VeriBound: PAC-Bayesian Generalization Bounds for Process Reward Models Trained with Formal Verification Tools

The article introduces VeriBound, a theoretical framework providing PAC-Bayesian generalization bounds for Process Reward Models (PRMs) trained using formal verification tools like Z3 and Isabelle. Key results include a generalization bound linking empirical verification error to expected error on unseen tasks, a sample complexity result indicating that \(O(d \log(d/\delta) / \epsilon^2)\) examples are sufficient for a given generalization error, and a convergence analysis proving linear convergence under specific conditions. This framework is significant for practitioners as it offers a theoretical foundation for understanding and improving the training efficiency and performance reliability of PRMs in LLM applications.