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.

Recent neural theorem provers use reinforcement learning with verifiable rewards (RLVR), where proof assistants provide binary correctness signals. While verifiable rewards are cheap and scalable without reward hacking issues, they suffer from sparse credit assignment: models receive no learning signal from difficult problems where partial progress goes unrewarded. This motivates learned reward models that can evaluate proof quality beyond binary verification. However, comparing reward models is challenging since it typically requires expensive RL training ablations. To address this, we introduce \textbf{FormalRewardBench}, the first benchmark for evaluating reward models in formal theorem proving with Lean 4. Our benchmark consists of 250 preference pairs where correct proofs are paired with incorrect variants generated through five expert curated error injection strategies: forced mistakes, minimal single-point variations, verbose incorrect proofs, natural language justification, and Python code injection. We evaluate frontier LLMs (e.g., Claude Opus 4.5), judge LLMs (e.g., CompassJudger-1-14B), general-purpose LLMs (e.g., Qwen2.5-72B-Instruct), and specialized theorem proving models (e.g., DeepSeek-Prover-V2-7B). Our results reveal that frontier LLMs achieve the highest performance (59.8%) while specialized theorem provers perform the worst (24.4%), suggesting that theorem proving ability does not transfer to proof evaluation. We provide further insights on various error injection mechanisms, highlighting the challenging nature of most injection mechanisms. We release \textbf{FormalRewardBench} publicly to encourage more research on developing reward models in formal mathematics.

Reinforcement learning for program repair is hindered by sparse execution feedback and coarse sequence-level rewards that obscure which edits actually fix bugs. We present BoostAPR, a three-stage framework addressing these challenges: (1) supervised fine-tuning on execution-verified demonstrations with reasoning traces, (2) training dual reward models--a sequence-level assessor and a line-level credit allocator--from execution outcomes, and (3) PPO optimization where the line-level model redistributes rewards to critical edit regions. This line-level credit assignment operates at an intermediate granularity naturally suited to code changes. Trained on SWE-Gym and evaluated on four benchmarks, BoostAPR achieves 40.7% on SWE-bench Verified (+22.9pp over base model), 24.8% on Defects4J (Python-to-Java transfer), 84.5% on HumanEval-Java, and 95.0% on QuixBugs, achieving competitive results among open-source models with strong cross-language generalization.

Inference-time scaling methods rely on Process Reward Models (PRMs), which are often poorly calibrated and overestimate success probabilities. We propose, to our knowledge, the first use of conditional optimal transport for calibrating PRMs, modifying conditional OT (CondOT) map learning \cite{bunne2022supervised} to estimate a monotonic conditional quantile function over success probabilities estimated by the PRM, conditioned on PRM hidden states. This yields structurally valid quantile estimates and enables efficient extraction of confidence bounds at arbitrary levels, which we integrate into the instance-adaptive scaling (IAS) framework of \cite{park2025know}. We evaluate on mathematical reasoning benchmarks spanning moderate-difficulty problems (MATH-500) and harder out-of-distribution problems (AIME). For PRMs with reliable ranking signals, our method substantially improves calibration over both uncalibrated PRMs and quantile regression. On downstream Best-of-N IAS performance, our method generally improves over uncalibrated PRMs. These results establish conditional optimal transport as another principled and practical approach to PRM calibration, offering structural guarantees and flexible uncertainty estimation.

Reinforcement learning with verifiable rewards has become a common way to improve explicit reasoning in large language models, but final-answer correctness alone does not reveal whether the reasoning trace is faithful, reliable, or useful to the model that consumes it. This outcome-only signal can reinforce traces that are right for the wrong reasons, overstate reasoning gains by rewarding shortcuts, and propagate flawed intermediate states in multi-step systems. To this end, we propose TraceLift, a planner-executor training framework that treats reasoning as a consumable intermediate artifact. During planner training, the planner emits tagged reasoning. A frozen executor turns this reasoning into the final artifact for verifier feedback, while an executor-grounded reward shapes the intermediate trace. This reward multiplies a rubric-based Reasoning Reward Model (RM) score by measured uplift on the same frozen executor, crediting traces that are both high-quality and useful. To make reasoning quality directly learnable, we introduce TRACELIFT-GROUPS, a rubric-annotated reason-only dataset built from math and code seed problems. Each example is a same-problem group containing a high-quality reference trace and multiple plausible flawed traces with localized perturbations that reduce reasoning quality or solution support while preserving task relevance. Extensive experiments on code and math benchmarks show that this executor-grounded reasoning reward improves the two-stage planner-executor system over execution-only training, suggesting that reasoning supervision should evaluate not only whether a trace looks good, but also whether it helps the model that consumes it. Our code is available at: https://github.com/MasaiahHan/TraceLift

