Daily Papers

Large language model (LLM)-based reasoning systems have recently achieved gold medal-level performance in the IMO 2025 competition, writing mathematical proofs where, to receive full credit, each step must be not only correct but also sufficiently supported. To train LLM-based reasoners in such challenging, open-ended settings, strong verifiers capable of catching step-level mistakes are necessary prerequisites. We introduce Hard2Verify, a human-annotated, step-level verification benchmark produced with over 500 hours of human labor. Hard2Verify is designed to rigorously assess step-level verifiers at the frontier: Verifiers must provide step-level annotations or identify the first error in responses generated by frontier LLMs for very recent, challenging, and open-ended math questions. We evaluate 29 generative critics and process reward models, demonstrating that, beyond a few standouts, open-source verifiers lag closed source models. We subsequently analyze what drives poor performance in step-level verification, the impacts of scaling verifier compute, as well as fundamental questions such as self-verification and verification-generation dynamics.

While Multimodal Large Language Models (MLLMs) have achieved impressive progress in vision-language understanding, they still struggle with complex multi-step reasoning, often producing logically inconsistent or partially correct solutions. A key limitation lies in the lack of fine-grained supervision over intermediate reasoning steps. To address this, we propose MM-PRM, a process reward model trained within a fully automated, scalable framework. We first build MM-Policy, a strong multimodal model trained on diverse mathematical reasoning data. Then, we construct MM-K12, a curated dataset of 10,000 multimodal math problems with verifiable answers, which serves as seed data. Leveraging a Monte Carlo Tree Search (MCTS)-based pipeline, we generate over 700k step-level annotations without human labeling. The resulting PRM is used to score candidate reasoning paths in the Best-of-N inference setup and achieves significant improvements across both in-domain (MM-K12 test set) and out-of-domain (OlympiadBench, MathVista, etc.) benchmarks. Further analysis confirms the effectiveness of soft labels, smaller learning rates, and path diversity in optimizing PRM performance. MM-PRM demonstrates that process supervision is a powerful tool for enhancing the logical robustness of multimodal reasoning systems. We release all our codes and data at https://github.com/ModalMinds/MM-PRM.

LLM web agents now browse and take actions on the open web, yet current agent evaluations are constrained to sandboxed environments or artificial tasks. We introduce BrowserArena, a live open-web agent evaluation platform that collects user-submitted tasks, runs Arena-style head-to-head comparisons, and uses step-level human feedback to surface failure modes. Collecting and analyzing step-level annotations on the agent traces, we identify three consistent failure modes: captcha resolution, pop-up banner removal, and direct navigation to URLs. By constructing targeted datasets to further study these tasks, we discover variations in how different language models navigate these failure modes. We find, for example, that o4-mini deploys a wider variety of strategies to circumvent captcha resolution than other models and DeepSeek-R1 consistently misleads users about pop-up banner closure. Our findings surface both the diversity and brittleness of current web agents. More broadly, our benchmarking methodology provides an approach to evaluating and understanding web agent failure modes at scale.

Recent advancements in Large Language Models (LLMs) have demonstrated that Process Reward Models (PRMs) play a crucial role in enhancing model performance. However, training PRMs typically requires step-level labels, either manually annotated or automatically generated, which can be costly and difficult to obtain at scale. To address this challenge, we introduce FreePRM, a weakly supervised framework for training PRMs without access to ground-truth step-level labels. FreePRM first generates pseudo step-level labels based on the correctness of final outcome, and then employs Buffer Probability to eliminate impact of noise inherent in pseudo labeling. Experimental results show that FreePRM achieves an average F1 score of 53.0% on ProcessBench, outperforming fully supervised PRM trained on Math-Shepherd by +24.1%. Compared to other open-source PRMs, FreePRM outperforms upon RLHFlow-PRM-Mistral-8B (28.4%) by +24.6%, EurusPRM (31.3%) by +21.7%, and Skywork-PRM-7B (42.1%) by +10.9%. This work introduces a new paradigm in PRM training, significantly reducing reliance on costly step-level annotations while maintaining strong performance.

