Daily Papers

Process Model Forecasting (PMF) aims to predict how the control-flow structure of a process evolves over time by modeling the temporal dynamics of directly-follows (DF) relations, complementing predictive process monitoring that focuses on single-case prefixes. Prior benchmarks show that machine learning and deep learning models provide only modest gains over statistical baselines, mainly due to the sparsity and heterogeneity of the DF time series. We investigate Time Series Foundation Models (TSFMs), large pre-trained models for generic time series, as an alternative for PMF. Using DF time series derived from real-life event logs, we compare zero-shot use of TSFMs, without additional training, with fine-tuned variants adapted on PMF-specific data. TSFMs generally achieve lower forecasting errors (MAE and RMSE) than traditional and specialized models trained from scratch on the same logs, indicating effective transfer of temporal structure from non-process domains. While fine-tuning can further improve accuracy, the gains are often small and may disappear on smaller or more complex datasets, so zero-shot use remains a strong default. Our study highlights the generalization capability and data efficiency of TSFMs for process-related time series and, to the best of our knowledge, provides the first systematic evaluation of temporal foundation models for PMF.

Business Process Model and Notation (BPMN) is a widely adopted standard for representing complex business workflows. While BPMN diagrams are often exchanged as visual images, existing methods primarily rely on XML representations for computational analysis. In this work, we present a pipeline that leverages Vision-Language Models (VLMs) to extract structured JSON representations of BPMN diagrams directly from images, without requiring source model files or textual annotations. We also incorporate optical character recognition (OCR) for textual enrichment and evaluate the generated element lists against ground truth data derived from the source XML files. Our approach enables robust component extraction in scenarios where original source files are unavailable. We benchmark multiple VLMs and observe performance improvements in several models when OCR is used for text enrichment. In addition, we conducted extensive statistical analyses of OCR-based enrichment methods and prompt ablation studies, providing a clearer understanding of their impact on model performance.

Deep learning models struggle with systematic compositional generalization, a hallmark of human cognition. We propose Mirage, a neuro-inspired dual-process model that offers a processing account for this ability. It combines a fast, intuitive ``System~1'' (a meta-trained Transformer) with a deliberate, rule-based ``System~2'' (a Schema Engine), mirroring the brain's neocortical and hippocampal--prefrontal circuits. Trained to perform general, single-step decomposition on a stream of random grammars, Mirage achieves >99\% accuracy on all splits of the SCAN benchmark in a task-agnostic setting. Ablations confirm that the model's systematic behavior emerges from the architectural interplay of its two systems, particularly its use of explicit, prioritized schemas and iterative refinement. In line with recent progress on recursive/recurrent Transformer approaches, Mirage preserves an iterative neural update while externalizing declarative control into an interpretable schema module. Our work provides a concrete computational model for interpreting how compositional reasoning can arise from a modular cognitive architecture.

Large language models (LLMs) can generate BPMN process models from natural-language descriptions, yet supervised fine-tuning (SFT) limits their output quality to the patterns present in the training data. Reinforcement learning (RL) can optimize beyond this ceiling using external quality measures, but how the reward function should be designed when quality is multi-dimensional remains unexplored. We present a systematic investigation of reward function design for RL-based process model generation, training two LLM families (Llama~3.1 8B, Qwen~2.5 14B) under 48 configurations using Group Sequence Policy Optimization with rewards derived from an automated evaluation framework comprising 38 metrics across syntactic, pragmatic, and semantic quality. Three findings emerge. First, RL significantly improves pragmatic and syntactic quality while preserving semantic fidelity, reducing output variability by more than sixfold. Second, equal reward weighting consistently outperforms targeted weighting: emphasizing a specific dimension fails to improve it and can collapse the model into a low-quality mode. Third, design choices interact with model architecture in non-trivial ways: the invalidity penalty is essential for one model but irrelevant for the other, and SFT initialization is indispensable for one architecture but counterproductive for another. These results demonstrate that reward composition is a primary determinant of optimization outcomes, with effects as large as the decision to apply RL itself. The findings generalize to any structured generation task where quality is assessed along multiple automated dimensions. We release our implementation and experimental code at https://github.com/chlauer99/RL_for_process_modeling.

