# Uncertainty Quantification for LLMs through Minimum Bayes Risk: Bridging Confidence and Consistency

arXiv: https://arxiv.org/abs/2502.04964 · HTML: https://mlsanity.com/paper/2502.04964/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 45 references that are in the map.
- First posted on arXiv 7 Feb 2025.

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

- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Don't Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization](https://mlsanity.com/paper/1808.08745/) (2018)
- [COMET: A Neural Framework for MT Evaluation](https://mlsanity.com/paper/2009.09025/) (2020)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [CoQA: A Conversational Question Answering Challenge](https://mlsanity.com/paper/1808.07042/) (2018)
- [Large Language Models Are State-of-the-Art Evaluators of Translation Quality](https://mlsanity.com/paper/2302.14520/) (2023)
- [Large Language Models for Information Retrieval: A Survey](https://mlsanity.com/paper/2308.07107/) (2023)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [AlignScore: Evaluating Factual Consistency with a Unified Alignment Function](https://mlsanity.com/paper/2305.16739/) (2023)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Unsupervised Quality Estimation for Neural Machine Translation](https://mlsanity.com/paper/2005.10608/) (2020)
- [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)
- [Benchmarking Uncertainty Quantification Methods for Large Language Models with LM-Polygraph](https://mlsanity.com/paper/2406.15627/) (2024)
- [MetricX-24: The Google Submission to the WMT 2024 Metrics Shared Task](https://mlsanity.com/paper/2410.03983/) (2024)
- [Nonparametric Uncertainty Quantification for Single Deterministic Neural Network](https://mlsanity.com/paper/2202.03101/) (2022)
- [Minimum Excess Risk in Bayesian Learning](https://mlsanity.com/paper/2012.14868/) (2020)
- [From Risk to Uncertainty: Generating Predictive Uncertainty Measures via Bayesian Estimation](https://mlsanity.com/paper/2402.10727/) (2024)
- [Rethinking Uncertainty Estimation in LLMs: A Principled Single-Sequence Measure](https://mlsanity.com/paper/2412.15176/) (2024)
- [On Subjective Uncertainty Quantification and Calibration in Natural Language Generation](https://mlsanity.com/paper/2406.05213/) (2024)