Process Reward Models (PRMs) have recently emerged as a powerful framework for enhancing the reasoning capabilities of large reasoning models (LRMs), particularly in the context of test-time scaling (TTS). However, their potential for supervising LRMs on tabular reasoning domains remains underexplored. Through detailed empirical analyses, we identify that existing PRMs, though widely adopted for supervising text-only reasoning steps, struggle with table-specific operations such as sub-table retrieval and schema interaction, leading to critical performance bottlenecks. To address this limitation, we propose TaTToo, a novel table-grounded PRM framework that (i) reasons explicitly over tabular reasoning steps and (ii) integrates tool-based verification to provide precise reward supervision. Concretely, we first design a scalable data curation pipeline that constructs over 60k high-quality step-level annotations by integrating table verification rationales with tool-based executions. Building on the collected data, we train TaTToo with a dual-stage paradigm: cold-start supervised fine-tuning to capture tool-use reasoning patterns, followed by reinforcement learning with tool-grounded reward shaping to align our model with table-based verification. We provide a comprehensive evaluation of the policy improvement induced by our newly designed PRM. Across 5 challenging tabular reasoning benchmarks covering numerical reasoning, fact-checking, and data analysis, TaTToo improves downstream policy LRMs by 30.9% at inference, surpasses strong PRM baselines such as Qwen-2.5-Math-PRM-72B with only 8B parameters, and demonstrates strong generalizability across diverse TTS strategies.

Large language models (LLMs) have shown remarkable progress in complex reasoning tasks, largely enabled by test-time scaling (TTS) paradigms that allocate additional compute during inference. Among these, external TTS (particularly the Best-of-N selection paradigm) yields scalable performance improvements by selecting from multiple independently generated reasoning trajectories. However, this approach faces key limitations: (i) the high computational overhead of deploying process reward models, (ii) the underutilization of the LLM's intrinsic latent representations. We introduce TrajSelector, an efficient and effective Best-of-N framework that exploit the hidden states in the sampler LLM for process-level scoring. A lightweight verifier (with only 0.6B parameters) evaluates the quality of step-wise trajectory, and then aggregates these scores to identify the optimal reasoning trajectory. Our framework employs a fully data-driven, end-to-end training recipe that eliminates reliance on massive step-level annotations. Experiential results across five benchmarks demonstrate that TrajSelector delivers consistent performance gains. In Best-of-32 settings, it surpasses majority voting by 4.61% accuracy and outperforms existing process reward models by 4.31% to 12.21%, all while maintaining lower inference costs.

Large language models (LLMs) have demonstrated strong reasoning abilities across specialized domains, motivating research into their application to legal reasoning. However, existing legal benchmarks often conflate factual recall with genuine inference, fragment the reasoning process, and overlook the quality of reasoning. To address these limitations, we introduce MSLR, the first Chinese multi-step legal reasoning dataset grounded in real-world judicial decision making. MSLR adopts the IRAC framework (Issue, Rule, Application, Conclusion) to model structured expert reasoning from official legal documents. In addition, we design a scalable Human-LLM collaborative annotation pipeline that efficiently produces fine-grained step-level reasoning annotations and provides a reusable methodological framework for multi-step reasoning datasets. Evaluation of multiple LLMs on MSLR shows only moderate performance, highlighting the challenges of adapting to complex legal reasoning. Further experiments demonstrate that Self-Initiated Chain-of-Thought prompts generated by models autonomously improve reasoning coherence and quality, outperforming human-designed prompts. MSLR contributes to advancing LLM reasoning and Chain-of-Thought strategies and offers open resources for future research. The dataset and code are available at https://github.com/yuwenhan07/MSLR-Bench and https://law.sjtu.edu.cn/flszyjzx/index.html.