Large language models excel at complex reasoning, yet evaluating their intermediate steps remains challenging. Although process reward models provide step-wise supervision, they often suffer from a risk compensation effect, where incorrect steps are offset by later correct ones, assigning high rewards to flawed reasoning paths. This issue is further exacerbated in knowledge graph (KG) reasoning, as there may exist multiple paths between the start and end entities in the KGs, and a risky step can make the reasoning path flawed. Those limitations are problematic in risk-sensitive tasks such as medical and legal KG reasoning. To address the issues, we propose a Schema-aware Cumulative Process Reward Model (SCPRM) that evaluates reasoning paths by conditioning on the reasoning prefix , and incorporating schema distance between current reasoning step and the implicit target parsed from the query, which provides cumulative and future rewards to guide the path explorations. We further integrate SCPRM into Monte Carlo Tree Search (MCTS) as SCPRM-MCTS to conduct multi-hop reasoning on KGs for question answering (QA) tasks. Across medical and legal KGQA and CWQ, SCPRM-MCTS improves the performance of Hits@k by an average of 1.18% over strong baselines, demonstrating more accurate and risk-sensitive reasoning evaluation.

Process reward models (PRMs) require supervision that identifies not only whether a reasoning trajectory is correct, but also where the reasoning process first becomes unsupported by its prefix. We frame this requirement as verifiable counterfactual process supervision with paired correct and erroneous trajectories in which the first invalid transition is known, the error mechanism is controlled, and the downstream continuation remains coherent under the corrupted state. Starting from a verified symbolic reasoning chain, our method injects a template-aware error at a selected intermediate step, recomputes all subsequent steps under the corrupted state, and verifies that the injected step is not derivable from its original prefix. The resulting trajectories provide prefix-valid first-error annotations and are translated into aligned natural-language processes for PRM training and evaluation. Experiments show that the synthesized data improve Best-of-8 reranking on logical reasoning benchmarks and show preliminary transfer to mathematical process evaluation.

Large language models pick up social biases from the data they are trained on and carry those biases into downstream applications, often reinforcing stereotypes around gender, race, religion, disability, age, and socioeconomic status. The standard fixes (retraining on curated data or fine-tuning with human feedback) are expensive, need access to model weights, and risk degrading the model on other tasks. In this paper we take a different route: we debias the model at decoding time, treating bias mitigation as a structured search over candidate tokens without ever touching model weights. A separate Process Reward Model (PRM) acts as a judge, scoring each candidate for both fairness and fluency. We design three schemes of increasing sophistication (Best-of-N selection, Sequential critique-and-revise, and Constitutional self-audit) and evaluate them on four models (GPT-4o-mini, Llama 3.2 3B, Gemma 3 4B, Qwen 2.5 3B) across a 200-prompt bilingual benchmark in English and Urdu covering eight bias categories. Sequential debiasing proves the most effective, raising mean bias scores by up to +0.40 over baseline while preserving (and sometimes improving) fluency. We then extend all three schemes to open-ended generation, where each token is debiased on the fly, and introduce a lightweight Bias Guard gate that fires only on potentially biased words, keeping overhead near 2x for well-calibrated models. A formal overhead metric that separates generator cost from judge cost reveals that Best-of-N is effectively free on the generator side in a native implementation. GPT-4o-mini, included as a strong proprietary anchor, confirms that the framework scales with model capability; the three open-weight models show where current small-scale LLMs still struggle.

