Process Supervision

Reinforcement Learning with Verifiable Rewards (RLVR) has advanced the reasoning capabilities of Large Language Models (LLMs) by leveraging direct outcome verification instead of learned reward models. Building on this paradigm, Group Relative Policy Optimization (GRPO) eliminates the need for critic models but suffers from indiscriminate credit assignment for intermediate steps, which limits its ability to identify effective reasoning strategies and incurs overthinking. In this work, we introduce a model-free and verifiable process supervision via probing the model's belief in the correct answer throughout its reasoning trajectory. By segmenting the generation into discrete steps and tracking the conditional probability of the correct answer appended at each segment boundary, we efficiently compute interpretable segment-wise progress measurements to refine GRPO's trajectory-level feedback. This approach enables more targeted and sample-efficient policy updates, while avoiding the need for intermediate supervision derived from costly Monte Carlo rollouts or auxiliary models. Experiments on mathematical and general-domain benchmarks show consistent gains over GRPO across diverse models: up to 2.6-point accuracy improvements and 13.7% reasoning-length reductions on math tasks, and up to 2.4 points and 4% on general-domain tasks, demonstrating strong generalization.

Reinforcement Learning with Verifiable Rewards (RLVR) improves multimodal reasoning by rewarding verifiable final answers. Yet answer-correct trajectories may still rely on incomplete derivations, weak evidence, or statements that contradict their conclusions. This gap between answer correctness and reasoning validity, which we call reasoning-answer inconsistency, motivates trajectory supervision in multimodal RL. We compare two main approaches: reward models (RMs), and Generative Rewards (GRs). RMs are efficient and help early in training, but their gains weaken as the policy distribution shifts; GRs improve performance, but may give unstable rewards and computationally expensive. We therefore propose Groupwise Ranking Reward, which ranks verifier-passed trajectories for the same prompt in one pass and redistributes reward accordingly. Groupwise comparison better separates stronger and weaker correct trajectories with lower judge overhead than GRs. Experiments show that RLVR aggravates reasoning-answer inconsistency, while trajectory supervision alleviates it. Groupwise Ranking Reward performs best overall, improving reliability-conditioned accuracy from 47.4% to 54.7% over RLVR.

The central challenge of reinforcement learning for reasoning lies not only in the sparsity of outcome-level supervision, but more fundamentally in how to transform feedback provided only at the end of a sequence into fine-grained learning signals that can guide intermediate reasoning steps. Existing approaches either rely on outcome-level rewards for sequence-level optimization, which makes precise credit assignment difficult, or depend on externally constructed process supervision, which is costly and difficult to scale sustainably. To address this, we propose a new perspective: reinforcement learning for reasoning can be understood as the problem of internalizing outcome supervision into process supervision. From this perspective, we introduce a supervision-internalization method for reinforcement learning for reasoning, enabling the model to automatically extract process-level learning signals through identifying, correcting, and reusing failed reasoning trajectories, thereby achieving finer-grained policy optimization under outcome-only supervision. We further abstract this idea into a new training paradigm, in which the model continually generates and refines its own internal process supervision during reinforcement learning, opening a new path for fine-grained credit assignment in reinforcement learning for reasoning that differs from externally provided process supervision.

Reasoning capabilities are crucial for reliable medical visual question answering (VQA); however, existing datasets rarely include reasoning explanations. We address this by generating reasoning trajectories for six medical VQA benchmarks using the COMCTS algorithm with open-source vision-language models, with an LLM serving as the verification judge. Building on these generated datasets, we propose a two-stage training framework: supervised fine-tuning followed by Group Relative Policy Optimization (GRPO) with a novel process-based reward. While standard approaches rely solely on exact-match rewards for final answers, we introduce a trajectory-aware reward that measures the similarity between generated and ground-truth reasoning processes. Specifically, we embed reasoning steps using sentence transformers and compute the Dynamic Time Warping (DTW) distance between the resulting vector sequences. Experiments across six benchmarks demonstrate that combining the DTW-based process reward with exact-match reward consistently outperforms SFT-only training, raising mean accuracy from 0.598 to 0.689, mean BERTScore from 0.845 to 0.881, and mean ROUGE-L from 0.665 to 0.748. Our results highlight the importance of process supervision in training reasoning-capable medical VLMs. We make our code and generated reasoning datasets publicly available at https://anonymous.4open.science/r/MICCAI-R1-MED-VQA-code-B14B/

Process supervision has emerged as a promising approach for enhancing LLM reasoning, yet existing methods fail to distinguish meaningful progress from mere verbosity, leading to limited reasoning capabilities and unresolved token inefficiency. To address this, we propose Stage-aware Hierarchical Advantage via Potential Estimation (SHAPE), a framework that formalizes reasoning as a trajectory through a state space of empirical solvability. SHAPE introduces a hierarchical credit assignment mechanism: at the segment level, it employs a stage-aware advantage function to prioritize efficient breakthroughs in low-potential states; at the token level, it utilizes entropy-driven redistribution to sharpen execution signals. Extensive experiments in math reasoning across three base models and five benchmarks demonstrate that SHAPE achieves an average accuracy gain of 3% with 30% reduced token consumption.

