# VERDI: Single-Call Confidence Estimation for Verification-Based LLM Judges via Decomposed Inference

arXiv: https://arxiv.org/abs/2605.11334 · HTML: https://mlsanity.com/paper/2605.11334/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 24 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 21 of 21)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [SummEval: Re-evaluating Summarization Evaluation](https://mlsanity.com/paper/2007.12626/) (2020)
- [Fact or Fiction: Verifying Scientific Claims](https://mlsanity.com/paper/2004.14974/) (2020)
- [Chain-of-Verification Reduces Hallucination in Large Language Models](https://mlsanity.com/paper/2309.11495/) (2023)
- [JudgeBench: A Benchmark for Evaluating LLM-based Judges](https://mlsanity.com/paper/2410.12784/) (2024)
- [Atla Selene Mini: A General Purpose Evaluation Model](https://mlsanity.com/paper/2501.17195/) (2025)
- [CoT-UQ: Improving Response-wise Uncertainty Quantification in LLMs with Chain-of-Thought](https://mlsanity.com/paper/2502.17214/) (2025)
- [Trace Length is a Simple Uncertainty Signal in Reasoning Models](https://mlsanity.com/paper/2510.10409/) (2025)
- [Overconfidence in LLM-as-a-Judge: Diagnosis and Confidence-Driven Solution](https://mlsanity.com/paper/2508.06225/) (2025)
- [Log Probability Tracking of LLM APIs](https://mlsanity.com/paper/2512.03816/) (2025)
- [Calibrating LLM Judges: Linear Probes for Fast and Reliable Uncertainty Estimation](https://mlsanity.com/paper/2512.22245/) (2025)
- [BaseCal: Unsupervised Confidence Calibration via Base Model Signals](https://mlsanity.com/paper/2601.03042/) (2026)
- [JudgeBoard: Benchmarking and Enhancing Small Language Models for Reasoning Evaluation](https://mlsanity.com/paper/2511.15958/) (2025)

## Abstract (arXiv)

LLM-as-Judge systems are widely deployed for automated evaluation, yet practitioners lack reliable methods to know when a judge's verdict should be trusted. Token log-probabilities, the standard post-hoc confidence signal, are unavailable for many commercial LLMs and, even when accessible, saturate above 0.999 with structured JSON output. We introduce VERDI (VERification-Decomposed Inference), a method that extracts confidence from the reasoning trace a structured judge already produces, with no additional inference calls. VERDI decomposes each verification-style evaluation into sub-checks and derives three structural signals: Step-Verdict Alignment, Claim-Level Margin, and Evidence Grounding Score. We combine them with Platt-scaled logistic regression. On three public benchmarks, VERDI achieves AUROC 0.72-0.91 on GPT-4.1-mini and 0.66-0.80 on GPT-5.4-mini. On Qwen3.5-4B/9B/27B, where answer-token logprobs are anti-calibrated (higher confidence on errors, AUROC 0.32-0.49), VERDI achieves 0.56-0.70. We additionally validate on a production system with eight rubrics (AUROC 0.73-0.88 on factual rubrics), demonstrate cross-model transfer (AUROC 0.66-0.69), and show that a 33M-parameter NLI (Natural Language Inference) model provides a scalable alternative to regex extraction.