# Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey

arXiv: https://arxiv.org/abs/2503.15850 · HTML: https://mlsanity.com/paper/2503.15850/

## Key facts

- Cited by 95 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 104 of its 166 references that are in the map.
- First posted on arXiv 20 Mar 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 104)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Calibrate Before Use: Improving Few-Shot Performance of Language Models](https://mlsanity.com/paper/2102.09690/) (2021)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [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)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [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)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [LLM Evaluators Recognize and Favor Their Own Generations](https://mlsanity.com/paper/2404.13076/) (2024)
- [CoQA: A Conversational Question Answering Challenge](https://mlsanity.com/paper/1808.07042/) (2018)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)

## Built on by (most cited first, 30 of 95)

- [LLM-based Agents Suffer from Hallucinations: A Survey of Taxonomy, Methods, and Directions](https://mlsanity.com/paper/2509.18970/) (2025)
- [Unlocking Exploration in RLVR: Uncertainty-aware Advantage Shaping for Deeper Reasoning](https://mlsanity.com/paper/2510.10649/) (2025)
- [BroRL: Scaling Reinforcement Learning via Broadened Exploration](https://mlsanity.com/paper/2510.01180/) (2025)
- [TokUR: Token-Level Uncertainty Estimation for Large Language Model Reasoning](https://mlsanity.com/paper/2505.11737/) (2025)
- [Metacognition and Uncertainty Communication in Humans and Large Language Models](https://mlsanity.com/paper/2504.14045/) (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)
- [Intelligent AI Delegation](https://mlsanity.com/paper/2602.11865/) (2026)
- [The Illusion of Certainty: Uncertainty Quantification for LLMs Fails under Ambiguity](https://mlsanity.com/paper/2511.04418/) (2025)
- [Geometric Uncertainty for Detecting and Correcting Hallucinations in LLMs](https://mlsanity.com/paper/2509.13813/) (2025)
- [Consensus Entropy: Harnessing Multi-VLM Agreement for Self-Verifying and Self-Improving OCR](https://mlsanity.com/paper/2504.11101/) (2025)
- [Check Yourself Before You Wreck Yourself: Selectively Quitting Improves LLM Agent Safety](https://mlsanity.com/paper/2510.16492/) (2025)
- [Learned Hallucination Detection in Black-Box LLMs using Token-level Entropy Production Rate](https://mlsanity.com/paper/2509.04492/) (2025)
- [Generalizability of Large Language Model-Based Agents: A Comprehensive Survey](https://mlsanity.com/paper/2509.16330/) (2025)
- [The Illusion of Stochasticity in LLMs](https://mlsanity.com/paper/2604.06543/) (2026)
- [Estimating Semantic Alphabet Size for LLM Uncertainty Quantification](https://mlsanity.com/paper/2509.14478/) (2025)
- [LEC: Linear Expectation Constraints for Selection-Conditioned Risk Control in Selective Prediction and Routing Systems](https://mlsanity.com/paper/2512.01556/) (2025)
- [LLMs as Signal Detectors: Sensitivity, Bias, and the Temperature-Criterion Analogy](https://mlsanity.com/paper/2603.14893/) (2026)
- [Uncertainty Quantification for Retrieval-Augmented Reasoning](https://mlsanity.com/paper/2510.11483/) (2025)
- [SafeGround: Know When to Trust GUI Grounding Models via Uncertainty Calibration](https://mlsanity.com/paper/2602.02419/) (2026)
- [Overconfidence and Calibration in Medical VQA: Empirical Findings and Hallucination-Aware Mitigation](https://mlsanity.com/paper/2604.02543/) (2026)
- [Do Large Language Models (Really) Need Statistical Foundations?](https://mlsanity.com/paper/2505.19145/) (2025)
- [Knowing What You Know Is Not Enough: Large Language Model Confidences Don't Align With Their Actions](https://mlsanity.com/paper/2511.13240/) (2025)
- [Semantic Self-Distillation for Language Model Uncertainty](https://mlsanity.com/paper/2602.04577/) (2026)
- [Organ-Agents: Virtual Human Physiology Simulator via LLMs](https://mlsanity.com/paper/2508.14357/) (2025)
- [Task-Awareness Improves LLM Generations and Uncertainty](https://mlsanity.com/paper/2601.21500/) (2026)
- [Know More, Know Clearer: A Meta-Cognitive Framework for Knowledge Augmentation in Large Language Models](https://mlsanity.com/paper/2602.12996/) (2026)
- [Real-Time Trustworthiness Scoring for LLM Structured Outputs and Data Extraction](https://mlsanity.com/paper/2603.18014/) (2026)
- [Drift is a Sampling Error: SNR-Aware Power Distributions for Long-Horizon Robotic Planning](https://mlsanity.com/paper/2605.09537/) (2026)
- [Compress the Context, Keep the Commitments: A Formal Framework for Verifiable LLM Context Compression](https://mlsanity.com/paper/2605.17304/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) excel in text generation, reasoning, and decision-making, enabling their adoption in high-stakes domains such as healthcare, law, and transportation. However, their reliability is a major concern, as they often produce plausible but incorrect responses. Uncertainty quantification (UQ) enhances trustworthiness by estimating confidence in outputs, enabling risk mitigation and selective prediction. However, traditional UQ methods struggle with LLMs due to computational constraints and decoding inconsistencies. Moreover, LLMs introduce unique uncertainty sources, such as input ambiguity, reasoning path divergence, and decoding stochasticity, that extend beyond classical aleatoric and epistemic uncertainty. To address this, we introduce a new taxonomy that categorizes UQ methods based on computational efficiency and uncertainty dimensions (input, reasoning, parameter, and prediction uncertainty). We evaluate existing techniques, assess their real-world applicability, and identify open challenges, emphasizing the need for scalable, interpretable, and robust UQ approaches to enhance LLM reliability.