Beyond Correctness: Harmonizing Process and Outcome Rewards through RL Training

Reinforcement Learning with Verifiable Rewards (RLVR) improves final-answer accuracy on reasoning tasks, but it does not reliably improve reasoning quality. Because outcome rewards only assess final answers, they also reward spurious successes: flawed reasoning can still receive maximal reward when it accidentally reaches the correct outcome. This outcome reward hacking creates biased gradients, making current RLVR insufficient for learning faithful reasoning. Process Reward Models (PRMs) provide step-wise supervision, but directly optimizing PRMs or naively combining them with outcome rewards is unstable under distribution shift during RL training process. We introduce PRocess cOnsistency Filter (PROF), a data curation method that uses PRM--ORM consistency for sample selection rather than direct reward optimization. PROF keeps correct responses with strong process support and incorrect responses with weak process support while maintaining a balanced training ratio. Experiments show that PROF consistently improves both final-answer accuracy and intermediate reasoning quality over strong baselines, with less dependence on strong PRMs.