Training language models to produce both correct answers and sound reasoning remains an open challenge. Reinforcement learning with verifiable rewards typically optimizes only final outcomes, which can improve task accuracy at the expense of reasoning quality, producing inaccurate, incomplete, or inconsistent traces. We propose verifiable process supervision (VPS), a post-training framework that jointly optimizes prediction accuracy and reasoning quality by supervising structured intermediate claims. We first apply supervised fine-tuning to induce a structured reasoning format, enabling deterministic extraction and verification of intermediate claims for process-level rewards. To address the heterogeneous difficulty of reasoning subtasks, we introduce adaptive weighting that prioritizes components with the largest remaining errors, creating an implicit curriculum. We evaluate VPS on chess as a controlled testbed where reasoning steps can be deterministically verified against engine signals. While outcome-only RL improves move accuracy, it sharply degrades reasoning quality, increasing win-rate error by up to 112% and reducing internal consistency by up to 69%. In contrast, VPS preserves accuracy while significantly improving reasoning quality, reducing win-rate error by up to 30% and restoring consistency to near saturation. A reasoning-space analysis further shows that, without a structured prior, outcome-only RL converges to budget-dependent shortcuts rather than sound multi-step reasoning. Beyond chess, we observe the same phenomenon on math reasoning, where outcome-only RL improves accuracy while degrading step-level arithmetic and consistency, whereas VPS maintains both. These results show that VPS enables language models to reason both accurately and reliably in verifiable domains.

Self-improvement training, where models learn from self-generated solutions, promises sustained capability gains but suffers from a pervasive failure mode: across multiple rounds, compounding reasoning errors cause accuracy to stall or degrade. We trace this drift to standard filtering criteria that retain solutions based solely on final answer correctness, which lets lucky guesses (correct answers with flawed reasoning) contaminate the training data. We propose Verified Self-Improvement (VSI), a framework that conditions data retention on step-level structural integrity rather than just the final output. VSI validates solutions by recomputing arithmetic steps via a computer-algebra library (sympy), checking intermediate consistency, and enforcing domain constraints. Evaluating VSI on GSM8K with Qwen3-4B-Thinking across 5 rounds of self-improvement against four baselines (no verification, outcome verification, majority voting, and VSI with DPO) shows that VSI rejects approximately 34% of correct-answer solutions, successfully isolating lucky guesses. This cleaner training signal drives sustained accuracy gains across all rounds (80.5% to 91.0%), whereas outcome verification plateaus and unverified training collapses. Finally, converting VSI checks into DPO preference pairs trains the model to distinguish sound reasoning from lucky answers, boosting reward accuracy from 46% to 63%. VSI offers a simple, reproducible recipe for robust self-improvement whenever automated reasoning checks are available.

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.

While Large Language Models (LLMs) have evolved into tool-using agents, they remain brittle in long-horizon interactions. Unlike mathematical reasoning where errors are often rectifiable via backtracking, tool-use failures frequently induce irreversible side effects, making accurate step-level verification critical. However, existing process-level benchmarks are predominantly confined to closed-world mathematical domains, failing to capture the dynamic and open-ended nature of tool execution. To bridge this gap, we introduce AgentProcessBench, the first benchmark dedicated to evaluating step-level effectiveness in realistic, tool-augmented trajectories. The benchmark comprises 1,000 diverse trajectories and 8,509 human-labeled step annotations with 89.1% inter-annotator agreement. It features a ternary labeling scheme to capture exploration and an error propagation rule to reduce labeling ambiguity. Extensive experiments reveal key insights: (1) weaker policy models exhibit inflated ratios of correct steps due to early termination; (2) distinguishing neutral and erroneous actions remains a significant challenge for current models; and (3) process-derived signals provide complementary value to outcome supervision, significantly enhancing test-time scaling. We hope AgentProcessBench can foster future research in reward models and pave the way toward general agents. The code and data are available at https://github.com/RUCBM/AgentProcessBench.