Large Language Models (LLMs) are increasingly applied for Process Modeling (PMo) tasks such as Process Model Generation (PMG). To support these tasks, researchers have introduced a variety of Process Model Representations (PMRs) that serve as model abstractions or generation targets. However, these PMRs differ widely in structure, complexity, and usability, and have never been systematically compared. Moreover, recent PMG approaches rely on distinct evaluation strategies and generation techniques, making comparison difficult. This paper presents the first empirical study that evaluates multiple PMRs in the context of PMo with LLMs. We introduce the PMo Dataset, a new dataset containing 55 process descriptions paired with models in nine different PMRs. We evaluate PMRs along two dimensions: suitability for LLM-based PMo and performance on PMG. Mermaid achieves the highest overall score across six PMo criteria, whereas BPMN text delivers the best PMG results in terms of process element similarity.

In this paper, we introduce the SAP Signavio Academic Models (SAP-SAM) dataset, a collection of hundreds of thousands of business models, mainly process models in BPMN notation. The model collection is a subset of the models that were created over the course of roughly a decade on academic.signavio.com, a free-of-charge software-as-a-service platform that researchers, teachers, and students can use to create business (process) models. We provide a preliminary analysis of the model collection, as well as recommendations on how to work with it. In addition, we discuss potential use cases and limitations of the model collection from academic and industry perspectives.

This paper presents BPMN Assistant, a tool that leverages Large Language Models (LLMs) for natural language-based creation and editing of BPMN diagrams. A specialized JSON-based representation is introduced as a structured alternative to the direct handling of XML to enhance the accuracy of process modifications. Process generation quality is evaluated using Graph Edit Distance (GED) and Relative Graph Edit Distance (RGED), while editing performance is evaluated with a binary success metric. Results show that JSON and XML achieve similar similarity scores in generation, but JSON offers greater reliability, faster processing, and significantly higher editing success rates. We discuss key trade-offs, limitations, and future improvements. The implementation is available at https://github.com/jtlicardo/bpmn-assistant.

Business Process Management (BPM) aims to improve organizational activities and their outcomes by managing the underlying processes. To achieve this, it is often necessary to consider information from various sources, including unstructured textual documents. Therefore, researchers have developed several BPM-specific solutions that extract information from textual documents using Natural Language Processing techniques. These solutions are specific to their respective tasks and cannot accomplish multiple process-related problems as a general-purpose instrument. However, in light of the recent emergence of Large Language Models (LLMs) with remarkable reasoning capabilities, such a general-purpose instrument with multiple applications now appears attainable. In this paper, we illustrate how LLMs can accomplish text-related BPM tasks by applying a specific LLM to three exemplary tasks: mining imperative process models from textual descriptions, mining declarative process models from textual descriptions, and assessing the suitability of process tasks from textual descriptions for robotic process automation. We show that, without extensive configuration or prompt engineering, LLMs perform comparably to or better than existing solutions and discuss implications for future BPM research as well as practical usage.

Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between variational inference (VI) and the learning target. While VI's lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, we show that a direct approximation of the marginal likelihood as in Expectation Propagation (EP) is a better learning objective for hyperparameter optimization. We design a hybrid training procedure to bring the best of both worlds: it leverages conjugate-computation VI for inference and uses an EP-like marginal likelihood approximation for hyperparameter learning. We compare VI, EP, Laplace approximation, and our proposed training procedure and empirically demonstrate the effectiveness of our proposal across a wide range of data sets.

Bayesian optimization (BO) has established itself as a leading strategy for efficiently optimizing expensive-to-evaluate functions. Existing BO methods mostly rely on Gaussian process (GP) surrogate models and are not applicable to (doubly-stochastic) Gaussian Cox processes, where the observation process is modulated by a latent intensity function modeled as a GP. In this paper, we propose a novel maximum a posteriori inference of Gaussian Cox processes. It leverages the Laplace approximation and change of kernel technique to transform the problem into a new reproducing kernel Hilbert space, where it becomes more tractable computationally. It enables us to obtain both a functional posterior of the latent intensity function and the covariance of the posterior, thus extending existing works that often focus on specific link functions or estimating the posterior mean. Using the result, we propose a BO framework based on the Gaussian Cox process model and further develop a Nystr\"om approximation for efficient computation. Extensive evaluations on various synthetic and real-world datasets demonstrate significant improvement over state-of-the-art inference solutions for Gaussian Cox processes, as well as effective BO with a wide range of acquisition functions designed through the underlying Gaussian Cox process model.

