# Uncertainty Quantification for Language Models: A Suite of Black-Box, White-Box, LLM Judge, and Ensemble Scorers

arXiv: https://arxiv.org/abs/2504.19254 · HTML: https://mlsanity.com/paper/2504.19254/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 62 references that are in the map.
- First posted on arXiv 27 Apr 2025.

## Builds on (most cited first, 30 of 47)

- [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)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [BLEURT: Learning Robust Metrics for Text Generation](https://mlsanity.com/paper/2004.04696/) (2020)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [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)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [BARTScore: Evaluating Generated Text as Text Generation](https://mlsanity.com/paper/2106.11520/) (2021)
- [Latent Retrieval for Weakly Supervised Open Domain Question Answering](https://mlsanity.com/paper/1906.00300/) (2019)
- [DecodingTrust: A Comprehensive Assessment of Trustworthiness in GPT Models](https://mlsanity.com/paper/2306.11698/) (2023)
- [A Survey on Hallucination in Large Vision-Language Models](https://mlsanity.com/paper/2402.00253/) (2024)
- [Replacing Judges with Juries: Evaluating LLM Generations with a Panel of Diverse Models](https://mlsanity.com/paper/2404.18796/) (2024)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [A Comprehensive Survey of Hallucination Mitigation Techniques in Large Language Models](https://mlsanity.com/paper/2401.01313/) (2024)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [A Stitch in Time Saves Nine: Detecting and Mitigating Hallucinations of LLMs by Validating Low-Confidence Generation](https://mlsanity.com/paper/2307.03987/) (2023)
- [Benchmarking Foundation Models with Language-Model-as-an-Examiner](https://mlsanity.com/paper/2306.04181/) (2023)
- [Generative Judge for Evaluating Alignment](https://mlsanity.com/paper/2310.05470/) (2023)
- [Fact-Checking the Output of Large Language Models via Token-Level Uncertainty Quantification](https://mlsanity.com/paper/2403.04696/) (2024)
- [LM vs LM: Detecting Factual Errors via Cross Examination](https://mlsanity.com/paper/2305.13281/) (2023)
- [LLaVA-Critic: Learning to Evaluate Multimodal Models](https://mlsanity.com/paper/2410.02712/) (2024)
- [Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthiness](https://mlsanity.com/paper/2308.16175/) (2023)

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

- [UQLM: A Python Package for Uncertainty Quantification in Large Language Models](https://mlsanity.com/paper/2507.06196/) (2025)
- [QA-Dragon: Query-Aware Dynamic RAG System for Knowledge-Intensive Visual Question Answering](https://mlsanity.com/paper/2508.05197/) (2025)
- [Verbalizing LLM's Higher-order Uncertainty via Imprecise Probabilities](https://mlsanity.com/paper/2603.10396/) (2026)
- [Fine-Grained Uncertainty Quantification for Long-Form Language Model Outputs: A Comparative Study](https://mlsanity.com/paper/2602.17431/) (2026)
- [Is Escalation Worth It? On the Depth of LLM Cascades](https://mlsanity.com/paper/2605.06350/) (2026)
- [Functional Entropy: Predicting Functional Correctness in LLM-Generated Code with Uncertainty Quantification](https://mlsanity.com/paper/2605.28500/) (2026)
- [Entropy Sentinel: Probing Entropy Traces for LLM Monitoring](https://mlsanity.com/paper/2601.09001/) (2026)
- [A Systematic Evaluation of Black-Box Uncertainty Estimation Methods for Large Language Models](https://mlsanity.com/paper/2606.19868/) (2026)
- [Two Pathways to Truthfulness: On the Intrinsic Encoding of LLM Hallucinations](https://mlsanity.com/paper/2601.07422/) (2026)
- [Zero-Shot Confidence Estimation for Small LLMs: When Supervised Baselines Aren't Worth Training](https://mlsanity.com/paper/2605.02241/) (2026)
- [Hallucination Mitigation with Agentic AI, Nested Learning, and AI Sustainability via Semantic Caching](https://mlsanity.com/paper/2605.29055/) (2026)
- [Beyond Single-Turn Confidence: Trajectory-Adapted Uncertainty Quantification for LLM Agents](https://mlsanity.com/paper/2608.11552/) (2026)
- [Echo-CoPilot: A Multiple-Perspective Agentic Framework for Reliable Echocardiography Interpretation](https://mlsanity.com/paper/2512.09944/) (2025)
- [DECK: A Consistency x Confidence Taxonomy of LLM Hallucinations](https://mlsanity.com/paper/2606.02289/) (2026)
- [When Do Supervised UQ Ensembles Improve LLM Hallucination Detection? A Robustness Study](https://mlsanity.com/paper/2608.24492/) (2026)
- [Certified Against Which Oracle? Execution Labels Set the Reported Risk of Conformal Abstention for Text-to-SQL](https://mlsanity.com/paper/2609.25938/) (2026)
- [Conformal Prediction with Paraphrase-Aware Scoring for LLM Uncertainty Quantification](https://mlsanity.com/paper/2610.04239/) (2026)
- [One-Sided Verification Under Limited Expert Review](https://mlsanity.com/paper/2610.18089/) (2026)

## Abstract (arXiv)

Hallucinations are a persistent problem with Large Language Models (LLMs). As these models become increasingly used in high-stakes domains, such as healthcare and finance, the need for effective hallucination detection is crucial. To this end, we outline a versatile framework for closed-book hallucination detection that practitioners can apply to real-world use cases. To achieve this, we adapt a variety of existing uncertainty quantification (UQ) techniques, including black-box UQ, white-box UQ, and LLM-as-a-Judge, transforming them as necessary into standardized response-level confidence scores ranging from 0 to 1. To enhance flexibility, we propose a tunable ensemble approach that incorporates any combination of the individual confidence scores. This approach enables practitioners to optimize the ensemble for a specific use case for improved performance. To streamline implementation, the full suite of scorers is offered in this paper's companion Python toolkit, UQLM. To evaluate the performance of the various scorers, we conduct an extensive set of experiments using several LLM question-answering benchmarks. We find that our tunable ensemble typically surpasses its individual components and outperforms existing hallucination detection methods. Our results demonstrate the benefits of customized hallucination detection strategies for improving the accuracy and reliability of LLMs.