Process Reward Models

Recent advances in medical large language models have explored Test-Time Reinforcement Learning (TTRL) to enhance reasoning. However, standard TTRL often relies on majority voting (MV) as a heuristic supervision signal, which can be unreliable in complex medical scenarios where the most frequent reasoning path is not necessarily the clinically correct one. In this work, we propose a novel and unified training paradigm that integrates medical process reward models with TTRL to bridge the gap between test-time scaling (TTS) and parametric model optimization. Specifically, we advance the TTRL framework by replacing the conventional MV with a fine-grained, expert-aligned supervision paradigm using Med-RPM. This integration ensures that reinforcement learning is guided by medical correctness rather than mere consensus, effectively distilling search-based intelligence into the model's parametric memory. Extensive evaluations on four different benchmarks have demonstrated that our developed method consistently and significantly outperforms current TTRL and standalone PRM selection. Our findings establish that transitioning from stochastic heuristics to structured, step-wise rewards is essential for developing reliable and scalable medical AI systems

In scientific reasoning tasks, the veracity of the reasoning process is as critical as the final outcome. While Process Reward Models (PRMs) offer a solution to the coarse-grained supervision problems inherent in Outcome Reward Models (ORMs), their deployment is hindered by the prohibitive cost of obtaining expert-verified step-wise labels. This paper addresses the challenge of training reliable PRMs using abundant but noisy "weak" supervision. We argue that existing Weak-to-Strong Generalization (W2SG) theories lack prescriptive guidelines for selecting high-quality training signals from noisy data. To bridge this gap, we introduce the Dual-Consensus Weak-to-Strong (DC-W2S) framework. By intersecting Self-Consensus (SC) metrics among weak supervisors with Neighborhood-Consensus (NC) metrics in the embedding space, we stratify supervision signals into distinct reliability regimes. We then employ a curriculum of instance-level balanced sampling and label-level reliability-aware masking to guide the training process. We demonstrate that DC-W2S enables the training of robust PRMs for complex reasoning without exhaustive expert annotation, proving that strategic data curation is more effective than indiscriminate training on large-scale noisy datasets.

We study post-training linear autoregressive models with outcome and process rewards. Given a context $\boldsymbol{x}$, the model must predict the response $\boldsymbol{y} \in Y^N$, a sequence of length $N$ that satisfies a $γ$ margin condition, an extension of the standard separability to sequences. We prove that on test samples where the base model achieves a non-trivial likelihood $α$, a variant of policy gradient (PG) can achieve likelihood $1 - \varepsilon$ with an essentially minimax optimal number of reward queries $\tilde{O}((α^{-1} + \varepsilon^{-1})/γ^2)$. However, a barrier arises for going beyond the support of the base model. We prove that the overall expected error after post-training with outcome rewards is governed by a property of the base model called the Likelihood Quantile (LQ), and that variants of PG, while minimax optimal, may require a number of reward queries exponential in $N$ to go beyond this support, regardless of the pre-training algorithm. To overcome this barrier, we study post-training with a process reward model, and demonstrate how PG variants in this setting avoid the curse of dimensionality in $N$ via dependence on a token-level LQ. Along the way, we prove that under the margin condition, SGD with adaptive learning rate (LR) achieves a near optimal test error for statistical learning, and PG with adaptive LR achieves a near optimal number of mistakes for online learning while being computationally efficient whenever possible, both of which may be of independent interest.

Large Language Models (LLMs) using chain-of-thought have demonstrated great potential for solving complex reasoning and planning tasks. Despite these advances, LLM-generated outputs remain susceptible to errors, making verification important for reliable reasoning systems. Learned verifiers can increase trust, enforce safety constraints, and ensure alignment with personal preferences, while also providing feedback to improve generation. This raises a central challenge: when learned verifiers are used to guide generation, the feedback loop between generator and verifier may induce a distribution shift. This is particularly salient for process reward models, a prominent class of learned verifiers that score or classify individual steps in a chain-of-thought reasoning trace. Motivated by this challenge, we propose a new online learning framework for chain-of-thought verifiers that, given a problem statement and a reasoning trace, check the correctness of each reasoning step given the preceding steps. Highlighting the asymmetric role of soundness errors (accepting an incorrect reasoning step) and completeness errors (flagging a correct step as wrong), we introduce novel notions of dimension that characterize their optimal tradeoff. We then show how our learned verifiers can boost the accuracy of a weak generator. Assuming that the generator can produce a correct next step with a small success probability, we show how to learn a strong generator with small error and abstention rates. Our results also allow learning from offline data when queries to an expert verifier can be simulated from a small set of correct reasoning traces. However, we establish a separation between our approach and learning from offline expert demonstrations: we show that learning from offline demonstrations cannot in general achieve the soundness-completeness guarantees produced by our interactive learning approach.

