Process reward models (PRMs) enhance the reasoning capabilities of large language models (LLMs) by providing fine-grained feedback, yet training PRMs typically requires expensive stepwise annotations. Outcome-supervised PRMs offer a scalable alternative by learning from final-answer correctness alone, but this introduces a fundamental credit assignment challenge, i.e., attributing outcomes to responsible reasoning steps. Existing approaches rely on either uniform or causal assignment, both of which fail to anchor credit in step correctness and thus hinder process error identification. In this work, we propose Outcome-Supervised Process Reward Modeling via Learnable Credit Assignment (LCA), an outcome-supervised PRM framework that jointly learns credit assignment and reward modeling under the principle of Weakest Link Assignment: a reasoning chain is as strong as its weakest link. To address mutual dependence between credit assignment and reward modeling, we formalize outcome-supervised PRM as a Multiple Instance Learning (MIL) problem and introduce Softmax-Weighted-Sum (SWS) pooling, an MIL pooling technique tailored for strong dependence and redundancy among reasoning states. We prove Bayes consistency of our algorithm under mild assumptions. Extensive experiments demonstrate that LCA consistently outperforms state-of-the-art outcome-supervised PRMs across multiple tasks and backbones. Code is available at https://anonymous.4open.science/r/LCA.
Process Reward Models (PRMs) are a powerful mechanism for steering large language model reasoning by providing fine-grained, step-level supervision. However, this effectiveness comes at a significant cost: PRMs require expert annotations for every reasoning step, making them costly and difficult to scale. Here, we propose a method for training unsupervised PRMs (uPRM) that requires no human supervision, neither at the level of step-by-step annotations nor through ground-truth verification of final answers. The key idea behind our approach is to define a scoring function, derived from LLM next-token probabilities, that jointly assesses candidate positions of first erroneous steps across a batch of reasoning trajectories. We demonstrate the effectiveness of uPRM across diverse scenarios: (i) uPRM achieves up to 15% absolute accuracy improvements over the LLM-as-a-Judge in identifying first erroneous steps on the ProcessBench dataset; (ii) as a verifier for test-time scaling, uPRM performs comparably to supervised PRMs and outperforms the majority voting baseline by up to 6.9%, and (iii) when used as a reward signal in reinforcement learning, uPRM enables more robust policy optimization throughout training compared to a supervised PRM trained using ground-truth labels. Overall, our results open a path toward scalable reward modeling for complex reasoning tasks.
Process Reward Models (PRMs) improve credit assignment for reasoning by providing step-level feedback. However, we identify a hidden bias in PRMs caused by severe imbalance in step-level training data. Standard cross-entropy training amplifies this bias, causing PRMs to overcredit plausible but incorrect steps and produce high false-positive rates. We show that these false positives have an asymmetric downstream effect: false negatives mainly slow exploration, whereas false positives actively steer Best-of-N selection, guided decoding, and policy optimization toward flawed reasoning. This suggests that PRM training should shift from pointwise label fitting to reliable relative comparisons. To address this, we propose PRISM (Precision Ranking for Improved Step Modeling), a policy-aware PRM training framework that learns from contrastive step-level comparisons and hard negatives generated by a temporal lookahead strategy, requiring no new human labels. We further use a difficulty-aware curriculum to optimize the contrastive step margin. Across PRMBench and ProcessBench, PRISM substantially reduces false positives (22% on PRMBench) and improves macro F1 over strong discriminative PRMs. When applied to policy optimization and search tasks, including guided decoding and Best-of-N selection, it consistently improves accuracy (up to 22% for guided decoding and 33% for Best-of-N) and robustness. More broadly, trustworthy process supervision is not just about assigning high rewards, but about rewarding the right reasoning for the right reasons.
Process rewards have been widely used in deep reinforcement learning to improve training efficiency, reduce variance, and prevent reward hacking. In LLM reasoning, existing works also explore various solutions for learning effective process reward models (PRM) with or without the help of an expert policy. However, existing methods either rely on strong assumptions about the expert policies (e.g., requiring their reward functions) or suffer intrinsic limitations (e.g., entropy collapse), resulting in weak PRMs or limited generalizability. In this paper, we introduce rePIRL, an inverse RL-inspired framework that learns effective PRMs with minimal assumptions about expert policies. Specifically, we design a dual learning process that updates the policy and the PRM interchangeably. Our learning algorithm has customized techniques to address the challenges of scaling traditional inverse RL to LLMs. We theoretically show that our proposed learning framework can unify both online and offline PRM learning methods, justifying that rePIRL can learn PRMs with minimal assumptions. Empirical evaluations on standardized math and coding reasoning datasets demonstrate the effectiveness of rePIRL over existing methods. We further show the application of our trained PRM in test-time training, test-time scaling, and providing an early signal for training hard problems. Finally, we validate our training recipe and key design choices via a detailed ablation study.