Practical deployment of Multi-Agent Systems (MAS) demands strong test-time performance, motivating methods that guide inference-time search and selectively spend compute to improve quality. We present the Multi-Agent System Process Reward Model (MASPRM). It assigns per-action, per-agent values to partial inter-agent transcripts and acts as an inference-time controller. MASPRM is trained from multi-agent Monte Carlo Tree Search (MCTS) rollouts without requiring step-level human annotations, by propagating returns to local targets. At inference, MASPRM guides step-level beam search and MCTS, focusing computation on promising branches and pruning early. On GSM8K and MATH, MASPRM-guided decoding with an outcome reward model (ORM) applied to the final answer, improves exact match (EM) over a single straight-through MAS pass by +30.7 and +22.9 points, respectively. A MASPRM trained on GSM8K transfers zero-shot to MATH without retraining, adding 8.4 EM points at the same budget. MASPRM is a plug-in value model that estimates per-agent progress and complements verifier-style decoders, enabling more reliable, compute-aware multi-agent reasoning. Code: https://github.com/milad1378yz/MASPRM

Direct Preference Optimization (DPO) using an implicit reward model has proven to be an effective alternative to reinforcement learning from human feedback (RLHF) for fine-tuning preference aligned large language models (LLMs). However, the overall preference annotations of responses do not fully capture the fine-grained quality of model outputs in complex multi-step reasoning tasks, such as mathematical reasoning. To address this limitation, we introduce a novel algorithm called Step-level Value Preference Optimization (SVPO). Our approach employs Monte Carlo Tree Search (MCTS) to automatically annotate step-level preferences for multi-step reasoning. Furthermore, from the perspective of learning-to-rank, we train an explicit value model to replicate the behavior of the implicit reward model, complementing standard preference optimization. This value model enables the LLM to generate higher reward responses with minimal cost during inference. Experimental results demonstrate that our method achieves state-of-the-art performance on both in-domain and out-of-domain mathematical reasoning benchmarks. Our code is available at https://github.com/MARIO-Math-Reasoning/Super_MARIO.

Process Reward Models (PRMs) aim to improve multi-step reasoning in Large Language Models (LLMs) by supervising intermediate steps and identifying errors. However, building effective PRMs remains challenging due to the lack of scalable, high-quality annotations. Existing approaches rely on costly human labeling, LLM-based self-evaluation that is prone to hallucination, or Monte Carlo (MC) estimation, which infers step quality solely from rollout outcomes and often introduces noisy, misaligned supervision due to credit misattribution. These issues result in three core limitations: noisy rewards, low factual fidelity, and misalignment with step-level reasoning objectives. To address these challenges, we introduce GroundedPRM, a tree-guided and fidelity-aware framework for automatic process supervision. To reduce reward noise and enable fine-grained credit assignment, we construct structured reasoning paths via Monte Carlo Tree Search (MCTS). To eliminate hallucinated supervision, we validate each intermediate step using an external tool, providing execution-grounded correctness signals. To combine both step-level validation and global outcome assessment, we design a hybrid reward aggregation mechanism that fuses tool-based verification with MCTS-derived feedback. Finally, we format the reward signal into a rationale-enhanced, generative structure to promote interpretability and compatibility with instruction-tuned LLMs. GroundedPRM is trained on only 40K automatically labeled samples, amounting to just 10% of the data used by the best-performing PRM trained with auto-labeled supervision. Nevertheless, it achieves up to a 26% relative improvement in average performance on ProcessBench. When used for reward-guided greedy search, GroundedPRM outperforms even PRMs trained with human-labeled supervision, offering a scalable and verifiable path toward high-quality process-level reasoning.

Recent advancements have seen Large Language Models (LLMs) and Large Multimodal Models (LMMs) surpassing general human capabilities in various tasks, approaching the proficiency level of human experts across multiple domains. With traditional benchmarks becoming less challenging for these models, new rigorous challenges are essential to gauge their advanced abilities. In this work, we present OlympiadBench, an Olympiad-level bilingual multimodal scientific benchmark, featuring 8,476 problems from Olympiad-level mathematics and physics competitions, including the Chinese college entrance exam. Each problem is detailed with expert-level annotations for step-by-step reasoning. Evaluating top-tier models on OlympiadBench, we implement a comprehensive assessment methodology to accurately evaluate model responses. Notably, the best-performing model, GPT-4V, attains an average score of 17.97% on OlympiadBench, with a mere 10.74% in physics, highlighting the benchmark rigor and the intricacy of physical reasoning. Our analysis orienting GPT-4V points out prevalent issues with hallucinations, knowledge omissions, and logical fallacies. We hope that our challenging benchmark can serve as a valuable resource for helping future AGI research endeavors. The data and evaluation code are available at https://github.com/OpenBMB/OlympiadBench