Currently, process reward models (PRMs) have exhibited remarkable potential for test-time scaling. Since large language models (LLMs) regularly generate flawed intermediate reasoning steps when tackling a broad spectrum of reasoning and decision-making tasks, PRMs are required to possess capabilities for detecting process-level errors in real-world scenarios. However, existing benchmarks primarily focus on mathematical reasoning, thereby failing to comprehensively evaluate the error detection ability of PRMs across diverse reasoning scenarios. To mitigate this gap, we introduce LSR-Ben, a process-level benchmark specifically designed for assessing PRM's performance across two primary reasoning domains (scientific and logical reasoning) and nine subdomains. We conduct extensive experiments on a diverse set of 22 models, encompassing both PRMs and LLMs, and derive two key findings: (1) In domains beyond mathematical reasoning, the error-detection ability of existing PRMs and LLMs is found to be markedly weaker by comparison. (2) In general, LLMs exhibit a tendency toward over-identification of errors compared to PRMs, whereas PRMs exhibit an inherent tendency to overlook errors compared to LLMs. We hope LSR-Ben can foster future researches on PRMs for broader domains, thereby enhancing the reasoning capabilities of LLMs.

Test-time scaling (TTS) has emerged as a powerful paradigm for improving the reasoning performance of large language models (LLMs) by investing additional compute at inference time. A central component of TTS is the \emph{verifier}, which selects or scores candidate solutions to guide the search process. While prior work has explored the benefit of verification, a fundamental question remains underexplored: \emph{what is the optimal granularity of verification under a given compute budget?} Coarse-grained outcome reward models (ORMs) and fine-grained process reward models (PRMs) represent two extremes, yet neither alone achieves compute-optimality across all regimes. In this paper, we establish a unified theoretical framework, called \textbf{GRACE} (\underline{G}ranularity-\underline{R}egulated \underline{A}daptive \underline{C}omputational \underline{E}fficiency), that characterizes the optimal verification granularity as an explicit function of problem difficulty, verifier accuracy, and compute budget. We prove that there exists a phase transition: fine-grained verification dominates when either the compute budget is large or the problem is hard, whereas coarse-grained verification is preferred in the low-budget, easy-problem regime. Our theory unifies Best-of-$N$, beam search, and step-level MCTS within a single Pareto-optimality framework, and motivates an adaptive granularity strategy that provably achieves the compute-performance Pareto frontier. Empirical results on MATH-500, GSM8K, and AIME benchmarks corroborate all four theoretical claims, with our adaptive strategy outperforming fixed-granularity baselines by up to 3.1% accuracy at matched compute.

Recent advancements in reinforcement learning with verifiable rewards (RLVR) have significantly improved the complex reasoning ability of vision-language models (VLMs). However, its outcome-level supervision is too coarse to diagnose and correct errors within the reasoning chain. To this end, we propose Perceval, a process reward model (PRM) that enables token-level error grounding, which can extract image-related claims from the response and compare them one by one with the visual evidence in the image, ultimately returning claims that contain perceptual errors. Perceval is trained with perception-intensive supervised training data. We then integrate Perceval into the RL training process to train the policy models. Specifically, compared to traditional GRPO, which applies sequence-level advantages, we apply token-level advantages by targeting penalties on hallucinated spans identified by Perceval, thus enabling fine-grained supervision signals. In addition to augmenting the training process, Perceval can also assist VLMs during the inference stage. Using Perceval, we can truncate the erroneous portions of the model's response, and then either have the model regenerate the response directly or induce the model to reflect on its previous output. This process can be repeated multiple times to achieve test-time scaling. Experiments show significant improvements on benchmarks from various domains across multiple reasoning VLMs trained with RL, highlighting the promise of perception-centric supervision as a general-purpose strategy. For test-time scaling, it also demonstrates consistent performance gains over other strategies, such as major voting. Our code and data will be publicly released at https://github.com/RUCAIBox/Perceval.

