arXiv Machine Learning By Zhongjian Qiao, Zhixiang Zhou, Jiafei Lyu, Peisong Wang, Qiaosheng Zhang, Siyang Gao, Shuang Qiu

Process Reward Modeling with Reliability- and Conservatism-Aware Bayesian Belief

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Process Reward Models (PRMs) are crucial for scaling large language model reasoning at test time, but they suffer from two types of uncertainty: PRM uncertainty from limited supervision and imperfect training, and policy uncertainty from mismatched data collection policies. The paper introduces BayesianPRM, which treats process rewards as random variables, discretizes the reward space with an ensemble, and applies two belief updates—reliability‑aware updating for PRM uncertainty and conservatism‑aware calibration for policy uncertainty—to form a Bayesian belief whose expectation yields a more accurate reward estimate. Experiments on multimodal reasoning benchmarks show that BayesianPRM improves reward accuracy and test‑time scaling performance.

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