Translating training data into many languages has emerged as a practical solution for improving cross-lingual transfer. For tasks that involve span-level annotations, such as information extraction or question answering, an additional label projection step is required to map annotated spans onto the translated texts. Recently, a few efforts have utilized a simple mark-then-translate method to jointly perform translation and projection by inserting special markers around the labeled spans in the original sentence. However, as far as we are aware, no empirical analysis has been conducted on how this approach compares to traditional annotation projection based on word alignment. In this paper, we present an extensive empirical study across 57 languages and three tasks (QA, NER, and Event Extraction) to evaluate the effectiveness and limitations of both methods, filling an important gap in the literature. Experimental results show that our optimized version of mark-then-translate, which we call EasyProject, is easily applied to many languages and works surprisingly well, outperforming the more complex word alignment-based methods. We analyze several key factors that affect the end-task performance, and show EasyProject works well because it can accurately preserve label span boundaries after translation. We will publicly release all our code and data.

Recent advancements in large language models (LLMs) have substantially enhanced their mathematical reasoning abilities. However, these models still struggle with complex problems that require multiple reasoning steps, frequently leading to logical or numerical errors. While numerical mistakes can be largely addressed by integrating a code interpreter, identifying logical errors within intermediate steps is more challenging. Moreover, manually annotating these steps for training is not only expensive but also labor-intensive, requiring the expertise of professional annotators. In our study, we introduce an innovative approach that bypasses the need for process annotations (from human or GPTs) by utilizing the Monte Carlo Tree Search (MCTS) framework. This technique automatically generates both the process supervision and the step-level evaluation signals. Our method iteratively trains the policy and value models, leveraging the capabilities of a well-pretrained LLM to progressively enhance its mathematical reasoning skills. Furthermore, we propose an efficient inference strategy-step-level beam search, where the value model is crafted to assist the policy model (i.e., LLM) in navigating more effective reasoning paths, rather than solely relying on prior probabilities. The experimental results on both in-domain and out-of-domain datasets demonstrate that even without GPT-4 or human-annotated process supervision, our AlphaMath framework achieves comparable or superior results to previous state-of-the-art methods.

Large language models (LLMs) often struggle with maintaining accuracy across a sequence of intermediate reasoning steps in mathematical reasoning, leading to error propagation that undermines the final result. The current methodology to mitigate this issue primarily involves using a verifier model to assess the correctness of generated solution candidates, focusing either on the overall reasoning path or on an incomplete reasoning path. By rethinking this approach, we argue that assessing potentials of incomplete reasoning paths could be more advantageous as it guides towards correct final answers, transforming the task into a planning problem. Our proposed verifier, the Outcome-supervision Value Model (OVM), employs outcome supervision for training, offering an efficient and intuitive method for planning by prioritizing steps that lead to accurate conclusions over mere per-step correctness. Furthermore, the OVM eschews the need for labor-intensive annotations on step-level correctness, enhancing its scalability. Our experiments on two multi-step mathematical reasoning datasets, GSM8K and Game of 24, demonstrate the superior performance of the OVM model. Notably, in GSM8K, our OVM-7B model achieves state-of-the-art results among LLMs up to 13B parameters; especially it does not utilize GPT-4 or code execution. These findings offer a novel perspective on the role of outcome supervision in training verifiers for multi-step reasoning tasks and provide theoretical justification for its advantage in value estimation for planning.

