mlsanityData to 14 Oct 2026

Rethinking Uncertainty Estimation in LLMs: A Principled Single-Sequence Measure

arXiv 2412.15176 ↗First posted 19 Dec 2024cs.LGcited by 18

On the map: LLM reasoning → Test-time compute and efficient thinking

Abstract (arXiv)

Large Language Models (LLMs) are increasingly employed in real-world applications, driving the need to evaluate the trustworthiness of their generated text. To this end, reliable uncertainty estimation is essential. Leading uncertainty estimation methods generate and analyze multiple output sequences, which is computationally expensive and impractical at scale. In this work, we inspect the theoretical foundations of these methods and explore new directions to enhance computational efficiency. Building on the framework of proper scoring rules, we find that the negative log-likelihood of the most likely output sequence constitutes a theoretically principled uncertainty measure. To approximate this alternative measure, we propose G-NLL, obtained using a single output sequence from greedy decoding. This approach streamlines uncertainty estimation while preserving theoretical rigor. Empirical results demonstrate that G-NLL achieves state-of-the-art performance across various scenarios. Our work lays the theoretical foundation for efficient and reliable uncertainty estimation in natural language generation, challenging the necessity of the prevalent methods that are more complex and resource-intensive.

Key facts. Cited by 18 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 47 of its 58 references that are in the map. First posted on arXiv 19 Dec 2024.

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47 of 58 references.

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  1. 2022Language Models (Mostly) Know What They Know11 Jul

Other references · 46

  1. 2024The Llama 3 Herd of Modelscited by 14,715
  2. 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,718
  3. 2016SQuAD: 100,000+ Questions for Machine Comprehension of Textcited by 4,148
  4. 2022OPT: Open Pre-trained Transformer Language Modelscited by 3,512
  5. 2014Sequence to Sequence Learning with Neural Networkscited by 2,986
  6. 2017TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehensioncited by 2,955
  7. 2019Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methodscited by 913
  8. 2021Are NLP Models really able to Solve Simple Math Word Problems?cited by 878
  9. 2023Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generationcited by 819
  10. 2023Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedbackcited by 812
  11. 2023SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Modelscited by 810
  12. 2022Teaching Models to Express Their Uncertainty in Wordscited by 751
34 more
  1. 2019Latent Retrieval for Weakly Supervised Open Domain Question Answeringcited by 695
  2. 2018Predictive Uncertainty Estimation via Prior Networkscited by 557
  3. 2024INSIDE: LLMs' Internal States Retain the Power of Hallucination Detectioncited by 323
  4. 2024Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMscited by 259
  5. 2020Reducing conversational agents' overconfidence through linguistic calibrationcited by 210
  6. 2023The Capacity for Moral Self-Correction in Large Language Modelscited by 173
  7. 2023Conformal Language Modelingcited by 170
  8. 2024Fact-Checking the Output of Large Language Models via Token-Level Uncertainty Quantificationcited by 162
  9. 2024Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similaritiescited by 159
  10. 2023LM vs LM: Detecting Factual Errors via Cross Examinationcited by 156
  11. 2023Shifting Attention to Relevance: Towards the Predictive Uncertainty Quantification of Free-Form Large Language Modelscited by 150
  12. 2023LM-Polygraph: Uncertainty Estimation for Language Modelscited by 131
  13. 2023Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthinesscited by 122
  14. 2018Correcting Length Bias in Neural Machine Translationcited by 120
  15. 2024To Believe or Not to Believe Your LLMcited by 120
  16. 2024Benchmarking Uncertainty Quantification Methods for Large Language Models with LM-Polygraphcited by 105
  17. 2021DEUP: Direct Epistemic Uncertainty Predictioncited by 104
  18. 2022Uncertainty Quantification with Pre-trained Language Models: A Large-Scale Empirical Analysiscited by 104
  19. 2023Navigating the Grey Area: How Expressions of Uncertainty and Overconfidence Affect Language Modelscited by 91
  20. 2023Crawling the Internal Knowledge-Base of Language Modelscited by 85
  21. 2023Self-Evaluation Improves Selective Generation in Large Language Modelscited by 76
  22. 2024SPUQ: Perturbation-Based Uncertainty Quantification for Large Language Modelscited by 56
  23. 2024MARS: Meaning-Aware Response Scoring for Uncertainty Estimation in Generative LLMscited by 46
  24. 2024Falcon Mamba: The First Competitive Attention-free 7B Language Modelcited by 46
  25. 2024Improving Uncertainty Estimation through Semantically Diverse Language Generationcited by 35
  26. 2023Quantification of Uncertainty with Adversarial Modelscited by 28
  27. 2023Introducing an Improved Information-Theoretic Measure of Predictive Uncertaintycited by 28
  28. 2024From Risk to Uncertainty: Generating Predictive Uncertainty Measures via Bayesian Estimationcited by 28
  29. 2024Do Not Design, Learn: A Trainable Scoring Function for Uncertainty Estimation in Generative LLMscited by 23
  30. 2024Quantifying Aleatoric and Epistemic Uncertainty with Proper Scoring Rulescited by 21
  31. 2022Uncertainty Estimates of Predictions via a General Bias-Variance Decompositioncited by 20
  32. 2024Probabilities of Chat LLMs Are Miscalibrated but Still Predict Correctness on Multiple-Choice Q&Acited by 16
  33. 2024On Information-Theoretic Measures of Predictive Uncertaintycited by 16
  34. 2024Your Finetuned Large Language Model is Already a Powerful Out-of-distribution Detectorcited by 11

