# Online Verification of Language Model Responses Under Cost Constraints

arXiv: https://arxiv.org/abs/2610.02632 · HTML: https://mlsanity.com/paper/2610.02632/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 29 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 17 of 17)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [Consistent Estimators for Learning to Defer to an Expert](https://mlsanity.com/paper/2006.01862/) (2020)
- [MiniCheck: Efficient Fact-Checking of LLMs on Grounding Documents](https://mlsanity.com/paper/2404.10774/) (2024)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [Differentiable Learning Under Triage](https://mlsanity.com/paper/2103.08902/) (2021)
- [Who Should Predict? Exact Algorithms For Learning to Defer to Humans](https://mlsanity.com/paper/2301.06197/) (2023)
- [Calibrated Learning to Defer with One-vs-All Classifiers](https://mlsanity.com/paper/2202.03673/) (2022)
- [Shrinking the Generation-Verification Gap with Weak Verifiers](https://mlsanity.com/paper/2506.18203/) (2025)
- [Online Selective Classification with Limited Feedback](https://mlsanity.com/paper/2110.14243/) (2021)
- [When to Trust the Cheap Check: Weak and Strong Verification for Reasoning](https://mlsanity.com/paper/2602.17633/) (2026)

## Abstract (arXiv)

As large language models are increasingly deployed for multi-step reasoning, verifying the correctness of their outputs has become essential for maintaining reliability at scale. Verifying the correctness of large language model outputs is often done by querying a costly ground-truth oracle, which is impractical to invoke at every step in an online setting. Prior work addresses this by querying a single weak verifier on every step, and using its score to decide whether the costly strong verifier needs to be queried as well, reserving strong verification for only a small fraction of the steps. However, a single fixed weak verifier may not perform consistently well as the subject matter or difficulty of incoming queries changes over time, and committing to one in advance risks either overly costly or inaccurate verification. We introduce OMVV (Online Multi-Verifier Verification), an algorithm that maintains a pool of K candidate weak verifiers with differing cost and verification performance, and adaptively routes each round's decision to a verifier selected via an online score combiner and an exponential-weights routing policy. OMVV provides a distribution-free, finite-time guarantee on false-accept and false-reject rates across the full pool of verifiers, and further achieves sublinear regret against the best fixed verifier in hindsight under a combined cost and consistency objective. Experiments on reasoning dataset benchmarks show that OMVV achieves higher accuracy at lower verification cost than any single fixed verifier, across a range of operating budgets.