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The paper introduces Implicit Prefix-Value Reward Models (IPVRM) to address the train-inference mismatch in implicit process reward models, where token-level scores are unreliable due to weak identification of token-level credits. IPVRM learns a prefix-conditioned value function estimating the probability of eventual correctness and derives step signals via temporal-difference differences, improving step-verification F1 on ProcessBench. By pairing IPVRM with Distribution-Level RL (DistRL), which computes TD advantages for both sampled and high-probability candidate tokens, the authors demonstrate consistent improvements in downstream reasoning.
Implicit reward models can now more accurately pinpoint correct reasoning steps, thanks to a novel prefix-value learning approach that closes the train-inference gap.
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.