Category-level 3D/6D pose estimation is a crucial step towards comprehensive 3D scene understanding, which would enable a broad range of applications in robotics and embodied AI. Recent works explored neural mesh models that approach a range of 2D and 3D tasks from an analysis-by-synthesis perspective. Despite the largely enhanced robustness to partial occlusion and domain shifts, these methods depended heavily on 3D annotations for part-contrastive learning, which confines them to a narrow set of categories and hinders efficient scaling. In this work, we present DINeMo, a novel neural mesh model that is trained with no 3D annotations by leveraging pseudo-correspondence obtained from large visual foundation models. We adopt a bidirectional pseudo-correspondence generation method, which produce pseudo correspondence utilize both local appearance features and global context information. Experimental results on car datasets demonstrate that our DINeMo outperforms previous zero- and few-shot 3D pose estimation by a wide margin, narrowing the gap with fully-supervised methods by 67.3%. Our DINeMo also scales effectively and efficiently when incorporating more unlabeled images during training, which demonstrate the advantages over supervised learning methods that rely on 3D annotations. Our project page is available at https://analysis-by-synthesis.github.io/DINeMo/.

Large Reasoning Models (LRMs) embed private or copyrighted information not only in their final answers but also throughout multi-step chain-of-thought (CoT) traces, making reliable unlearning far more demanding than in standard LLMs. We introduce Reasoning-TOFU (R-TOFU), the first benchmark tailored to this setting. R-TOFU augments existing unlearning tasks with realistic CoT annotations and provides step-wise metrics that expose residual knowledge invisible to answer-level checks. Using R-TOFU, we carry out a comprehensive comparison of gradient-based and preference-optimization baselines and show that conventional answer-only objectives leave substantial forget traces in reasoning. We further propose Reasoned IDK, a preference-optimization variant that preserves coherent yet inconclusive reasoning, achieving a stronger balance between forgetting efficacy and model utility than earlier refusal styles. Finally, we identify a failure mode: decoding variants such as ZeroThink and LessThink can still reveal forgotten content despite seemingly successful unlearning, emphasizing the need to evaluate models under diverse decoding settings. Together, the benchmark, analysis, and new baseline establish a systematic foundation for studying and improving unlearning in LRMs while preserving their reasoning capabilities.

In this paper, we provide 20,000 non-trivial human annotations on popular datasets as a first step to bridge gap to studying how natural semantic spurious features affect image classification, as prior works often study datasets mixing low-level features due to limitations in accessing realistic datasets. We investigate how natural background colors play a role as spurious features by annotating the test sets of CIFAR10 and CIFAR100 into subgroups based on the background color of each image. We name our datasets CIFAR10-B and CIFAR100-B and integrate them with CIFAR-Cs. We find that overall human-level accuracy does not guarantee consistent subgroup performances, and the phenomenon remains even on models pre-trained on ImageNet or after data augmentation (DA). To alleviate this issue, we propose FlowAug, a semantic DA that leverages decoupled semantic representations captured by a pre-trained generative flow. Experimental results show that FlowAug achieves more consistent subgroup results than other types of DA methods on CIFAR10/100 and on CIFAR10/100-C. Additionally, it shows better generalization performance. Furthermore, we propose a generic metric, MacroStd, for studying model robustness to spurious correlations, where we take a macro average on the weighted standard deviations across different classes. We show MacroStd being more predictive of better performances; per our metric, FlowAug demonstrates improvements on subgroup discrepancy. Although this metric is proposed to study our curated datasets, it applies to all datasets that have subgroups or subclasses. Lastly, we also show superior out-of-distribution results on CIFAR10.1.

Inequality proving, crucial across diverse scientific and mathematical fields, tests advanced reasoning skills such as discovering tight bounds and strategic theorem application. This makes it a distinct, demanding frontier for large language models (LLMs), offering insights beyond general mathematical problem-solving. Progress in this area is hampered by existing datasets that are often scarce, synthetic, or rigidly formal. We address this by proposing an informal yet verifiable task formulation, recasting inequality proving into two automatically checkable subtasks: bound estimation and relation prediction. Building on this, we release IneqMath, an expert-curated dataset of Olympiad-level inequalities, including a test set and training corpus enriched with step-wise solutions and theorem annotations. We also develop a novel LLM-as-judge evaluation framework, combining a final-answer judge with four step-wise judges designed to detect common reasoning flaws. A systematic evaluation of 29 leading LLMs on IneqMath reveals a surprising reality: even top models like o1 achieve less than 10% overall accuracy under step-wise scrutiny; this is a drop of up to 65.5% from their accuracy considering only final answer equivalence. This discrepancy exposes fragile deductive chains and a critical gap for current LLMs between merely finding an answer and constructing a rigorous proof. Scaling model size and increasing test-time computation yield limited gains in overall proof correctness. Instead, our findings highlight promising research directions such as theorem-guided reasoning and self-refinement. Code and data are available at https://ineqmath.github.io/.