Diffusion language models generate without a fixed left-to-right order, leaving token ordering as a central algorithmic choice. Existing systems mainly use random masking or confidence-driven ordering, which respectively suffer from train--test mismatch and myopic exploration. We introduce DPRM (Doob -transform Process Reward Model), a plug-in token-ordering module that keeps the host architecture, denoising objective and supervision unchanged, and modifies only the ordering policy. DPRM starts from confidence-driven ordering and gradually shifts to process-reward-guided ordering through online estimates. We characterize the exact DPRM policy as a reward-tilted Gibbs reveal law, prove convergence of its stagewise Soft-BoN approximation, show that the online bucketized controller tracks the exact DPRM score at empirical-Bernstein rates, and establish a sample-complexity advantage under tractable optimization assumptions. Across nine hosts covering language reasoning, test-time scaling, protein, single-cell, molecular, DNA, text-to-image generation, and VQA, DPRM order variants improve several language, DNA, and multimodal settings while also identifying boundary cases where confidence-only ordering or task-specific utilities are preferable. Code is available at: https://github.com/DakeBU/DPRM-DLLM

Process Reward Models (PRMs) have achieved remarkable success in augmenting the reasoning capabilities of Large Language Models (LLMs) within static domains such as mathematics. However, their potential in dynamic data analysis tasks remains underexplored. In this work, we first present a empirical study revealing that general-domain PRMs struggle to supervise data analysis agents. Specifically, they fail to detect silent errors, logical flaws that yield incorrect results without triggering interpreter exceptions, and erroneously penalize exploratory actions, mistaking necessary trial-and-error exploration for grounding failures. To bridge this gap, we introduce DataPRM, a novel environment-aware generative process reward model that (1) can serve as an active verifier, autonomously interacting with the environment to probe intermediate execution states and uncover silent errors, and (2) employs a reflection-aware ternary reward strategy that distinguishes between correctable grounding errors and irrecoverable mistakes. We design a scalable pipeline to construct over 8K high-quality training instances for DataPRM via diversity-driven trajectory generation and knowledge-augmented step-level annotation. Experimental results demonstrate that DataPRM improves downstream policy LLMs by 7.21% on ScienceAgentBench and 11.28% on DABStep using Best-of-N inference. Notably, with only 4B parameters, DataPRM outperforms strong baselines, and exhibits robust generalizability across diverse Test-Time Scaling strategies. Furthermore, integrating DataPRM into Reinforcement Learning yields substantial gains over outcome-reward baselines, achieving 78.73% on DABench and 64.84% on TableBench, validating the effectiveness of process reward supervision. Code is available at https://github.com/zjunlp/DataMind.

Reward models in RLHF are trained to score only the final token of a response - a choice that discards rich signal from every intermediate position and produces models whose token-level outputs are noise. We argue this is a missed opportunity: a well-trained reward model's output at any token should represent the conditional expectation of the final reward given the response so far. We introduce Temporally Coherent Reward Modeling (TCRM), which induces this property via two regularization terms on top of the standard Bradley-Terry loss, with minimizers provably equal to conditional expectations. The regularizers correspond to Monte Carlo and TD value-learning objectives, establishing a direct connection to RL value functions. TCRM requires zero changes to architecture, data, or inference, yet unlocks three capabilities from one principle: interpretable token-level reward trajectories (middle-token pairwise accuracy improved from 50% to 88.9%, final-token accuracy preserved); state-of-the-art PRM performance on ProcessBench (44.9% average F1) among models trained only on outcome data; and unified reward/value modeling in PPO, reducing peak GPU memory by 27% and step time by 19% with matching LLM quality.

