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FUSE: Ensembling Verifiers with Zero Labeled Data

ICML 2026 · Large language models › Reasoning and chain of thought · approach: Routing, pruning and distillation for reasoning · 0 citations (OpenAlex)

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Proposes FUSE, an unsupervised method that ensembles LLM verifiers for best-of-N selection by transforming scores to satisfy triplet conditional independence, estimating verifier accuracies via method-of-moments, and fitting a logistic ensemble on pseudo-labels, with no ground-truth labels.

Problem

Selecting correct responses from repeated LLM samples using imperfect verifiers when no ground-truth correctness labels are available; naive averaging or majority vote perform poorly when verifiers differ in quality or are conditionally dependent.

Approach

Adaptively binarize verifier scores by minimizing an empirical triplet conditional independence violation statistic, apply a method-of-moments spectral estimator to recover verifier sensitivities/specificities, average triplet posterior estimates into pseudo-labels, and optimize a logistic-regression ensemble against these pseudo-labels, avoiding the joint conditional independence assumption.

Key results

• On Llama 3.3 70B, FUSE reaches 91.4% on MMLU Pro vs 90.2% for WEAVER and 87.0% for naive ensemble (Best-of-100), and on 8B MATH500 83.9% vs 74.8% for WEAVER.
• On Humanity's Last Exam (649 questions, Best-of-50), FUSE achieves 54.3% vs 52.1% Pass@1 and 53.5% for the oracle best verifier.
• On IMO Shortlist (Best-of-50), FUSE matches naive ensemble at 63.8% and beats WEAVER at 62.1%.

Surprising findings

• Naive ensemble is worse than random single-response selection (Pass@1) on Humanity's Last Exam (51.4% vs 52.1%).
• Under the joint conditional independence assumption, the Jaffe et al. ensemble underperforms a naive ensemble in 7 of 10 settings.

Limitations

• Requires sampling from multiple distinct verifier models, which is computationally cumbersome at inference.
• Performance on IMO Shortlist is matched by naive ensemble, so gains are limited when verifiers are homogeneous.
• Ground-truth extraction relies on an LLM (Qwen3-Next-80B) and partial hand-audit.

Experimental setup

Datasets: GPQA GPQA Diamond MATH500 MMLU MMLU Pro Humanity's Last Exam IMO AnswerBench

Benchmarks: GPQA GPQA Diamond MATH500 MMLU MMLU Pro Humanity's Last Exam IMO AnswerBench IMO Shortlist subset

Metrics: Best-of-N accuracy

Baselines: WEAVER Naive Bayes Logistic Regression Majority Vote Naive Ensemble Pass@1 Oracle Best Verifier

Builds on: Dawid-Skene style crowd-sourcing Jaffe et al. spectral method of moments estimator WEAVER

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