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

- [Token-Level Density-Based Uncertainty Quantification Methods for Eliciting Truthfulness of Large Language Models](https://mlsanity.com/paper/2502.14427/) (2025)
- [Uncertainty Quantification for Language Models: A Suite of Black-Box, White-Box, LLM Judge, and Ensemble Scorers](https://mlsanity.com/paper/2504.19254/) (2025)
- [Don't Pass@k: A Bayesian Framework for Large Language Model Evaluation](https://mlsanity.com/paper/2510.04265/) (2025)
- [Towards Agents That Know When They Don't Know: Uncertainty as a Control Signal for Structured Reasoning](https://mlsanity.com/paper/2509.02401/) (2025)
- [EAGer: Entropy-Aware GEneRation for Adaptive Inference-Time Scaling](https://mlsanity.com/paper/2510.11170/) (2025)
- [UQLM: A Python Package for Uncertainty Quantification in Large Language Models](https://mlsanity.com/paper/2507.06196/) (2025)
- [ReDAct: Uncertainty-Aware Deferral for LLM Agents](https://mlsanity.com/paper/2604.07036/) (2026)
- [Calibration-Aware Policy Optimization for Reasoning LLMs](https://mlsanity.com/paper/2604.12632/) (2026)
- [The Alignment Tax: Response Homogenization in Aligned LLMs and Its Implications for Uncertainty Estimation](https://mlsanity.com/paper/2603.24124/) (2026)
- [Towards Label-Free Biological Reasoning Synthetic Dataset Creation via Uncertainty Filtering](https://mlsanity.com/paper/2510.05871/) (2025)
- [Systematic Evaluation of Uncertainty Estimation Methods in Large Language Models](https://mlsanity.com/paper/2510.20460/) (2025)
- [Don't Throw Away Your Beams: Improving Consistency-based Uncertainties in LLMs via Beam Search](https://mlsanity.com/paper/2512.09538/) (2025)
- [Task-Awareness Improves LLM Generations and Uncertainty](https://mlsanity.com/paper/2601.21500/) (2026)
- [Functional Entropy: Predicting Functional Correctness in LLM-Generated Code with Uncertainty Quantification](https://mlsanity.com/paper/2605.28500/) (2026)
- [Towards Generation-Efficient Uncertainty Estimation in Large Language Models](https://mlsanity.com/paper/2605.06053/) (2026)
- [Hallucination as Commitment Failure: Larger LLMs Misfire Despite Knowing the Answer](https://mlsanity.com/paper/2605.22007/) (2026)
- [Uncertainty Quantification for Computer-Use Agents: A Benchmark across Vision-Language Models and GUI Grounding Datasets](https://mlsanity.com/paper/2606.25760/) (2026)
- [Multidimensional Uncertainty Quantification via Optimal Transport](https://mlsanity.com/paper/2509.22380/) (2025)
- [MADE: A Living Benchmark for Multi-Label Text Classification with Uncertainty Quantification of Medical Device Adverse Events](https://mlsanity.com/paper/2604.15203/) (2026)
- [HIVE: Hidden-Evidence Verification for Hallucination Detection in Diffusion Large Language Models](https://mlsanity.com/paper/2604.26139/) (2026)
- [Failing to See or Failing to Know? Attributing Errors in Vision-Language Models](https://mlsanity.com/paper/2607.04683/) (2026)
- [SABER: Stability-Aware Early Exit for LLM Reasoning via Adversarial Branch Probing](https://mlsanity.com/paper/2608.27963/) (2026)
- [Estimating the Black-box LLM Uncertainty with Distribution-Aligned Adversarial Distillation](https://mlsanity.com/paper/2605.05777/) (2026)
- [Uncertainty Quantification for Large Language Diffusion Models](https://mlsanity.com/paper/2605.14570/) (2026)
- [Position: Uncertainty Quantification in LLMs is Just Unsupervised Clustering](https://mlsanity.com/paper/2605.19220/) (2026)
- [How Do Uncertainty Estimators Align with Hallucination Occurrence in LLMs?](https://mlsanity.com/paper/2605.27016/) (2026)
- [Localizing Input Uncertainty Quantification for Large Language Models via Shapley Values](https://mlsanity.com/paper/2605.28170/) (2026)
- [The Role of Ambiguity in Error Prediction via Uncertainty Quantification](https://mlsanity.com/paper/2606.02093/) (2026)
- [When Do Supervised UQ Ensembles Improve LLM Hallucination Detection? A Robustness Study](https://mlsanity.com/paper/2608.24492/) (2026)
- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)

## Abstract (arXiv)

Uncertainty quantification (UQ) methods for Large Language Models (LLMs) encompass a variety of approaches, with two major types being particularly prominent: information-based, which focus on model confidence expressed as token probabilities, and consistency-based, which assess the semantic relationship between multiple outputs generated using repeated sampling. Several recent methods have combined these two approaches to boost UQ performance. However, they sometimes fail to outperform much simpler baseline methods. Our work discusses the fundamental approach to constructing uncertainty measures that directly links uncertainty with the minimum Bayes risks achieved by LLM decoding. Building on these findings, we propose a novel approach to integrating model confidence with output consistency, resulting in a family of efficient and robust UQ methods. Our investigation reveals distinctive characteristics of LLMs as probabilistic models, which help to explain why these UQ methods underperform in certain tasks. Based on these findings, we propose a new way of synthesizing model confidence and output consistency, leading to a family of efficient and robust UQ methods. We evaluate our approach across various tasks such as question answering, abstractive summarization, and machine translation, demonstrating sizable improvements over state-of-the-art UQ approaches.