Title: Generalizable Process Reward Models via Formally Verified Training Data
Primary area: foundation or frontier models, including LLMs
Keywords: large language model, process reward model, reasoning

Abstract: Process Reward Models (PRMs), which provide step-level feedback on reasoning traces generated by Large Language Models (LLMs), are receiving increasing attention. However, two key research gaps remain: creating PRM training data requires costly human annotation to label accurate step-level errors, and existing PRMs are limited to math reasoning domains. In response to these gaps, this paper aims to enable automatic synthesis of accurate PRM training data and the generalization of PRMs to diverse reasoning tasks beyond math reasoning. We propose FoVer, an approach to synthesize PRM training data with accurate step-level error labels automatically annotated by formal verification tools, such as Z3 and Isabelle. To show the practical effectiveness of FoVer, we synthesize a training dataset by annotating step-level error labels on LLM responses to formal logic and theorem proving tasks, without relying on human annotation. While FoVer creates training data with symbolic tasks compatible with formal verification, our experiments show that PRMs trained on our dataset exhibit cross-task generalization, enabling a single PRM to effectively perform verification across diverse reasoning tasks. Specifically, LLM-based PRMs trained with FoVer significantly outperform PRMs based on the original LLMs and achieve competitive or superior results compared to state-of-the-art PRMs, as measured by step-level verification on ProcessBench and Best-of-K performance across 12 reasoning benchmarks, including MATH, AIME, ANLI, MMLU, and BBH. The dataset and code are in the supplementary material and will be made public.

TL;DR: We propose FoVer, a method to create training data for PRMs by using formal verification tools such as Z3 and Isabelle. PRMs trained with FoVer improve performance on diverse reasoning tasks, including MATH, AIME, and MMLU.