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning](https://mlsanity.com/paper/2002.06715/) (2020)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)
- [Deep Deterministic Uncertainty: A Simple Baseline](https://mlsanity.com/paper/2102.11582/) (2021)
- [Out-of-Distribution Detection and Selective Generation for Conditional Language Models](https://mlsanity.com/paper/2209.15558/) (2022)
- [On Hallucination and Predictive Uncertainty in Conditional Language Generation](https://mlsanity.com/paper/2103.15025/) (2021)
- [LM-Polygraph: Uncertainty Estimation for Language Models](https://mlsanity.com/paper/2311.07383/) (2023)
- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthiness](https://mlsanity.com/paper/2308.16175/) (2023)
- [GTBench: Uncovering the Strategic Reasoning Limitations of LLMs via Game-Theoretic Evaluations](https://mlsanity.com/paper/2402.12348/) (2024)
- [Decomposing Uncertainty for Large Language Models through Input Clarification Ensembling](https://mlsanity.com/paper/2311.08718/) (2023)
- [Deep Active Learning for Named Entity Recognition](https://mlsanity.com/paper/1707.05928/) (2017)
- [Uncertainty Quantification with Pre-trained Language Models: A Large-Scale Empirical Analysis](https://mlsanity.com/paper/2210.04714/) (2022)
- [SAC3: Reliable Hallucination Detection in Black-Box Language Models via Semantic-aware Cross-check Consistency](https://mlsanity.com/paper/2311.01740/) (2023)
- [Quantifying Uncertainties in Natural Language Processing Tasks](https://mlsanity.com/paper/1811.07253/) (2018)
- [LLMs Will Always Hallucinate, and We Need to Live With This](https://mlsanity.com/paper/2409.05746/) (2024)
- [Rejection Improves Reliability: Training LLMs to Refuse Unknown Questions Using RL from Knowledge Feedback](https://mlsanity.com/paper/2403.18349/) (2024)
- [A Comprehensive guide to Bayesian Convolutional Neural Network with Variational Inference](https://mlsanity.com/paper/1901.02731/) (2019)
- [Llamas Know What GPTs Don't Show: Surrogate Models for Confidence Estimation](https://mlsanity.com/paper/2311.08877/) (2023)

## Built on by (most cited first, 30 of 55)

- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey](https://mlsanity.com/paper/2503.15850/) (2025)
- [PlanGenLLMs: A Modern Survey of LLM Planning Capabilities](https://mlsanity.com/paper/2502.11221/) (2025)
- [A Survey of Uncertainty Estimation Methods on Large Language Models](https://mlsanity.com/paper/2503.00172/) (2025)
- [Calibrating Verbal Uncertainty as a Linear Feature to Reduce Hallucinations](https://mlsanity.com/paper/2503.14477/) (2025)
- [Knowledge Boundary of Large Language Models: A Survey](https://mlsanity.com/paper/2412.12472/) (2024)
- [Beyond Semantic Entropy: Boosting LLM Uncertainty Quantification with Pairwise Semantic Similarity](https://mlsanity.com/paper/2506.00245/) (2025)
- [Estimating LLM Uncertainty with Evidence](https://mlsanity.com/paper/2502.00290/) (2025)
- [Revisiting Uncertainty Estimation and Calibration of Large Language Models](https://mlsanity.com/paper/2505.23854/) (2025)
- [From Calibration to Collaboration: LLM Uncertainty Quantification Should Be More Human-Centered](https://mlsanity.com/paper/2506.07461/) (2025)
- [Semantic Energy: Detecting LLM Hallucination Beyond Entropy](https://mlsanity.com/paper/2508.14496/) (2025)
- [MetaFaith: Faithful Natural Language Uncertainty Expression in LLMs](https://mlsanity.com/paper/2505.24858/) (2025)
- [Anthropomimetic Uncertainty: What Verbalized Uncertainty in Language Models is Missing](https://mlsanity.com/paper/2507.10587/) (2025)
- [Enhancing LLM Reliability via Explicit Knowledge Boundary Modeling](https://mlsanity.com/paper/2503.02233/) (2025)
- [Reflections on the Reproducibility of Commercial LLM Performance in Empirical Software Engineering Studies](https://mlsanity.com/paper/2510.25506/) (2025)
- [TruthPrInt: Mitigating Large Vision-Language Models Object Hallucination Via Latent Truthful-Guided Pre-Intervention](https://mlsanity.com/paper/2503.10602/) (2025)
- [Do not Abstain! Identify and Solve the Uncertainty](https://mlsanity.com/paper/2506.00780/) (2025)
- [AmbiK: Dataset of Ambiguous Tasks in Kitchen Environment](https://mlsanity.com/paper/2506.04089/) (2025)
- [On Calibration of Large Language Models: From Response To Capability](https://mlsanity.com/paper/2602.13540/) (2026)
- [Inv-Entropy: A Fully Probabilistic Framework for Uncertainty Quantification in Language Models](https://mlsanity.com/paper/2506.09684/) (2025)
- [ProcCtrlBench: Evaluating Process-Level Defects and Control Preservation in LLM Coding Agents](https://mlsanity.com/paper/2605.20251/) (2026)
- [Beyond Early-Token Bias: Model-Specific and Language-Specific Position Effects in Multilingual LLMs](https://mlsanity.com/paper/2505.16134/) (2025)
- [Generalized Correctness Models: Learning Calibrated and Model-Agnostic Correctness Predictors from Historical Patterns](https://mlsanity.com/paper/2509.24988/) (2025)
- [DiSRouter: Distributed Self-Routing for LLM Selections](https://mlsanity.com/paper/2510.19208/) (2025)
- [Epistemic Gain, Aleatoric Cost: Uncertainty Decomposition in Multi-Agent Debate for Math Reasoning](https://mlsanity.com/paper/2603.01221/) (2026)
- [Delusions of Large Language Models](https://mlsanity.com/paper/2503.06709/) (2025)
- [Instinct vs. Reflection: Unifying Token and Verbalized Confidence in Multimodal Large Models](https://mlsanity.com/paper/2604.17274/) (2026)
- [Walking Through Uncertainty: An Empirical Study of Uncertainty Estimation for Audio-Aware Large Language Models](https://mlsanity.com/paper/2604.25591/) (2026)
- [Reinforcement Learning with Metacognitive Feedback Elicits Faithful Uncertainty Expression in LLMs](https://mlsanity.com/paper/2606.32032/) (2026)
- [KScope: A Framework for Characterizing the Knowledge Status of Language Models](https://mlsanity.com/paper/2506.07458/) (2025)

## Abstract (arXiv)

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.