Efficient Process Reward Modeling via Contrastive Mutual Information

Training process reward models (PRMs) requires step-level correctness labels, obtained either through expensive human annotation or by relying on ground-truth answers, limiting the ability to scale process-level supervision. We propose ScalePRM, which scales verification compute as an alternative: given a problem and a candidate solution, we generate multiple independent verifications of each reasoning step and aggregate their judgments to produce synthetic step-level labels without ground truth. We explore two representative inference-time scaling strategies, parallel scaling through self-consistency and sequential scaling through meta-critique, and train generative PRMs on the resulting synthetic data. On ProcessBench, a benchmark for identifying erroneous steps in mathematical reasoning, PRMs trained on step-level self-consistency data achieve 67.5 F1, surpassing reference-guided training with ground-truth access (66.4 F1) and GPT-4o as a critic (61.9 F1). When deployed as reward signals in RL training with Qwen2.5-Math-7B, our best PRM achieves 47.4% average accuracy across six mathematical reasoning benchmarks, outperforming ground-truth-based RLVR (43.9%). We also identify and address reward exploitation patterns unique to generative PRM-based RL. Our results demonstrate that scaling verification compute is a viable alternative to ground-truth supervision for training process reward models.

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.

Understanding and evaluating multi-step reasoning in LLMs at the level of individual steps remains a key challenge. Process reward models (PRMs) provide a solution by scoring each step, enabling fine-grained supervision and improved reliability. However, training them requires costly human annotation or computationally intensive rollout-based labeling. To solve this, we introduce MCNIG, a scalable method for automatically labeling the quality of individual reasoning steps in any verifiable domain. Its step score, net information gain (NetIG), improves upon single-reference information gain (IG) by comparing the most-supported correct answer against the most-supported incorrect one, yielding a robust signal even for long and structured outputs like code and SQL, where IG fails. We show that the signal produced by MCNIG correlates with human judgments of step quality, and we apply MCNIG labels to train PRMs that achieve the best average best-of-K accuracy across eight benchmarks spanning mathematics, code generation, text-to-SQL, and scientific QA. Crucially, MCNIG generates no rollouts, cutting labeling complexity to O(N) and making it up to X times cheaper than rollout-based methods at comparable label quality, which makes large-scale process supervision practical.