SCAN: Self-Denoising Monte Carlo Annotation for Robust Process Reward Learning

Process reward models (PRMs) offer fine-grained, step-level evaluations that facilitate deeper reasoning processes in large language models (LLMs), proving effective in complex tasks like mathematical reasoning. However, developing PRMs is challenging due to the high cost and limited scalability of human-annotated data. Synthetic data from Monte Carlo (MC) estimation is a promising alternative but suffers from a high noise ratio, which can cause overfitting and hinder large-scale training. In this work, we conduct a preliminary study on the noise distribution in synthetic data from MC estimation, identifying that annotation models tend to both underestimate and overestimate step correctness due to limitations in their annotation capabilities. Building on these insights, we propose {\bf S}elf-Denoising Monte {\bf C}arlo {\bf An}notation (\textsc{Scan}), an efficient data synthesis and noise-tolerant learning framework. Our key findings indicate that: (1) Even lightweight models (e.g., 1.5B parameters) can produce high-quality annotations through self-denoising strategy, enabling PRMs to achieve superior performance with only 6\% the inference cost required by vanilla MC estimation. (2) With our robust learning strategy, PRMs can effectively learn from this weak supervision, achieving a 39.2 F1 score improvement (from 19.9 to 59.1) in ProcessBench. Despite using only a compact synthetic dataset, our models surpass strong baselines, including those trained on large-scale human-annotated datasets such as PRM800K. Furthermore, performance continues to improve as we scale up the synthetic data, highlighting the potential of \textsc{Scan} for scalable, cost-efficient, and robust PRM training.