# FUSE: Ensembling Verifiers with Zero Labeled Data

arXiv: https://arxiv.org/abs/2604.18547 · HTML: https://mlsanity.com/paper/2604.18547/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 32 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 24 of 24)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Rubrics as Rewards: Reinforcement Learning Beyond Verifiable Domains](https://mlsanity.com/paper/2507.17746/) (2025)
- [Replacing Judges with Juries: Evaluating LLM Generations with a Panel of Diverse Models](https://mlsanity.com/paper/2404.18796/) (2024)
- [Statistical Rejection Sampling Improves Preference Optimization](https://mlsanity.com/paper/2309.06657/) (2023)
- [Reward Model Ensembles Help Mitigate Overoptimization](https://mlsanity.com/paper/2310.02743/) (2023)
- [Helping or Herding? Reward Model Ensembles Mitigate but do not Eliminate Reward Hacking](https://mlsanity.com/paper/2312.09244/) (2023)
- [Fast Best-of-N Decoding via Speculative Rejection](https://mlsanity.com/paper/2410.20290/) (2024)
- [Towards Robust Mathematical Reasoning](https://mlsanity.com/paper/2511.01846/) (2025)
- [Multi-Agent Verification: Scaling Test-Time Compute with Multiple Verifiers](https://mlsanity.com/paper/2502.20379/) (2025)
- [Sample, Scrutinize and Scale: Effective Inference-Time Search by Scaling Verification](https://mlsanity.com/paper/2502.01839/) (2025)
- [Evaluation of Best-of-N Sampling Strategies for Language Model Alignment](https://mlsanity.com/paper/2502.12668/) (2025)
- [Shrinking the Generation-Verification Gap with Weak Verifiers](https://mlsanity.com/paper/2506.18203/) (2025)
- [Ranking and combining multiple predictors without labeled data](https://mlsanity.com/paper/1303.3257/) (2013)
- [Unsupervised Ensemble Learning with Dependent Classifiers](https://mlsanity.com/paper/1510.05830/) (2015)
- [Estimating the Accuracies of Multiple Classifiers Without Labeled Data](https://mlsanity.com/paper/1407.7644/) (2014)
- [Unsupervised Risk Estimation Using Only Conditional Independence Structure](https://mlsanity.com/paper/1606.05313/) (2016)
- [A Deep Learning Approach to Unsupervised Ensemble Learning](https://mlsanity.com/paper/1602.02285/) (2016)
- [Best-of-Majority: Minimax-Optimal Strategy for Pass@k Inference Scaling](https://mlsanity.com/paper/2510.03199/) (2025)
- [Majority of the Bests: Improving Best-of-N via Bootstrapping](https://mlsanity.com/paper/2511.18630/) (2025)
- [Unsupervised Crowdsourcing with Accuracy and Cost Guarantees](https://mlsanity.com/paper/2207.01988/) (2022)

## Built on by (most cited first, 4 of 4)

- [Agentic Systems as Boosting Weak Reasoning Models](https://mlsanity.com/paper/2605.14163/) (2026)
- [Abductive Corroboration of Probabilistic AI Models for Forensic Synthetic Media Detection](https://mlsanity.com/paper/2607.05434/) (2026)
- [Distilling Directional Verification](https://mlsanity.com/paper/2610.00997/) (2026)
- [Verifier-Harness Co-Evolution for Training-Free Self-Improvement on Open-Ended Tasks](https://mlsanity.com/paper/2610.17609/) (2026)

## Abstract (arXiv)

Verification of model outputs is rapidly emerging as a key primitive for both training and real-world deployment of large language models (LLMs). In practice, this often involves using imperfect LLM judges and reward models since ground truth acquisition can be time-consuming and expensive. We introduce Fully Unsupervised Score Ensembling (FUSE), a method for improving verification quality by ensembling verifiers without access to ground truth correctness labels. The key idea behind FUSE is to control conditional dependencies between verifiers in a manner that improves the unsupervised performance of a class of spectral algorithms from the ensembling literature. Despite requiring zero ground truth labels, FUSE typically matches or improves upon semi-supervised alternatives in test-time scaling experiments with diverse sets of generator models, verifiers, and benchmarks. In particular, we validate our method on both conventional academic benchmarks such as GPQA Diamond and on frontier, unsaturated benchmarks such as Humanity's Last Exam and IMO Shortlist questions.