DEEPTHINK methods improve reasoning by generating, refining, and aggregating populations of candidate solutions, which enables strong performance on complex mathematical and scientific tasks. However, existing frameworks can still suffer from unreliable correctness signals during inference, which creates a population- enhancement bottleneck where deeper deliberation amplifies errors, suppresses correct minority solutions, and yields weak returns to additional compute. In this paper, we introduce a functional decomposition of DEEPTHINK systems and propose PRISM, a Process Reward Model (PRM)-guided inference algorithm that uses step-level verification to guide resampling, proposal acceptance, and solution aggregation. During refinement, PRISM uses PRM scores to guide population resampling and stochastic local refinement, which concentrates computation on higher-quality reasoning while preserving diversity. When paired with PRM- score-vote, a PRM-guided aggregation method, PRISM is competitive with or outperforms existing DEEPTHINK methods, reaching 90.0%, 75.4%, and 71.4% with gpt-oss-20b on AIME25, HMMT25, and GPQA Diamond, respectively, while exceeding gpt-oss-120b. Additionally, our analysis shows that PRISM produces consistent net-directional correction during refinement and maintains competitive accuracy when the initial population contains few correct candidates.

Reinforcement learning has emerged as an effective paradigm for training large language models to interleave reasoning with search engine calls. However, existing approaches face a fundamental credit assignment problem: methods like Search-R1 assign a single outcome reward to the entire multi-step trajectory, providing no signal about which reasoning or retrieval decisions were responsible for success or failure. Process-reward methods such as StepSearch introduce step-level supervision but still sample complete trajectories independently, so advantage estimates at any given step are contaminated by the randomness of all other steps. We propose SLATE (Step-Level Advantage estimation for Truncated Exploration), which addresses both problems through two complementary ideas. First, truncated step-level sampling generates k continuations from a shared prefix, isolating all variation to a single decision point. We prove this reduces the variance of advantage estimates by up to a factor of T compared to full-trajectory sampling for T-step trajectories, the first formal variance guarantee for step-level RL in retrieval-augmented reasoning. Second, dense, decomposed process rewards separately evaluate reasoning quality, query quality, and answer correctness on a ternary scale via an LLM judge, providing richer supervision than binary outcome signals or heuristic step-level scores. Experiments on seven QA benchmarks show that SLATE consistently outperforms both sparse-reward and process-reward baselines, achieving a 7.0% relative improvement over Search-R1 on the 7B model and 30.7% on the 3B model. Gains are largest on challenging multi-hop tasks, and ablations confirm that truncated sampling and dense rewards provide complementary benefits.

We propose ContextRL, a novel framework that leverages context augmentation to overcome these bottlenecks. Specifically, to enhance Identifiability, we provide the reward model with full reference solutions as context, enabling fine-grained process verification to filter out false positives (samples with the right answer but low-quality reasoning process). To improve Reachability, we introduce a multi-turn sampling strategy where the reward model generates mistake reports for failed attempts, guiding the policy to "recover" correct responses from previously all-negative groups. Experimental results on 11 perception and reasoning benchmarks show that ContextRL significantly improves knowledge discovery efficiency. Notably, ContextRL enables the Qwen3-VL-8B model to achieve performance comparable to the 32B model, outperforming standard RLVR baselines by a large margin while effectively mitigating reward hacking. Our in-depth analysis reveals the significant potential of contextual information for improving reward model accuracy and document the widespread occurrence of reward hacking, offering valuable insights for future RLVR research.

Process Reward Models (PRMs) are rapidly becoming the backbone of LLM reasoning pipelines, yet we demonstrate that state-of-the-art PRMs are systematically exploitable under adversarial optimization pressure. To address this, we introduce a three-tiered diagnostic framework that applies increasing adversarial pressure to quantify these vulnerabilities. Static perturbation analysis uncovers a fluency-logic dissociation: high invariance to surface-level style changes reward changes $<$0.1, yet inconsistent detection of logically-corrupted reasoning, with different models failing on different attack types. Adversarial optimization demonstrates that gradient-based attacks inflate rewards on invalid trajectories, with reward landscapes exhibiting wide, exploitable peaks. RL-induced reward hacking exposes the critical failure mode: policies trained on AIME problems achieve near-perfect PRM rewards ($>$0.9), while ground-truth accuracy remains low (below 4%), with 43% of reward gains attributable to stylistic shortcuts. These findings reveal that current PRMs function as fluency detectors rather than reasoning verifiers, creating systematic blind spots that undermine their use as training signals. We release PRM-BiasBench and a diagnostic toolkit to enable robustness evaluation before deployment. The code and dataset are available at https://github.com/SqueezeAILab/reward-under-attack.

