mlsanityData to 7 Oct 2026

Uncertainty Estimation and Quantification for LLMs: A Simple Supervised Approach

arXiv 2404.15993 ↗First posted 24 Apr 2024cs.LG cs.CLcited by 73

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Abstract (arXiv)

In this paper, we study the problem of uncertainty estimation and calibration for LLMs. We begin by formulating the uncertainty estimation problem, a relevant yet underexplored area in existing literature. We then propose a supervised approach that leverages labeled datasets to estimate the uncertainty in LLMs' responses. Based on the formulation, we illustrate the difference between the uncertainty estimation for LLMs and that for standard ML models and explain why the hidden neurons of the LLMs may contain uncertainty information. Our designed approach demonstrates the benefits of utilizing hidden activations to enhance uncertainty estimation across various tasks and shows robust transferability in out-of-distribution settings. We distinguish the uncertainty estimation task from the uncertainty calibration task and show that better uncertainty estimation leads to better calibration performance. Furthermore, our method is easy to implement and adaptable to different levels of model accessibility including black box, grey box, and white box.

Key facts. Cited by 73 papers in the map (data through 7 Oct 2026). Builds on 29 of its 52 references that are in the map. First posted on arXiv 24 Apr 2024.

Builds on

29 of 52 references.

References · 29

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2022Training language models to follow instructions with human feedbackcited by 15,712
  3. 2023Llama 2: Open Foundation and Fine-Tuned Chat Modelscited by 12,865
  4. 2020Measuring Massive Multitask Language Understandingcited by 7,768
  5. 2017On Calibration of Modern Neural Networkscited by 4,860
  6. 2017TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehensioncited by 2,895
  7. 2023Sparks of Artificial General Intelligence: Early experiments with GPT-4cited by 2,579
  8. 2022Language Models (Mostly) Know What They Knowcited by 1,783
  9. 2023Inference-Time Intervention: Eliciting Truthful Answers from a Language Modelcited by 1,259
  10. 2020A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challengescited by 813
  11. 2023Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedbackcited by 788
  12. 2022Discovering Latent Knowledge in Language Models Without Supervisioncited by 733
17 more
  1. 2023The Internal State of an LLM Knows When It's Lyingcited by 644
  2. 2023A Survey of Hallucination in Large Foundation Modelscited by 365
  3. 2024INSIDE: LLMs' Internal States Retain the Power of Hallucination Detectioncited by 317
  4. 2020Calibration of Pre-trained Transformerscited by 307
  5. 2020Unsupervised Quality Estimation for Neural Machine Translationcited by 210
  6. 2020Reducing conversational agents' overconfidence through linguistic calibrationcited by 209
  7. 2023Conformal Prediction with Large Language Models for Multi-Choice Question Answeringcited by 131
  8. 2024Language Models with Conformal Factuality Guaranteescited by 128
  9. 2023Decomposing Uncertainty for Large Language Models through Input Clarification Ensemblingcited by 113
  10. 2023Do Androids Know They're Only Dreaming of Electric Sheep?cited by 67
  11. 2023Cognitive Dissonance: Why Do Language Model Outputs Disagree with Internal Representations of Truthfulness?cited by 62
  12. 2024Do LLMs Know about Hallucination? An Empirical Investigation of LLM's Hidden Statescited by 50
  13. 2024Distinguishing the Knowable from the Unknowable with Language Modelscited by 45
  14. 2023A Study on the Calibration of In-context Learningcited by 21
  15. 2021Can Explanations Be Useful for Calibrating Black Box Models?cited by 20
  16. 2024Probabilities of Chat LLMs Are Miscalibrated but Still Predict Correctness on Multiple-Choice Q&Acited by 16
  17. 2023Reducing LLM Hallucinations using Epistemic Neural Networkscited by 8

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 15; 2025: 40; 2026: 18.

73 papers.