Recent advances in interactive video generations have demonstrated diffusion model's potential as world models by capturing complex physical dynamics and interactive behaviors. However, existing interactive world models depend on bidirectional attention and lengthy inference steps, severely limiting real-time performance. Consequently, they are hard to simulate real-world dynamics, where outcomes must update instantaneously based on historical context and current actions. To address this, we present Matrix-Game 2.0, an interactive world model generates long videos on-the-fly via few-step auto-regressive diffusion. Our framework consists of three key components: (1) A scalable data production pipeline for Unreal Engine and GTA5 environments to effectively produce massive amounts (about 1200 hours) of video data with diverse interaction annotations; (2) An action injection module that enables frame-level mouse and keyboard inputs as interactive conditions; (3) A few-step distillation based on the casual architecture for real-time and streaming video generation. Matrix Game 2.0 can generate high-quality minute-level videos across diverse scenes at an ultra-fast speed of 25 FPS. We open-source our model weights and codebase to advance research in interactive world modeling.

In precision medicine, quantitative multi-omic features, topological context, and textual biological knowledge play vital roles in identifying disease-critical signaling pathways and targets. Existing pipelines capture only part of these-numerical omics ignore topological context, text-centric LLMs lack quantitative grounded reasoning, and graph-only models underuse node semantics and the generalization of LLMs-limiting mechanistic interpretability. Although Process Reward Models (PRMs) aim to guide reasoning in LLMs, they remain limited by unreliable intermediate evaluation, and vulnerability to reward hacking with computational cost. These gaps motivate integrating quantitative multi-omic signals, topological structure with node annotations, and literature-scale text via LLMs, using subgraph reasoning as the principle bridge linking numeric evidence, topological knowledge and language context. Therefore, we propose GALAX (Graph Augmented LAnguage model with eXplainability), an innovative framework that integrates pretrained Graph Neural Networks (GNNs) into Large Language Models (LLMs) via reinforcement guided by a Graph Process Reward Model (GPRM), which generates disease-relevant subgraphs in a step-wise manner initiated by an LLM and iteratively evaluated by a pretrained GNN, enabling process-level supervision without explicit intermediate reasoning annotations. As an application, we also introduced Target-QA, a benchmark combining CRISPR-identified targets, multi-omic profiles, and biomedical graph knowledge across diverse cancer cell lines, which enables GNN pretraining for supervising step-wise graph construction and supports long-context reasoning over text-numeric graphs (TNGs), providing a scalable and biologically grounded framework for explainable, reinforcement-guided subgraph reasoning toward reliable and interpretable target and pathway discovery in precision medicine.

Evaluating the step-by-step reliability of large language model (LLM) reasoning, such as Chain-of-Thought, remains challenging due to the difficulty and cost of obtaining high-quality step-level supervision. In this paper, we introduce Self-Play Critic (SPC), a novel approach where a critic model evolves its ability to assess reasoning steps through adversarial self-play games, eliminating the need for manual step-level annotation. SPC involves fine-tuning two copies of a base model to play two roles, namely a "sneaky generator" that deliberately produces erroneous steps designed to be difficult to detect, and a "critic" that analyzes the correctness of reasoning steps. These two models engage in an adversarial game in which the generator aims to fool the critic, while the critic model seeks to identify the generator's errors. Using reinforcement learning based on the game outcomes, the models iteratively improve; the winner of each confrontation receives a positive reward and the loser receives a negative reward, driving continuous self-evolution. Experiments on three reasoning process benchmarks (ProcessBench, PRM800K, DeltaBench) demonstrate that our SPC progressively enhances its error detection capabilities (e.g., accuracy increases from 70.8% to 77.7% on ProcessBench) and surpasses strong baselines, including distilled R1 model. Furthermore, applying SPC to guide the test-time search of diverse LLMs significantly improves their mathematical reasoning performance on MATH500 and AIME2024, outperforming state-of-the-art process reward models.

