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

arXiv: https://arxiv.org/abs/2412.15176 · HTML: https://mlsanity.com/paper/2412.15176/

## 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.

## 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 47)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [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)
- [Latent Retrieval for Weakly Supervised Open Domain Question Answering](https://mlsanity.com/paper/1906.00300/) (2019)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Reducing conversational agents' overconfidence through linguistic calibration](https://mlsanity.com/paper/2012.14983/) (2020)
- [The Capacity for Moral Self-Correction in Large Language Models](https://mlsanity.com/paper/2302.07459/) (2023)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [Fact-Checking the Output of Large Language Models via Token-Level Uncertainty Quantification](https://mlsanity.com/paper/2403.04696/) (2024)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [LM vs LM: Detecting Factual Errors via Cross Examination](https://mlsanity.com/paper/2305.13281/) (2023)
- [Shifting Attention to Relevance: Towards the Predictive Uncertainty Quantification of Free-Form Large Language Models](https://mlsanity.com/paper/2307.01379/) (2023)
- [LM-Polygraph: Uncertainty Estimation for Language Models](https://mlsanity.com/paper/2311.07383/) (2023)
- [Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthiness](https://mlsanity.com/paper/2308.16175/) (2023)
- [Correcting Length Bias in Neural Machine Translation](https://mlsanity.com/paper/1808.10006/) (2018)
- [To Believe or Not to Believe Your LLM](https://mlsanity.com/paper/2406.02543/) (2024)
- [Benchmarking Uncertainty Quantification Methods for Large Language Models with LM-Polygraph](https://mlsanity.com/paper/2406.15627/) (2024)
- [DEUP: Direct Epistemic Uncertainty Prediction](https://mlsanity.com/paper/2102.08501/) (2021)

## Built on by (most cited first, 18 of 18)

- [Uncertainty Quantification for LLMs through Minimum Bayes Risk: Bridging Confidence and Consistency](https://mlsanity.com/paper/2502.04964/) (2025)
- [Robust Hallucination Detection in LLMs via Adaptive Token Selection](https://mlsanity.com/paper/2504.07863/) (2025)
- [The Illusion of Certainty: Uncertainty Quantification for LLMs Fails under Ambiguity](https://mlsanity.com/paper/2511.04418/) (2025)
- [Efficient Hallucination Detection for LLMs Using Uncertainty-Aware Attention Heads](https://mlsanity.com/paper/2505.20045/) (2025)
- [Addressing Pitfalls in the Evaluation of Uncertainty Estimation Methods for Natural Language Generation](https://mlsanity.com/paper/2510.02279/) (2025)
- [Uncertainty as Feature Gaps: Epistemic Uncertainty Quantification of LLMs in Contextual Question-Answering](https://mlsanity.com/paper/2510.02671/) (2025)
- [SelfReflect: Can LLMs Communicate Their Internal Answer Distribution?](https://mlsanity.com/paper/2505.20295/) (2025)
- [Hallucination Detection on a Budget: Efficient Bayesian Estimation of Semantic Entropy](https://mlsanity.com/paper/2504.03579/) (2025)
- [Semantic Self-Distillation for Language Model Uncertainty](https://mlsanity.com/paper/2602.04577/) (2026)
- [Reasoning's Razor: Reasoning Improves Accuracy but Can Hurt Recall at Critical Operating Points in Safety and Hallucination Detection](https://mlsanity.com/paper/2510.21049/) (2025)
- [Know More, Know Clearer: A Meta-Cognitive Framework for Knowledge Augmentation in Large Language Models](https://mlsanity.com/paper/2602.12996/) (2026)
- [Towards Generation-Efficient Uncertainty Estimation in Large Language Models](https://mlsanity.com/paper/2605.06053/) (2026)
- [Mind the Gap: Benchmarking LLM Uncertainty and Calibration with Specialty-Aware Clinical QA and Reasoning-Based Behavioural Features](https://mlsanity.com/paper/2506.10769/) (2025)
- [Analysis of Image-and-Text Uncertainty Propagation in Multimodal Large Language Models with Cardiac MR-Based Applications](https://mlsanity.com/paper/2507.12945/) (2025)
- [RREDCoT: Segment-Level Reward Redistribution for Reasoning Models](https://mlsanity.com/paper/2606.06475/) (2026)
- [Gradients with Respect to Semantics Preserving Embeddings Tell the Uncertainty of Large Language Models](https://mlsanity.com/paper/2605.04638/) (2026)
- [Building Reliable Long-Form Generation via Hallucination Rejection Sampling](https://mlsanity.com/paper/2606.03628/) (2026)
- [TRACE: Single-Pass Decoding-Trace Risk Localization for Generation Calibration](https://mlsanity.com/paper/2609.35387/) (2026)

## 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.