Beyond Correctness: Harmonizing Process and Outcome Rewards through RL
  Training
Authors: name: Chenlu Ye, name: Zhou Yu, name: Ziji Zhang, name: Hao Chen, name: Narayanan Sadagopan, name: Jing Huang, name: Tong Zhang, name: Anurag Beniwal

Reinforcement learning with verifiable rewards (RLVR) has emerged to be a
predominant paradigm for mathematical reasoning tasks, offering stable
improvements in reasoning ability. However, Outcome Reward Models (ORMs) in
RLVR are too coarse-grained to distinguish flawed reasoning within correct
answers or valid reasoning within incorrect answers. This lack of granularity
introduces noisy and misleading gradients significantly and hinders further
progress in reasoning process quality. While Process Reward Models (PRMs) offer
fine-grained guidance for intermediate steps, they frequently suffer from
inaccuracies and are susceptible to reward hacking.
  To resolve this dilemma, we introduce PRocess cOnsistency Filter (PROF), an
effective data process curation method that harmonizes noisy, fine-grained
process rewards with accurate, coarse-grained outcome rewards. Rather than
naively blending PRM and ORM in the objective function
(arXiv:archive/2506.18896), PROF leverages their complementary strengths
through consistency-driven sample selection. Our approach retains correct
responses with higher averaged process values and incorrect responses with
lower averaged process values, while maintaining positive/negative training
sample balance. Extensive experiments demonstrate that our method not only
consistently improves the final accuracy over 4% compared to the blending
approaches, but also strengthens the quality of intermediate reasoning steps.
Codes and training recipes are available at https://github.com/Chenluye99/PROF.