Temporal Point Processes (TPPs) serve as the standard mathematical framework for modeling asynchronous event sequences in continuous time. However, classical TPP models are often constrained by strong assumptions, limiting their ability to capture complex real-world event dynamics. To overcome this limitation, researchers have proposed Neural TPPs, which leverage neural network parametrizations to offer more flexible and efficient modeling. While recent studies demonstrate the effectiveness of Neural TPPs, they often lack a unified setup, relying on different baselines, datasets, and experimental configurations. This makes it challenging to identify the key factors driving improvements in predictive accuracy, hindering research progress. To bridge this gap, we present a comprehensive large-scale experimental study that systematically evaluates the predictive accuracy of state-of-the-art neural TPP models. Our study encompasses multiple real-world and synthetic event sequence datasets, following a carefully designed unified setup. We thoroughly investigate the influence of major architectural components such as event encoding, history encoder, and decoder parametrization on both time and mark prediction tasks. Additionally, we delve into the less explored area of probabilistic calibration for neural TPP models. By analyzing our results, we draw insightful conclusions regarding the significance of history size and the impact of architectural components on predictive accuracy. Furthermore, we shed light on the miscalibration of mark distributions in neural TPP models. Our study aims to provide valuable insights into the performance and characteristics of neural TPP models, contributing to a better understanding of their strengths and limitations.

Modern data acquisition routinely produce massive amounts of event sequence data in various domains, such as social media, healthcare, and financial markets. These data often exhibit complicated short-term and long-term temporal dependencies. However, most of the existing recurrent neural network based point process models fail to capture such dependencies, and yield unreliable prediction performance. To address this issue, we propose a Transformer Hawkes Process (THP) model, which leverages the self-attention mechanism to capture long-term dependencies and meanwhile enjoys computational efficiency. Numerical experiments on various datasets show that THP outperforms existing models in terms of both likelihood and event prediction accuracy by a notable margin. Moreover, THP is quite general and can incorporate additional structural knowledge. We provide a concrete example, where THP achieves improved prediction performance for learning multiple point processes when incorporating their relational information.

Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach called Type II maximum likelihood or ML-II). An alternative learning procedure is to infer the posterior over hyperparameters in a hierarchical specification of GPs we call Fully Bayesian Gaussian Process Regression (GPR). This work considers two approximation schemes for the intractable hyperparameter posterior: 1) Hamiltonian Monte Carlo (HMC) yielding a sampling-based approximation and 2) Variational Inference (VI) where the posterior over hyperparameters is approximated by a factorized Gaussian (mean-field) or a full-rank Gaussian accounting for correlations between hyperparameters. We analyze the predictive performance for fully Bayesian GPR on a range of benchmark data sets.

A temporal point process is a mathematical model for a time series of discrete events, which covers various applications. Recently, recurrent neural network (RNN) based models have been developed for point processes and have been found effective. RNN based models usually assume a specific functional form for the time course of the intensity function of a point process (e.g., exponentially decreasing or increasing with the time since the most recent event). However, such an assumption can restrict the expressive power of the model. We herein propose a novel RNN based model in which the time course of the intensity function is represented in a general manner. In our approach, we first model the integral of the intensity function using a feedforward neural network and then obtain the intensity function as its derivative. This approach enables us to both obtain a flexible model of the intensity function and exactly evaluate the log-likelihood function, which contains the integral of the intensity function, without any numerical approximations. Our model achieves competitive or superior performances compared to the previous state-of-the-art methods for both synthetic and real datasets.

Accurate modeling is crucial in many engineering and scientific applications, yet obtaining a reliable process model for complex systems is often challenging. To address this challenge, we propose a novel framework, reservoir computing with unscented Kalman filtering (RCUKF), which integrates data-driven modeling via reservoir computing (RC) with Bayesian estimation through the unscented Kalman filter (UKF). The RC component learns the nonlinear system dynamics directly from data, serving as a surrogate process model in the UKF prediction step to generate state estimates in high-dimensional or chaotic regimes where nominal mathematical models may fail. Meanwhile, the UKF measurement update integrates real-time sensor data to correct potential drift in the data-driven model. We demonstrate RCUKF effectiveness on well-known benchmark problems and a real-time vehicle trajectory estimation task in a high-fidelity simulation environment.

