@inproceedings{kamoi-etal-2026-efficient,
title = "Efficient {PRM} Training Data Synthesis via Formal Verification",
author = "Kamoi, Ryo and
Zhang, Yusen and
Zhang, Nan and
Das, Sarkar Snigdha Sarathi and
Zhang, Ranran Haoran and
Yin, Wenpeng and
Zhang, Rui",
editor = "Liakata, Maria and
Moreira, Viviane P. and
Zhang, Jiajun and
Jurgens, David",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
month = jul,
year = "2026",
address = "San Diego, California, United States",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-acl.403/",
pages = "8246--8265",
ISBN = "979-8-89176-395-1",
abstract = "Process Reward Models (PRMs) have emerged as a promising approach for improving LLM reasoning capabilities by providing process supervision over reasoning traces. However, existing approaches for constructing PRM training data remain costly and noisy, as they typically rely on human annotation or sampling-based labeling methods that require repeated LLM calls. In this work, we propose FoVer, a framework that synthesizes PRM training data from formal reasoning tasks by annotating step-level error labels using formal verification tools such as Z3 and Isabelle. By leveraging formal verification, FoVer enables efficient and accurate PRM data construction without requiring human annotation or additional LLM calls. Using FoVer, we create PRM training data from formal logic and theorem proving tasks. Experiments on 12 reasoning benchmarks show that fine-tuning on our training data improves PRMs not only on math and logic reasoning tasks, which are informal variants of the training tasks, but also on NLI and BBH benchmarks, which differ substantially from the tasks used to construct the training data. These results demonstrate the practical effectiveness of FoVer, showing that PRM training data created using formal verification improves PRMs on informal reasoning tasks written in natural language. The datasets, models, and code are provided at https://github.com/psunlpgroup/FoVer."
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<abstract>Process Reward Models (PRMs) have emerged as a promising approach for improving LLM reasoning capabilities by providing process supervision over reasoning traces. However, existing approaches for constructing PRM training data remain costly and noisy, as they typically rely on human annotation or sampling-based labeling methods that require repeated LLM calls. In this work, we propose FoVer, a framework that synthesizes PRM training data from formal reasoning tasks by annotating step-level error labels using formal verification tools such as Z3 and Isabelle. By leveraging formal verification, FoVer enables efficient and accurate PRM data construction without requiring human annotation or additional LLM calls. Using FoVer, we create PRM training data from formal logic and theorem proving tasks. Experiments on 12 reasoning benchmarks show that fine-tuning on our training data improves PRMs not only on math and logic reasoning tasks, which are informal variants of the training tasks, but also on NLI and BBH benchmarks, which differ substantially from the tasks used to construct the training data. These results demonstrate the practical effectiveness of FoVer, showing that PRM training data created using formal verification improves PRMs on informal reasoning tasks written in natural language. The datasets, models, and code are provided at https://github.com/psunlpgroup/FoVer.</abstract>
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%0 Conference Proceedings
%T Efficient PRM Training Data Synthesis via Formal Verification
%A Kamoi, Ryo
%A Zhang, Yusen
%A Zhang, Nan
%A Das, Sarkar Snigdha Sarathi
%A Zhang, Ranran Haoran
%A Yin, Wenpeng
%A Zhang, Rui
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Findings of the Association for Computational Linguistics: ACL 2026
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-395-1
%F kamoi-etal-2026-efficient
%X Process Reward Models (PRMs) have emerged as a promising approach for improving LLM reasoning capabilities by providing process supervision over reasoning traces. However, existing approaches for constructing PRM training data remain costly and noisy, as they typically rely on human annotation or sampling-based labeling methods that require repeated LLM calls. In this work, we propose FoVer, a framework that synthesizes PRM training data from formal reasoning tasks by annotating step-level error labels using formal verification tools such as Z3 and Isabelle. By leveraging formal verification, FoVer enables efficient and accurate PRM data construction without requiring human annotation or additional LLM calls. Using FoVer, we create PRM training data from formal logic and theorem proving tasks. Experiments on 12 reasoning benchmarks show that fine-tuning on our training data improves PRMs not only on math and logic reasoning tasks, which are informal variants of the training tasks, but also on NLI and BBH benchmarks, which differ substantially from the tasks used to construct the training data. These results demonstrate the practical effectiveness of FoVer, showing that PRM training data created using formal verification improves PRMs on informal reasoning tasks written in natural language. The datasets, models, and code are provided at https://github.com/psunlpgroup/FoVer.
%U https://aclanthology.org/2026.findings-acl.403/
%P 8246-8265
Markdown (Informal)
[Efficient PRM Training Data Synthesis via Formal Verification](https://aclanthology.org/2026.findings-acl.403/) (Kamoi et al., Findings 2026)
ACL
- Ryo Kamoi, Yusen Zhang, Nan Zhang, Sarkar Snigdha Sarathi Das, Ranran Haoran Zhang, Wenpeng Yin, and Rui Zhang. 2026. Efficient PRM Training Data Synthesis via Formal Verification. In Findings of the Association for Computational Linguistics: ACL 2026, pages 8246–8265, San Diego, California, United States. Association for Computational Linguistics.