JuDi: Revisiting Judge Decoding from First Principles via Training-Free Distributional Divergence

LLM-as-a-judge is now the default measurement instrument for open-ended generation, but on the public JudgeBench benchmark even strong instruction-tuned judges barely scrape past random on objective-correctness pairwise items. We introduce RTLC, a three-stage prompting recipe -- Research, Teach-to-Learn, Critique -- that promotes a single black-box LLM into an ensemble-of-thought judge with no fine-tuning, retrieval, or external tools. Stage 1 wraps the input in a fixed pedagogical scaffold porting the Feynman Learning Technique (study $\to$ teach $\to$ find gaps $\to$ simplify) into LLM prompting. Stage 2 draws N=10 independent candidate verdicts at temperature 0.4. Stage 3 acts as its own critic, cross-comparing the candidate set against the original question to emit one critiqued verdict at temperature 0. On JudgeBench-GPT (350 hard pairwise items), Claude 3.7 Sonnet's pairwise accuracy climbs from 64.6% (single-shot vanilla prompt) to 78.6% (RTLC critique-of-10) -- an absolute 14.0-percentage-point gain. RTLC also beats N=10 self-consistency majority voting (77.7%) and a zero-shot first candidate (74.0%). A clean three-step ablation attributes +9.4 pp to the Teach-to-Learn scaffold, +3.7 pp to N=10 marginalisation, and +0.9 pp to explicit critique. We discuss the cost-accuracy frontier (RTLC sits above self-consistency at every working point), the error-budget breakdown across the four JudgeBench categories (knowledge, reasoning, math, coding), and how RTLC composes orthogonally with post-hoc judge-score calibration, with the two interventions compounding multiplicatively in practice.

Reasoning-capable large language models (LLMs) have recently been adopted as automated judges, but their benefits and costs in LLM-as-a-Judge settings remain unclear. Through controlled comparisons between reasoning and non-reasoning judges, we show that explicit reasoning substantially improves judgment accuracy on tasks requiring structured verification (e.g., math and coding), while offering limited or even negative gains on simpler evaluations and incurring significantly higher computational cost. These findings motivate that reasoning should be used selectively rather than universally, with awareness of possible distribution shift. We propose a Robust Adaptive Cost-Efficient Routing (RACER), which dynamically selects between reasoning and non-reasoning judges under a fixed budget by formulating routing as a constrained distributionally robust optimization problem. RACER explicitly accounts for distribution shift via a KL-divergence uncertainty set, admits an efficient primal--dual algorithm, and enjoys theoretical guarantees including uniqueness of the optimal policy and linear convergence. Extensive experiments show that RACER achieves superior accuracy--cost trade-offs under distribution shift.

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.