From mathematical reasoning to code: Generalization of process reward models in test-time scaling

Analysis

Why This Paper Matters

Process Reward Models (PRMs) have emerged as a powerful technique for improving the reasoning capabilities of Large Language Models (LLMs) by providing step-by-step feedback during problem-solving. However, most existing work has focused on mathematical reasoning, leaving open the question of whether PRMs can generalize to other domains. This paper addresses that gap by demonstrating that PRMs trained on mathematical reasoning can effectively transfer to code generation, a domain that shares structural similarities with math but also presents unique challenges. The findings are significant because they suggest that process supervision is not domain-specific but can be leveraged across tasks, potentially reducing the need for costly domain-specific reward models.

Moreover, the paper situates its contributions within the context of test-time scaling, a paradigm where additional computation is allocated during inference to improve model outputs. By showing that PRMs enhance reasoning in this setting, the work highlights a practical pathway for deploying LLMs in complex, multi-step tasks without retraining. This is particularly relevant for AI practitioners who seek to improve model performance on code-related tasks, where correctness and logical coherence are paramount.

Technical Contributions

• Cross-Domain Generalization of PRMs: The paper demonstrates that PRMs trained on mathematical reasoning data can be directly applied to code generation, achieving significant improvements without domain-specific fine-tuning.
• Test-Time Scaling with PRMs: It integrates PRMs into a test-time scaling framework, where the reward model guides the search or verification process during inference, leading to better reasoning outcomes.
• Empirical Validation Across Domains: The authors provide evidence that PRMs enhance LLM reasoning not only in math but also in code, suggesting broader applicability.
• Potential for Unified Reward Modeling: The work hints at the possibility of developing a single PRM that generalizes across multiple reasoning domains, simplifying deployment.

Results

The abstract reports that PRMs significantly enhance LLM reasoning capabilities across diverse domains, particularly when generalizing from math to code. While specific metrics are not provided in the abstract, the qualitative claim is that the improvement is substantial. This aligns with prior findings that process supervision yields better performance than outcome-based rewards in complex reasoning tasks. The paper likely presents comparisons showing that PRM-guided test-time scaling outperforms baseline methods such as majority voting or outcome reward models. However, without concrete numbers, the exact magnitude of improvement remains unclear.

Significance

This research has several important implications. First, it validates the idea that process supervision can be domain-agnostic, which could lead to more efficient development of reward models. Second, it strengthens the case for test-time scaling as a viable strategy for improving LLM reasoning without additional training. Third, it opens avenues for applying PRMs to other structured domains such as theorem proving, planning, and scientific discovery. For practitioners, the findings suggest that investing in high-quality process annotations for math can pay off across multiple applications. Overall, the paper contributes to the growing body of work on aligning LLMs with human reasoning processes and enhancing their reliability in critical tasks.