Step-level reward models (SRMs) can significantly enhance mathematical reasoning performance through process supervision or step-level preference alignment based on reinforcement learning. The performance of SRMs is pivotal, as they serve as critical guidelines, ensuring that each step in the reasoning process is aligned with desired outcomes. Recently, AlphaZero-like methods, where Monte Carlo Tree Search (MCTS) is employed for automatic step-level preference annotation, have proven particularly effective. However, the precise mechanisms behind the success of SRMs remain largely unexplored. To address this gap, this study delves into the counterintuitive aspects of SRMs, particularly focusing on MCTS-based approaches. Our findings reveal that the removal of natural language descriptions of thought processes has minimal impact on the efficacy of SRMs. Furthermore, we demonstrate that SRMs are adept at assessing the complex logical coherence present in mathematical language while having difficulty in natural language. These insights provide a nuanced understanding of the core elements that drive effective step-level reward modeling in mathematical reasoning. By shedding light on these mechanisms, this study offers valuable guidance for developing more efficient and streamlined SRMs, which can be achieved by focusing on the crucial parts of mathematical reasoning.

We present rStar-Math to demonstrate that small language models (SLMs) can rival or even surpass the math reasoning capability of OpenAI o1, without distillation from superior models. rStar-Math achieves this by exercising "deep thinking" through Monte Carlo Tree Search (MCTS), where a math policy SLM performs test-time search guided by an SLM-based process reward model. rStar-Math introduces three innovations to tackle the challenges in training the two SLMs: (1) a novel code-augmented CoT data sythesis method, which performs extensive MCTS rollouts to generate step-by-step verified reasoning trajectories used to train the policy SLM; (2) a novel process reward model training method that avoids na\"ive step-level score annotation, yielding a more effective process preference model (PPM); (3) a self-evolution recipe in which the policy SLM and PPM are built from scratch and iteratively evolved to improve reasoning capabilities. Through 4 rounds of self-evolution with millions of synthesized solutions for 747k math problems, rStar-Math boosts SLMs' math reasoning to state-of-the-art levels. On the MATH benchmark, it improves Qwen2.5-Math-7B from 58.8% to 90.0% and Phi3-mini-3.8B from 41.4% to 86.4%, surpassing o1-preview by +4.5% and +0.9%. On the USA Math Olympiad (AIME), rStar-Math solves an average of 53.3% (8/15) of problems, ranking among the top 20% the brightest high school math students. Code and data will be available at https://github.com/microsoft/rStar.

Process Reward Models (PRMs), which provide step-by-step feedback on the reasoning generated by Large Language Models (LLMs), are receiving increasing attention. However, two key research gaps remain: collecting accurate step-level error labels for training typically requires costly human annotation, and existing PRMs are limited to math reasoning problems. In response to these gaps, this paper aims to address the challenges of automatic dataset creation and the generalization of PRMs to diverse reasoning tasks. To achieve this goal, we propose FoVer, an approach for training PRMs on step-level error labels automatically annotated by formal verification tools, such as Z3 for formal logic and Isabelle for theorem proof, which provide automatic and accurate verification for symbolic tasks. Using this approach, we synthesize a training dataset with error labels on LLM responses for formal logic and theorem proof tasks without human annotation. Although this data synthesis is feasible only for tasks compatible with formal verification, we observe that LLM-based PRMs trained on our dataset exhibit cross-task generalization, improving verification across diverse reasoning tasks. Specifically, PRMs trained with FoVer significantly outperform baseline PRMs based on the original LLMs and achieve competitive or superior results compared to state-of-the-art PRMs trained on labels annotated by humans or stronger models, as measured by step-level verification on ProcessBench and Best-of-K performance across 12 reasoning benchmarks, including MATH, AIME, ANLI, MMLU, and BBH. The datasets, models, and code are provided at https://github.com/psunlpgroup/FoVer.