Group Relative Policy Optimization (GRPO) is effective for training language models on complex reasoning. However, since the objective is defined relative to a group of sampled trajectories, extended deliberation can create more chances to realize relative gains, leading to inefficient reasoning and overthinking, and complicating the trade-off between correctness and rollout efficiency. Controlling this behavior is difficult in practice, considering (i) Length penalties are hard to calibrate because longer rollouts may reflect harder problems that require longer reasoning, penalizing tokens risks truncating useful reasoning along with redundant continuation; and (ii) supervision that directly indicates when to continue or stop is typically unavailable beyond final answer correctness. We propose Weakly Supervised GRPO (WS-GRPO), which improves rollout efficiency by converting terminal rewards into correctness-aware guidance over partial trajectories. Unlike global length penalties that are hard to calibrate, WS-GRPO trains a preference model from outcome-only correctness to produce prefix-level signals that indicate when additional continuation is beneficial. Thus, WS-GRPO supplies outcome-derived continue/stop guidance, reducing redundant deliberation while maintaining accuracy. We provide theoretical results and empirically show on reasoning benchmarks that WS-GRPO substantially reduces rollout length while remaining competitive with GRPO baselines.

Large Language Models (LLMs) demonstrate transformative potential, yet their reasoning remains inconsistent and unreliable. Reinforcement learning (RL)-based fine-tuning is a key mechanism for improvement, but its effectiveness is fundamentally governed by reward design. Despite its importance, the relationship between reward modeling and core LLM challenges--such as evaluation bias, hallucination, distribution shift, and efficient learning--remains poorly understood. This work argues that reward modeling is not merely an implementation detail but a central architect of reasoning alignment, shaping what models learn, how they generalize, and whether their outputs can be trusted. We introduce Reasoning-Aligned Reinforcement Learning (RARL), a reasoning-centric taxonomic perspective that organizes diverse reward paradigms for multi-step reasoning. Within this perspective, we present a taxonomy of reward mechanisms, analyze reward hacking as a pervasive failure mode, and examine how reward signals unify challenges ranging from inference-time scaling to hallucination mitigation. We further critically evaluate existing benchmarks, highlighting vulnerabilities such as data contamination and reward misalignment, and outline directions for more robust evaluation. By integrating fragmented research threads and clarifying the interplay between reward design and fundamental reasoning capabilities, this work provides a foundational roadmap for building reasoning models that are robust, verifiable, and trustworthy.

Mathematical reasoning in large language models has improved substantially with reinforcement learning using verifiable rewards, where final answers can be checked automatically and converted into reliable training signals. Most such pipelines optimize outcome correctness only, which yields sparse feedback for long, multi-step solutions and offers limited guidance on intermediate reasoning errors. Recent work therefore introduces process reward models (PRMs) to score intermediate steps and provide denser supervision. In practice, PRM scores are often imperfectly aligned with final correctness and can reward locally fluent reasoning that still ends in an incorrect answer. When optimized as absolute rewards, such signals can amplify fluent failure modes and induce reward hacking. We propose PROGRS, a framework that leverages PRMs while keeping outcome correctness dominant. PROGRS treats process rewards as relative preferences within outcome groups rather than absolute targets. We introduce outcome-conditioned centering, which shifts PRM scores of incorrect trajectories to have zero mean within each prompt group. It removes systematic bias while preserving informative rankings. PROGRS combines a frozen quantile-regression PRM with a multi-scale coherence evaluator. We integrate the resulting centered process bonus into Group Relative Policy Optimization (GRPO) without auxiliary objectives or additional trainable components. Across MATH-500, AMC, AIME, MinervaMath, and OlympiadBench, PROGRS consistently improves Pass@1 over outcome-only baselines and achieves stronger performance with fewer rollouts. These results show that outcome-conditioned centering enables safe and effective use of process rewards for mathematical reasoning.

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.