While large language models demonstrate remarkable capabilities across numerous domains, social intelligence - the capacity to perceive social cues, infer mental states, and generate appropriate responses - remains a critical challenge, particularly for enabling effective human-AI collaboration and developing AI that truly serves human needs. Current models often rely on superficial patterns rather than genuine social reasoning. We argue that cultivating human-like social intelligence requires training with challenging cases that resist shortcut solutions. To this end, we introduce ToMBench-Hard, an adversarial benchmark designed to provide hard training examples for social reasoning. Building on this, we propose Social-R1, a reinforcement learning framework that aligns model reasoning with human cognition through multi-dimensional rewards. Unlike outcome-based RL, Social-R1 supervises the entire reasoning process, enforcing structural alignment, logical integrity, and information density. Results show that our approach enables a 4B parameter model to surpass much larger counterparts and generalize robustly across eight diverse benchmarks. These findings demonstrate that challenging training cases with trajectory-level alignment offer a path toward efficient and reliable social intelligence.

Reinforcement learning has recently improved the reasoning ability of Large Language Models and Multimodal LLMs, yet prevailing reward designs emphasise final-answer correctness and consequently tolerate process hallucinations--cases where models reach the right answer while misperceiving visual evidence. We address this process-level misalignment with PaLMR, a framework that aligns not only outcomes but also the reasoning process itself. PaLMR comprises two complementary components: a perception-aligned data layer that constructs process-aware reasoning data with structured pseudo-ground-truths and verifiable visual facts, and a process-aligned optimisation layer that constructs a hierarchical reward fusion scheme with a process-aware scoring function to encourage visually faithful chains-of-thought and improve training stability. Experiments on Qwen2.5-VL-7B show that our approach substantially reduces reasoning hallucinations and improves visual reasoning fidelity, achieving state-of-the-art results on HallusionBench while maintaining strong performance on MMMU, MathVista, and MathVerse. These findings indicate that PaLMR offers a principled and practical route to process-aligned multimodal reasoning, advancing the reliability and interpretability of MLLMs.

The real-time supervision of production processes is a common challenge across several industries. It targets process component monitoring and its predictive maintenance in order to ensure safety, uninterrupted production and maintain high efficiency level. The rise of advanced tools for the simulation of physical systems in addition to data-driven machine learning models offers the possibility to design numerical tools dedicated to efficient system monitoring. In that respect, the digital twin concept presents an adequate framework that proffers solution to these challenges. The main purpose of this paper is to develop such a digital twin dedicated to fault detection and diagnosis in the context of a thermal-hydraulic process supervision. Based on a numerical simulation of the system, in addition to machine learning methods, we propose different modules dedicated to process parameter change detection and their on-line estimation. The proposed fault detection and diagnosis algorithm is validated on a specific test scenario, with single one-off parameter change occurrences in the system. The numerical results show good accuracy in terms of parameter variation localization and the update of their values.

Deepfake detection models often generate natural-language explanations, yet their reasoning is frequently ungrounded in visual evidence, limiting reliability. Existing evaluations measure classification accuracy but overlook reasoning fidelity. We propose DeepfakeJudge, a framework for scalable reasoning supervision and evaluation, that integrates an out-of-distribution benchmark containing recent generative and editing forgeries, a human-annotated subset with visual reasoning labels, and a suite of evaluation models, that specialize in evaluating reasoning rationales without the need for explicit ground truth reasoning rationales. The Judge is optimized through a bootstrapped generator-evaluator process that scales human feedback into structured reasoning supervision and supports both pointwise and pairwise evaluation. On the proposed meta-evaluation benchmark, our reasoning-bootstrapped model achieves an accuracy of 96.2%, outperforming 30x larger baselines. The reasoning judge attains very high correlation with human ratings and 98.9% percent pairwise agreement on the human-annotated meta-evaluation subset. These results establish reasoning fidelity as a quantifiable dimension of deepfake detection and demonstrate scalable supervision for interpretable deepfake reasoning. Our user study shows that participants preferred the reasonings generated by our framework 70% of the time, in terms of faithfulness, groundedness, and usefulness, compared to those produced by other models and datasets. All of our datasets, models, and codebase are open-sourced.

Recent advancements have endowed Large Language Models with impressive general reasoning capabilities. However, these reasoning models often perform worse than non-reasoning models on personalization tasks. While some methods use outcome-based RL to improve personalization reasoning, they fail to supervise the reasoning process. As a result, models may reach correct answers through flawed reasoning chains, limiting further improvement. To address this, we propose TagPR, a novel framework that adds semantic tags to the reasoning process for step-by-step guidance. TagPR first automatically generates a structured, tagged dataset for Supervised Fine-Tuning. It then employs a multi-stage RL process guided by a composite reward signal, which integrates tag-based process supervision with a novel Personalization Reward Model with User Embeddings to achieve fine-grained alignment with user-specific logic. Extensive experiments on public LaMP, LongLaMP, PGraphRAG, and a self-constructed dataset demonstrate that our approach achieves state-of-the-art results, delivering an average improvement of 32.65% over the base model across all LaMP benchmark tasks. Our work demonstrates that tag-guided process supervision is an effective approach for personalization reasoning.