Process or step-wise supervision has played a crucial role in advancing complex multi-step reasoning capabilities of Large Language Models (LLMs). However, efficient, high-quality automated process annotation remains a significant challenge. To address this, we introduce Single-Pass Annotation with Reference-Guided Evaluation (SPARE), a novel structured framework that enables single-pass, per-step annotation by aligning each solution step to one or multiple steps in a reference solution, accompanied by explicit reasoning for evaluation. We show that reference-guided step-level evaluation effectively facilitates process supervision on four datasets spanning three domains: mathematical reasoning, multi-hop compositional question answering, and spatial reasoning. We demonstrate that SPARE, when compared to baselines, improves reasoning performance when used for: (1) fine-tuning models in an offline RL setup for inference-time greedy-decoding, and (2) training reward models for ranking/aggregating multiple LLM-generated outputs. Additionally, SPARE achieves competitive performance on challenging mathematical datasets while offering 2.6 times greater efficiency, requiring only 38% of the runtime, compared to tree search-based automatic annotation. The codebase, along with a trained SPARE-PRM model, is publicly released to facilitate further research and reproducibility.

Process reward models (PRMs) offer fine-grained, step-level evaluations that facilitate deeper reasoning processes in large language models (LLMs), proving effective in complex tasks like mathematical reasoning. However, developing PRMs is challenging due to the high cost and limited scalability of human-annotated data. Synthetic data from Monte Carlo (MC) estimation is a promising alternative but suffers from a high noise ratio, which can cause overfitting and hinder large-scale training. In this work, we conduct a preliminary study on the noise distribution in synthetic data from MC estimation, identifying that annotation models tend to both underestimate and overestimate step correctness due to limitations in their annotation capabilities. Building on these insights, we propose Self-Denoising Monte Carlo Annotation (SCAN), an efficient data synthesis and noise-tolerant learning framework. Our key findings indicate that: (1) Even lightweight models (e.g., 1.5B parameters) can produce high-quality annotations through a self-denoising strategy, enabling PRMs to achieve superior performance with only 6% the inference cost required by vanilla MC estimation. (2) With our robust learning strategy, PRMs can effectively learn from this weak supervision, achieving a 39.2 F1 score improvement (from 19.9 to 59.1) in ProcessBench. Despite using only a compact synthetic dataset, our models surpass strong baselines, including those trained on large-scale human-annotated datasets such as PRM800K. Furthermore, performance continues to improve as we scale up the synthetic data, highlighting the potential of SCAN for scalable, cost-efficient, and robust PRM training.

This paper presents the Entropy-Driven Unified Process Reward Model (EDU-PRM), a novel framework that approximates state-of-the-art performance in process supervision while drastically reducing training costs. EDU-PRM introduces an entropy-guided dynamic step partitioning mechanism, using logit distribution entropy to pinpoint high-uncertainty regions during token generation dynamically. This self-assessment capability enables precise step-level feedback without manual fine-grained annotation, addressing a critical challenge in process supervision. Experiments on the Qwen2.5-72B model with only 7,500 EDU-PRM-generated training queries demonstrate accuracy closely approximating the full Qwen2.5-72B-PRM (71.1% vs. 71.6%), achieving a 98% reduction in query cost compared to prior methods. This work establishes EDU-PRM as an efficient approach for scalable process reward model training.

Process Reward Models (PRMs) provide step-level supervision to large language models (LLMs), but scaling up training data annotation remains challenging for both humans and LLMs. To address this limitation, we propose an active learning approach, ActPRM, which proactively selects the most uncertain samples for training, substantially reducing labeling costs. During training, we use the PRM to estimate uncertainty after the forward pass, retaining only highly uncertain data. A capable yet costly reasoning model then labels this data. Then we compute the loss with respect to the labels and update the PRM's weights. We compare ActPRM vs. vanilla fine-tuning, on a pool-based active learning setting, demonstrating that ActPRM reduces 50% annotation, but achieving the comparable or even better performance. Beyond annotation efficiency, we further advance the actively trained PRM by filtering over 1M+ math reasoning trajectories with ActPRM, retaining 60% of the data. A subsequent training on this selected dataset yields a new state-of-the-art (SOTA) PRM on ProcessBench (75.0%) and PRMBench (65.5%) compared with same sized models.