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  1. 2024A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directionscited by 115
  2. 2025Uncertainty Quantification and Confidence Calibration in Large Language Models: A Surveycited by 93
  3. 2024LLM Internal States Reveal Hallucination Risk Faced With a Querycited by 80
  4. 2024Learning to Route LLMs with Confidence Tokenscited by 66
  5. 2025A Survey of Uncertainty Estimation Methods on Large Language Modelscited by 57
  6. 2024Latent Space Chain-of-Embedding Enables Output-free LLM Self-Evaluationcited by 56
  7. 2024Do LLMs estimate uncertainty well in instruction-following?cited by 26
  8. 2025Revisiting Uncertainty Estimation and Calibration of Large Language Modelscited by 22
  9. 2024A Survey on the Honesty of Large Language Modelscited by 21
  10. 2025From Calibration to Collaboration: LLM Uncertainty Quantification Should Be More Human-Centeredcited by 21
  11. 2025Semantic Volume: Quantifying and Detecting both External and Internal Uncertainty in LLMscited by 19
  12. 2025Semantic Energy: Detecting LLM Hallucination Beyond Entropycited by 18
38 more
  1. 2024RadFlag: A Black-Box Hallucination Detection Method for Medical Vision Language Modelscited by 16
  2. 2026A Survey on LLM-based Conversational User Simulationcited by 14
  3. 2025Geometric Uncertainty for Detecting and Correcting Hallucinations in LLMscited by 12
  4. 2024Graph-based Confidence Calibration for Large Language Modelscited by 10
  5. 2025Gatekeeper: Improving Model Cascades Through Confidence Tuningcited by 10
  6. 2024LLMs are not Zero-Shot Reasoners for Biomedical Information Extractioncited by 9
  7. 2024Fine-Tuning Large Language Models to Appropriately Abstain with Semantic Entropycited by 9
  8. 2026Complementing Self-Consistency with Cross-Model Disagreement for Uncertainty Quantificationcited by 9
  9. 2025Tools in the Loop: Quantifying Uncertainty of LLM Question Answering Systems That Use Toolscited by 7
  10. 2024LLM Confidence Evaluation Measures in Zero-Shot CSS Classificationcited by 6
  11. 2025Conformal Prediction Beyond the Seen: A Missing Mass Perspective for Uncertainty Quantification in Generative Modelscited by 6
  12. 2025Loki's Dance of Illusions: A Comprehensive Survey of Hallucination in Large Language Modelscited by 6
  13. 2025Transformers Discover Molecular Structure Without Graph Priorscited by 6
  14. 2025Scaling Textual Gradients via Sampling-Based Momentumcited by 5
  15. 2025Uncertainty Under the Curve: A Sequence-Level Entropy Area Metric for Reasoning LLMcited by 5
  16. 2025Generalized Correctness Models: Learning Calibrated and Model-Agnostic Correctness Predictors from Historical Patternscited by 5
  17. 2025Uncertainty Quantification for Retrieval-Augmented Reasoningcited by 5
  18. 2026Are LLM Evaluators Really Narcissists? Sanity Checking Self-Preference Evaluationscited by 5
  19. 2024VernaCopter: Disambiguated Natural-Language-Driven Robot via Formal Specificationscited by 4
  20. 2025Confidence Elicitation: A New Attack Vector for Large Language Modelscited by 4
  21. 2025Quasar: A Programming Language Specialized for LLM Code Actionscited by 4
  22. 2025The Geometry of Creative Variability: How Credal Sets Expose Calibration Gaps in Language Modelscited by 4
  23. 2026LLM Performance Predictors: Learning When to Escalate in Hybrid Human-AI Moderation Systemscited by 4
  24. 2026Semantic Self-Distillation for Language Model Uncertaintycited by 4
  25. 2026Online Reasoning Calibration: Test-Time Training Enables Generalizable Conformal LLM Reasoningcited by 4
  26. 2024Uncertainty Quantification for Clinical Outcome Predictions with (Large) Language Modelscited by 3
  27. 2025Multimodal Graph Representation Learning for Robust Surgical Workflow Recognition with Adversarial Feature Disentanglementcited by 3
  28. 2025Revealing economic facts: LLMs know more than they saycited by 3
  29. 2025Towards Harmonized Uncertainty Estimation for Large Language Modelscited by 3
  30. 2025GENUINE: Graph Enhanced Multi-level Uncertainty Estimation for Large Language Modelscited by 3
  31. 2025The Narrative Continuity Test: A Conceptual Framework for Evaluating Identity Persistence in AI Systemscited by 3
  32. 2025Shapley Uncertainty in Natural Language Generationcited by 2
  33. 2025Open-Source Agentic Hybrid RAG Framework for Scientific Literature Reviewcited by 2
  34. 2025Online-Optimized RAG for Tool Use and Function Callingcited by 2
  35. 2025Confidence-Based Response Abstinence: Improving LLM Trustworthiness via Activation-Based Uncertainty Estimationcited by 2
  36. 2025SIMBA UQ: Similarity-Based Aggregation for Uncertainty Quantification in Large Language Modelscited by 2
  37. 2025HaluNet: Learning Hallucination Risk from Internal Signals in LLM Question Answeringcited by 2
  38. 2024LaMsS: When Large Language Models Meet Self-Skepticismcited by 1

50 most cited of 73 All 73 (JSON)