Shang Gao

Shiping Gao, Hongzhan Chen, Xiaojun Quan et al.

Process reward models (PRMs) provide fine-grained reward signals along the reasoning process, but training reliable PRMs often requires step annotations or heavy verification pipelines, making them expensive to scale and refresh during online RL. Implicit PRMs mitigate this cost by learning decomposable token- or step-level rewards from trajectory-level outcome labels. However, they suffer from a train-inference mismatch: training only constrains a sequence-level aggregate, whereas inference requires token-level scores to reflect local step quality. As a result, token-level credits are weakly identified and may fail to faithfully reflect which reasoning steps are actually correct. This unreliability undermines a key promise of implicit PRMs: scoring many candidate tokens. In practice, noisy per-token advantages may systematically reinforce incorrect continuations. We address this problem with a novel Implicit Prefix-Value Reward Model (IPVRM), which directly learns a prefix-conditioned value function estimating the probability of eventual correctness, and derives step signals via temporal-difference (TD) differences. IPVRM substantially improves step-verification F1 on ProcessBench. Building on these calibrated prefix values, we further propose Distribution-Level RL (DistRL), which computes TD advantages for both sampled tokens and high-probability candidate tokens, enabling dense counterfactual updates without additional rollouts. While DistRL offers limited gains when powered by miscalibrated implicit rewards, it consistently improves downstream reasoning once paired with IPVRM.

Hongzhan Chen, Tao Yang, Shiping Gao et al.

Process reward models (PRMs) provide more nuanced supervision compared to outcome reward models (ORMs) for optimizing policy models, positioning them as a promising approach to enhancing the capabilities of LLMs in complex reasoning tasks. Recent efforts have advanced PRMs from step-level to token-level granularity by integrating reward modeling into the training of generative models, with reward scores derived from token generation probabilities. However, the conflict between generative language modeling and reward modeling may introduce instability and lead to inaccurate credit assignments. To address this challenge, we revisit token-level reward assignment by decoupling reward modeling from language generation and derive a token-level reward model through the optimization of a discriminative policy, termed the Q-function Reward Model (Q-RM). We theoretically demonstrate that Q-RM explicitly learns token-level Q-functions from preference data without relying on fine-grained annotations. In our experiments, Q-RM consistently outperforms all baseline methods across various benchmarks. For example, when integrated into PPO/REINFORCE algorithms, Q-RM enhances the average Pass@1 score by 5.85/4.70 points on mathematical reasoning tasks compared to the ORM baseline, and by 4.56/5.73 points compared to the token-level PRM counterpart. Moreover, reinforcement learning with Q-RM significantly enhances training efficiency, achieving convergence 12 times faster than ORM on GSM8K and 11 times faster than step-level PRM on MATH. Code and data are available at https://github.com/homzer/Q-RM.