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 11; 2026: 7.

18 papers.

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  1. 2025Uncertainty Quantification for LLMs through Minimum Bayes Risk: Bridging Confidence and Consistencycited by 30
  2. 2025Robust Hallucination Detection in LLMs via Adaptive Token Selectioncited by 19
  3. 2025The Illusion of Certainty: Uncertainty Quantification for LLMs Fails under Ambiguitycited by 17
  4. 2025Efficient Hallucination Detection for LLMs Using Uncertainty-Aware Attention Headscited by 16
  5. 2025Addressing Pitfalls in the Evaluation of Uncertainty Estimation Methods for Natural Language Generationcited by 7
  6. 2025Uncertainty as Feature Gaps: Epistemic Uncertainty Quantification of LLMs in Contextual Question-Answeringcited by 7
  7. 2025SelfReflect: Can LLMs Communicate Their Internal Answer Distribution?cited by 6
  8. 2025Hallucination Detection on a Budget: Efficient Bayesian Estimation of Semantic Entropycited by 5
  9. 2026Semantic Self-Distillation for Language Model Uncertaintycited by 4
  10. 2025Reasoning's Razor: Reasoning Improves Accuracy but Can Hurt Recall at Critical Operating Points in Safety and Hallucination Detectioncited by 3
  11. 2026Know More, Know Clearer: A Meta-Cognitive Framework for Knowledge Augmentation in Large Language Modelscited by 3
  12. 2026Towards Generation-Efficient Uncertainty Estimation in Large Language Modelscited by 2
6 more
  1. 2025Mind the Gap: Benchmarking LLM Uncertainty and Calibration with Specialty-Aware Clinical QA and Reasoning-Based Behavioural Featurescited by 1
  2. 2025Analysis of Image-and-Text Uncertainty Propagation in Multimodal Large Language Models with Cardiac MR-Based Applicationscited by 1
  3. 2026RREDCoT: Segment-Level Reward Redistribution for Reasoning Modelscited by 1
  4. 2026Gradients with Respect to Semantics Preserving Embeddings Tell the Uncertainty of Large Language Modelscited by 0
  5. 2026Building Reliable Long-Form Generation via Hallucination Rejection Samplingcited by 0
  6. 2026TRACE: Single-Pass Decoding-Trace Risk Localization for Generation Calibrationcited by 0

Similar, not cited

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  1. 2024Graph-based Uncertainty Metrics for Long-form Language Model Outputs
  2. 2025Revisiting Uncertainty Estimation and Calibration of Large Language Models
  3. 2026The Origins of Stochasticity: Comprehensive Investigations on Uncertainty Quantification for Large Language Models
  4. 2025Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey
  5. 2026Dissecting Training-Free Uncertainty Estimation in Multimodal Large Language Models
  6. 2024ConU: Conformal Uncertainty in Large Language Models with Correctness Coverage Guarantees
  7. 2024Rethinking the Uncertainty: A Critical Review and Analysis in the Era of Large Language Models
  8. 2025Semantic uncertainty in advanced decoding methods for LLM generation