Multi-Agent Systems (MAS) built on Large Language Models (LLMs) often exhibit high variance in their reasoning trajectories. Process verification, which evaluates intermediate steps in trajectories, has shown promise in general reasoning settings, and has been suggested as a potential tool for guiding coordination of MAS; however, its actual effectiveness in MAS remains unclear. To fill this gap, we present MAS-ProVe, a systematic empirical study of process verification for multi-agent systems (MAS). Our study spans three verification paradigms (LLM-as-a-Judge, reward models, and process reward models), evaluated across two levels of verification granularity (agent-level and iteration-level). We further examine five representative verifiers and four context management strategies, and conduct experiments over six diverse MAS frameworks on multiple reasoning benchmarks. We find that process-level verification does not consistently improve performance and frequently exhibits high variance, highlighting the difficulty of reliably evaluating partial multi-agent trajectories. Among the methods studied, LLM-as-a-Judge generally outperforms reward-based approaches, with trained judges surpassing general-purpose LLMs. We further observe a small performance gap between LLMs acting as judges and as single agents, and identify a context-length-performance trade-off in verification. Overall, our results suggest that effective and robust process verification for MAS remains an open challenge, requiring further advances beyond current paradigms. Code is available at https://github.com/Wang-ML-Lab/MAS-ProVe.

Training reliable tool-augmented agents remains a significant challenge, largely due to the difficulty of credit assignment in multi-step reasoning. While process-level reward models offer a promising direction, existing LLM-based judges often produce noisy and inconsistent signals because they lack fine-grained, task-specific rubrics to distinguish high-level planning from low-level execution. In this work, we introduce SCRIBE (Skill-Conditioned Reward with Intermediate Behavioral Evaluation), a reinforcement learning framework that intervenes at a novel mid-level abstraction. SCRIBE grounds reward modeling in a curated library of skill prototypes, transforming open-ended LLM evaluation into a constrained verification problem. By routing each subgoal to a corresponding prototype, the reward model is equipped with precise, structured rubrics that substantially reduce reward variance. Experimental results show that SCRIBE achieves state-of-the-art performance across a range of reasoning and tool-use benchmarks. In particular, it improves the AIME25 accuracy of a Qwen3-4B model from 43.3% to 63.3%, and significantly increases success rates in complex multi-turn tool interactions. Further analysis of training dynamics reveals a co-evolution across abstraction levels, where mastery of mid-level skills consistently precedes the emergence of effective high-level planning behaviors. Finally, we demonstrate that SCRIBE is additive to low-level tool optimizations, providing a scalable and complementary pathway toward more autonomous and reliable tool-using agents.

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.

Large Language Models (LLMs) in multi-agent systems (MAS) have shown promise for complex tasks, yet current training methods lack principled ways to connect system-level evaluation with agent- and message-level learning. We propose a theoretical framework that unifies cooperative game-theoretic attribution with process reward modeling to transform system evaluation to agent credit to response-level signals. Unlike prior approaches that rely only on attribution (Shapley) or step-level labels (PRM), our method produces local, signed, and credit-conserving signals. In success cases, Shapley-based credit assignment fairly allocates outcomes across agents and is refined into per-message rewards that promote cooperation while discouraging redundancy or sabotage; in failure cases, first-error localization yields repair-aware preferences that penalize harmful steps while rewarding corrective attempts. The resulting signals are bounded, cooperative, and directly compatible with reinforcement- or preference-based post-training, providing a unified and auditable pathway from global evaluation to local supervision in LLM multi-agent training. Our contribution is conceptual: we present a theoretical foundation and training signals, leaving empirical validation for future work.

Inference-time search over multi-agent systems (MAS) wastes compute when it cannot identify which agent's intermediate message advanced progress. We present the Multi-Agent System Process Reward Model (MASPRM), which scores routed transcripts (ordered sequences of messages between agents) and acts as an inference controller for step-level beam search (SBS) and Monte Carlo Tree Search (MCTS). MASPRM is trained from multi-agent MCTS rollouts labeled only with terminal outcome rewards, without human step-level annotations. We evaluate on GSM8K, MATH, MMLU, and LogiQA. Under matched scorer size and comparable MCTS budget, MASPRM exceeds a size-matched ORM by $+2.0$ to $+3.0$ points at 1.5B and $+4.1$ to $+14.5$ at 7B across all four benchmarks, with additional scorer-scaling gains over policy likelihood at 7B (avg $+13.4$ under MCTS). MASPRM also improves ranking quality, reducing Hit@1 to Hit@5 gaps by up to $10.3$ points, with the largest gains under stepwise search that uses intermediate decisions. Code: https://github.com/milad1378yz/MASPRM

