# Analyzing Uncertainty of LLM-as-a-Judge: Interval Evaluations with Conformal Prediction

arXiv: https://arxiv.org/abs/2509.18658 · HTML: https://mlsanity.com/paper/2509.18658/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 74 references that are in the map.
- First posted on arXiv 23 Sep 2025.

## Builds on (most cited first, 30 of 50)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [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)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [SummEval: Re-evaluating Summarization Evaluation](https://mlsanity.com/paper/2007.12626/) (2020)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [e-SNLI: Natural Language Inference with Natural Language Explanations](https://mlsanity.com/paper/1812.01193/) (2018)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [ROSCOE: A Suite of Metrics for Scoring Step-by-Step Reasoning](https://mlsanity.com/paper/2212.07919/) (2022)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [Conformal Prediction with Large Language Models for Multi-Choice Question Answering](https://mlsanity.com/paper/2305.18404/) (2023)
- [A Note on Shumailov et al. (2024): `AI Models Collapse When Trained on Recursively Generated Data'](https://mlsanity.com/paper/2410.12954/) (2024)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [SaySelf: Teaching LLMs to Express Confidence with Self-Reflective Rationales](https://mlsanity.com/paper/2405.20974/) (2024)
- [Trust or Escalate: LLM Judges with Provable Guarantees for Human Agreement](https://mlsanity.com/paper/2407.18370/) (2024)
- [Can Large Language Models Faithfully Express Their Intrinsic Uncertainty in Words?](https://mlsanity.com/paper/2405.16908/) (2024)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [A comparison of some conformal quantile regression methods](https://mlsanity.com/paper/1909.05433/) (2019)
- [API Is Enough: Conformal Prediction for Large Language Models Without Logit-Access](https://mlsanity.com/paper/2403.01216/) (2024)
- [ConU: Conformal Uncertainty in Large Language Models with Correctness Coverage Guarantees](https://mlsanity.com/paper/2407.00499/) (2024)
- [Can You Trust LLM Judgments? Reliability of LLM-as-a-Judge](https://mlsanity.com/paper/2412.12509/) (2024)
- [Conformal Prediction for Natural Language Processing: A Survey](https://mlsanity.com/paper/2405.01976/) (2024)
- [Calibrating the Confidence of Large Language Models by Eliciting Fidelity](https://mlsanity.com/paper/2404.02655/) (2024)
- [RocketEval: Efficient Automated LLM Evaluation via Grading Checklist](https://mlsanity.com/paper/2503.05142/) (2025)

## Built on by (most cited first, 27 of 27)

- [WebCoderBench: Benchmarking Web Application Generation with Comprehensive and Interpretable Evaluation Metrics](https://mlsanity.com/paper/2601.02430/) (2026)
- [Diagnosing the Reliability of LLM-as-a-Judge via Item Response Theory](https://mlsanity.com/paper/2602.00521/) (2026)
- [VLM Judges Can Rank but Cannot Score: Task-Dependent Uncertainty in Multimodal Evaluation](https://mlsanity.com/paper/2604.25235/) (2026)
- [Adaptive Stopping for Multi-Turn LLM Reasoning](https://mlsanity.com/paper/2604.01413/) (2026)
- [Geometry-Calibrated Conformal Abstention for Language Models](https://mlsanity.com/paper/2604.27914/) (2026)
- [URAG: A Benchmark for Uncertainty Quantification in Retrieval-Augmented Large Language Models](https://mlsanity.com/paper/2603.19281/) (2026)
- [Beyond LLM-as-a-Judge: Deterministic Metrics for Multilingual Generative Text Evaluation](https://mlsanity.com/paper/2604.05083/) (2026)
- [Label Effects: Shared Heuristic Reliance in Trust Assessment by Humans and LLM-as-a-Judge](https://mlsanity.com/paper/2604.05593/) (2026)
- [From Actions to Understanding: Conformal Interpretability of Temporal Concepts in LLM Agents](https://mlsanity.com/paper/2604.19775/) (2026)
- [Robust Uncertainty Quantification for Self-Evolving Large Language Models via Continual Domain Pretraining](https://mlsanity.com/paper/2510.22931/) (2025)
- [A Finite-Calibration Regime Map for LLM Judge Panels](https://mlsanity.com/paper/2606.01034/) (2026)
- [From Uncertain Judgments to Calibrated Rankings: Conformal Elo Estimation for LLM Evaluation](https://mlsanity.com/paper/2606.13221/) (2026)
- [Towards Provably Unbiased LLM Judges via Bias-Bounded Evaluation](https://mlsanity.com/paper/2603.05485/) (2026)
- [PaperJury: Due-Process Review for Bounded LaTeX Revision](https://mlsanity.com/paper/2606.16322/) (2026)
- [Multimodal Learning on Low-Quality Data with Conformal Predictive Self-Calibration](https://mlsanity.com/paper/2605.03820/) (2026)
- [An Interpretable and Scalable Framework for Evaluating Large Language Models](https://mlsanity.com/paper/2605.07046/) (2026)
- [The Ghost Annotator: a Framework to Explore Human Label Variation in Content Moderation through Conformal Prediction](https://mlsanity.com/paper/2606.02911/) (2026)
- [Data-Centric Benchmarking of Exploit Generation in LLMs: Understanding the Impact of Fine-Tuning](https://mlsanity.com/paper/2606.15123/) (2026)
- [Judgment-Grounded Expansion for Peer Review Generation](https://mlsanity.com/paper/2606.23233/) (2026)
- [When Trust Meets Truth: Trust-Truth Separability in LLM-as-Judge](https://mlsanity.com/paper/2608.21097/) (2026)
- [Robust Conformal Consensus: Multi-Agent LLM-as-a-Judge Interval Evaluation with Conformal Prediction](https://mlsanity.com/paper/2609.06367/) (2026)
- [Decomposing LLM-Judge Uncertainty to Target Expert Labels](https://mlsanity.com/paper/2609.06444/) (2026)
- [Optimizing the Score, Losing Sight of the Task: Reward Hacking Across Weights, Selection, and Prompts](https://mlsanity.com/paper/2609.25848/) (2026)
- [When Accuracy Gaps Fail to Certify: Auditing Cross-Domain Recalibration of LLM Judges](https://mlsanity.com/paper/2609.27954/) (2026)
- [CS-WCP: Robust Conformal Sets for LLM-Judge Traffic Shifts with Uncertain Group Proportions](https://mlsanity.com/paper/2609.27955/) (2026)
- [Range-GRPO: Policy Optimization via Pairwise Relations among Reward Intervals](https://mlsanity.com/paper/2610.01548/) (2026)
- [Reliable Self-Evolution with Imperfect Proxy Rewards](https://mlsanity.com/paper/2610.02975/) (2026)

## Abstract (arXiv)

LLM-as-a-judge has become a promising paradigm for using large language models (LLMs) to evaluate natural language generation (NLG), but the uncertainty of its evaluation remains underexplored. This lack of reliability may limit its deployment in many applications. This work presents the first framework to analyze the uncertainty by offering a prediction interval of LLM-based scoring via conformal prediction. Conformal prediction constructs continuous prediction intervals from a single evaluation run, and we design an ordinal boundary adjustment for discrete rating tasks. We also suggest a midpoint-based score within the interval as a low-bias alternative to raw model score and weighted average. We perform extensive experiments and analysis, which show that conformal prediction can provide valid prediction interval with coverage guarantees. We also explore the usefulness of interval midpoint and judge reprompting for better judgment.