Visual question answering increasingly requires multi-step reasoning. Recent post-training with reinforcement learning under verifiable rewards (RLVR) and Group Relative Policy Optimization (GRPO) can improve multimodal reasoning, but most approaches rely on sparse outcome-only rewards. As a result, they struggle to tell whether an incorrect answer comes from a small mistake late in the reasoning or from an unhelpful trajectory from the start. A common solution is to train a process reward model (PRM) for step-level supervision, but this typically requires large-scale high-quality chain-of-thought annotations and additional training cost. We propose ProcessThinker, a practical post-training pipeline that provides step-level process rewards without training an explicit PRM. ProcessThinker first rewrites reasoning traces into a step-tagged format for cold-start supervised fine-tuning, then applies GRPO with a standard format reward and our rollout-based process reward. Concretely, for each intermediate step, we sample multiple continuations from that step and use the empirical success rate (final-answer verification) as the step reward. This gives dense credit assignment and encourages reasoning steps that more reliably support a correct conclusion, helping reduce inconsistent or self-contradictory progress across steps -- a key issue in logical reasoning. Across four challenging video benchmarks (Video-MMMU, MMVU, VideoMathQA, and LongVideoBench), ProcessThinker consistently improves over the baseline model Qwen3-VL-8B-Instruct

Training multimodal agents via reinforcement learning for knowledge-intensive visual reasoning is fundamentally hindered by the extreme sparsity of outcome-based supervision and the unpredictability of live web environments. To resolve these algorithmic and environmental bottlenecks, we introduce ProMMSearchAgent, establishing a novel Sim-to-Real training paradigm for multimodal search. We decouple policy learning into a deterministic, local static sandbox. Crucially, to learn effectively within this constrained environment, we propose an introspective process-oriented reward. By probing the agent's own parametric knowledge boundaries, we generate dense behavioral metadata that explicitly rewards the correct cognitive decision, initiating a multimodal or text search only when visually or factually uncertain. Extensive experiments demonstrate that our locally-trained policy transfers zero-shot to the live Google Search API. ProMMSearchAgent achieves new SOTA performance, outperforming MMSearch-R1 by +5.1% on FVQA-test, +6.3% on InfoSeek, and +11.3% on MMSearch.

Process Reward Models (PRMs) have emerged as a powerful tool for providing step-level feedback when evaluating the reasoning of Large Language Models (LLMs), which frequently produce chains of thought (CoTs) containing errors even when the final answer is correct. However, existing PRM datasets remain expensive to construct, prone to annotation errors, and predominantly limited to the mathematical domain. This work introduces a novel and scalable approach to PRM dataset generation based on planning logical problems expressed in the Planning Domain Definition Language (PDDL). Using this method, we generate a corpus of approximately one million reasoning steps across various PDDL domains and use it to train PRMs. Experimental results show that augmenting widely-used PRM training datasets with PDDL-derived data yields substantial improvements in both mathematical and non-mathematical reasoning, as demonstrated across multiple benchmarks. These findings indicate that planning problems constitute a scalable and effective resource for generating robust, precise, and fine-grained training data for PRMs, going beyond the classical mathematical sources that dominate this field.

Process-Level Reward Models (PRMs) are essential for guiding complex reasoning in large language models, yet existing PRM benchmarks cover only general domains such as mathematics, failing to address medical reasoning -- which is uniquely characterized by safety criticality, knowledge intensity, and diverse error patterns. Without a reliable medical PRM evaluation framework, we cannot quantify models' error detection capabilities in clinical reasoning, leaving their safety in real-world healthcare applications unverified. We propose MedPRMBench, the first process-level reward model benchmark for the medical domain. Built through a three-phase pipeline based on Clinical Reasoning Blueprints (CRBs), MedPRMBench systematically generates high-quality evaluation data from seven medical QA sources, covering 14 fine-grained error types across three categories (Simplicity, Soundness, and Sensitivity) with the first 4-level severity grading system to quantify clinical impact. The benchmark comprises 6{,}500 questions with 13{,}000 reasoning chains and 113{,}910 step-level labels, plus 6{,}879 questions for training. Our medical PRM baseline achieves an 87.1% overall PRMScore -- substantially surpassing all baselines -- and serves as a plug-and-play verifier that improves downstream medical QA accuracy by 3.2--6.7 percentage points. Systematic evaluation spanning proprietary frontier models, open-source reasoning models, and medical-specialized models reveals critical weaknesses in current models' medical reasoning error detection capabilities, providing clear directions for future PRM improvement.

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.

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.

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.

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.

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 \emph{external verifiers} or \emph{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 \href{https://github.com/db-Lee/Multi-RM}{\underline{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.