Efficient PRM Training Data Synthesis via Formal Verification

[2505.15960] Efficient PRM Training Data Synthesis via Formal Verification Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Computation and Language arXiv:2505.15960 (cs) [Submitted on 21 May 2025 ( v1 ), last revised 8 Apr 2026 (this version, v3)] Title: Efficient PRM Training Data Synthesis via Formal Verification Authors: Ryo Kamoi , Yusen Zhang , Nan Zhang , Sarkar Snigdha Sarathi Das , Ranran Haoran Zhang , Wenpeng Yin , Rui Zhang View a PDF of the paper titled Efficient PRM Training Data Synthesis via Formal Verification, by Ryo Kamoi and 6 other authors View PDF HTML (experimental) 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 this https URL . Comments: ACL 2026 Findings. Datasets, models, and code are provided at this https URL . Please also refer to our project website at this https URL Subjects: Computation and Language (cs.CL) Cite as: arXiv:2505.15960 [cs.CL] (or arXiv:2505.15960v3 [cs.CL] for this version) https://doi.org/10.48550/arXiv.2505.15960 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ryo Kamoi [ view email ] [v1] Wed, 21 May 2025 19:23:45 UTC (632 KB) [v2] Sat, 27 Sep 2025 21:15:03 UTC (730 KB) [v3] Wed, 8 Apr 2026 19:23:50 UTC (704 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient PRM Training Data Synthesis via Formal Verification, by Ryo Kamoi and 6 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.CL < prev | next > new | recent | 2025-05 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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