The reliability of large language models (LLMs) during test-time scaling is often assessed with external verifiers or reward models that distinguish correct reasoning from flawed logic. Prior work has studied both outcome reward models (ORMs), which assess only the final answer, and process reward models (PRMs), which score intermediate reasoning steps. Although PRMs are often viewed as advantageous due to their finer-grained supervision, much of the supporting evidence comes from math-adjacent settings, and their relative benefits across broader domains remain unclear. We present the first unified evaluation of four reward model variants, discriminative ORM and PRM (dORM, dPRM) and generative ORM and PRM (gORM, gPRM), across 14 diverse domains. Contrary to conventional wisdom, we find that (i) dORM performs on par with dPRM, (ii) gPRM is not competitive, and (iii) overall, gORM is the most robust, yielding significant and consistent gains across every tested domain. We attribute the worse performance of gPRM to the stepwise scoring process, which inherits label noise from LLM-based automatic labeling, leading to difficulties in evaluating long reasoning trajectories, including those involving self-correcting reasoning. Both our theoretical analysis and empirical observations indicate that stepwise aggregation compounds errors as reasoning length increases. These findings challenge the common assumption that fine-grained supervision is always better and support generative outcome verification for multi-domain deployment. Our code is publicly available to facilitate future research in multi-domain settings.

Long-horizon GUI automation remains challenging due to error accumulation over extended interaction sequences. Process Reward Models (PRMs) provide dense step-level supervision for mitigating error accumulation, yet standard PRMs are poorly suited to GUI verification. Standard PRM judgments often rely on superficial visual alignment rather than functional correctness, reflecting an evaluative knowledge gap caused by missing domain-specific adjudication logic. Standard PRMs also perform passive, single-pass visual assessment, which creates Visual Ambiguity when reliable judgment requires actively locating, parsing, or inspecting task-relevant UI evidence. We introduce GUI-PRA, a Process Reward Agent that transforms GUI process evaluation from passive scoring into active investigation. GUI-PRA couples Experience-Injected Criterion Synthesis, which distills generalized verification principles into state-specific criteria, with Criterion-Guided Autoregressive Perception, which uses these criteria to navigate multi-granularity visual tools and gather grounded evidence. On AndroidWorld and Mobile-MiniWoB++, GUI-PRA achieves improvements of 5.0% and 6.5% over standard PRMs on the Qwen-VL series, with Qwen3-VL attaining 54.74% success rate on AndroidWorld. On the offline OS-Critic Bench, GUI-PRA demonstrates strong competitiveness against fully trained critic models.

Process Reward Models (PRMs) provide fine-grained supervision over intermediate reasoning steps, yet most existing models lack long-range reasoning and deep thinking capabilities. Although prior work has introduced Chain-of-Thought (CoT) to reward models, the high annotation cost of CoT-PRM still limits its scalability. To address these challenges, we propose the Visual Reasoning Process Reward Model (VRPRM) and design a label-efficient two-stage training strategy. Experimental results demonstrate that with only 5.5K CoT-PRM supervised step labels and 40K non-CoT PRM reinforcement learning training examples, VRPRM achieves a macro F1 score of 69.18 on VisualProcessBench, outperforming VisualPRM-8B, a non-thinking PRM trained on 400K examples, by 7.00 points. In Best-of-N evaluation, VRPRM-RL brings absolute Overall improvements of 21.77, 23.42, and 23.12 points on InternVL2.5-8B, 26B, and 38B policies, respectively, with a maximum relative improvement of 59.0%.

Process Reward Models (PRMs), which assign fine-grained scores to intermediate reasoning steps within a solution trajectory, have emerged as a promising approach to enhance the reasoning quality of Large Language Models (LLMs). However, most existing PRMs rely on a unidirectional left-to-right (L2R) evaluation scheme, which restricts their utilization of global context. In light of this challenge, we propose a novel bidirectional evaluation paradigm, named Bidirectional Process Reward Model (BiPRM). BiPRM incorporates a parallel right-to-left (R2L) evaluation stream, implemented via prompt reversal, alongside the conventional L2R flow. Then a gating mechanism is introduced to adaptively fuse the reward scores from both streams to yield a holistic quality assessment. Remarkably, compared to the original PRM, BiPRM introduces only a 0.3% parameter increase for the gating module, and the parallel execution of two streams incurs merely 5% inference time latency. Our extensive empirical evaluations spanning diverse benchmarks, LLM backbones, PRM objectives and sampling policies demonstrate that BiPRM consistently surpasses unidirectional baselines, achieving an average relative gain of 10.6% over 54 solution-level configurations and 37.7% in 12 step-level error detection scenarios. Generally, our results highlight the effectiveness, robustness and general applicability of BiPRM, offering a promising new direction for process-based reward modeling.