Enterprise Resource Planning (ERP) systems serve as the digital backbone of modern financial institutions, yet they continue to rely on static, rule-based workflows that limit adaptability, scalability, and intelligence. As business operations grow more complex and data-rich, conventional ERP platforms struggle to integrate structured and unstructured data in real time and to accommodate dynamic, cross-functional workflows. In this paper, we present the first AI-native, agent-based framework for ERP systems, introducing a novel architecture of Generative Business Process AI Agents (GBPAs) that bring autonomy, reasoning, and dynamic optimization to enterprise workflows. The proposed system integrates generative AI with business process modeling and multi-agent orchestration, enabling end-to-end automation of complex tasks such as budget planning, financial reporting, and wire transfer processing. Unlike traditional workflow engines, GBPAs interpret user intent, synthesize workflows in real time, and coordinate specialized sub-agents for modular task execution. We validate the framework through case studies in bank wire transfers and employee reimbursements, two representative financial workflows with distinct complexity and data modalities. Results show that GBPAs achieve up to 40% reduction in processing time, 94% drop in error rate, and improved regulatory compliance by enabling parallelism, risk control insertion, and semantic reasoning. These findings highlight the potential of GBPAs to bridge the gap between generative AI capabilities and enterprise-grade automation, laying the groundwork for the next generation of intelligent ERP systems.

Model-Based Reinforcement Learning (MBRL) has been widely studied for Heating, Ventilation, and Air Conditioning (HVAC) control in buildings. One of the critical challenges is the large amount of data required to effectively train neural networks for modeling building dynamics. This paper presents CLUE, an MBRL system for HVAC control in buildings. CLUE optimizes HVAC operations by integrating a Gaussian Process (GP) model to model building dynamics with uncertainty awareness. CLUE utilizes GP to predict state transitions as Gaussian distributions, effectively capturing prediction uncertainty and enhancing decision-making under sparse data conditions. Our approach employs a meta-kernel learning technique to efficiently set GP kernel hyperparameters using domain knowledge from diverse buildings. This drastically reduces the data requirements typically associated with GP models in HVAC applications. Additionally, CLUE incorporates these uncertainty estimates into a Model Predictive Path Integral (MPPI) algorithm, enabling the selection of safe, energy-efficient control actions. This uncertainty-aware control strategy evaluates and selects action trajectories based on their predicted impact on energy consumption and human comfort, optimizing operations even under uncertain conditions. Extensive simulations in a five-zone office building demonstrate that CLUE reduces the required training data from hundreds of days to just seven while maintaining robust control performance. It reduces comfort violations by an average of 12.07% compared to existing MBRL methods, without compromising on energy efficiency.

We introduce a novel machine learning model for credit risk by combining tree-boosting with a latent spatio-temporal Gaussian process model accounting for frailty correlation. This allows for modeling non-linearities and interactions among predictor variables in a flexible data-driven manner and for accounting for spatio-temporal variation that is not explained by observable predictor variables. We also show how estimation and prediction can be done in a computationally efficient manner. In an application to a large U.S. mortgage credit risk data set, we find that both predictive default probabilities for individual loans and predictive loan portfolio loss distributions obtained with our novel approach are more accurate compared to conventional independent linear hazard models and also linear spatio-temporal models. Using interpretability tools for machine learning models, we find that the likely reasons for this outperformance are strong interaction and non-linear effects in the predictor variables and the presence of large spatio-temporal frailty effects.

This paper describes a novel nonparametric model for modeling diffusion MRI signals in q-space. In q-space, diffusion MRI signal is measured for a sequence of magnetic strengths (b-values) and magnetic gradient directions (b-vectors). We propose a Poly-RBF model, which employs a bidirectional framework with polynomial bases to model the signal along the b-value direction and Gaussian radial bases across the b-vectors. The model can accommodate sparse data on b-values and moderately dense data on b-vectors. The utility of Poly-RBF is inspected for two applications: 1) prediction of the dMRI signal, and 2) harmonization of dMRI data collected under different acquisition protocols with different scanners. Our results indicate that the proposed Poly-RBF model can more accurately predict the unmeasured diffusion signal than its competitors such as the Gaussian process model in {\tt Eddy} of FSL. Applying it to harmonizing the diffusion signal can significantly improve the reproducibility of derived white matter microstructure measures.

Domain models are central to software engineering, as they enable a shared understanding, guide implementation, and support automated analyses and model-driven development. Yet, despite these benefits, practitioners often skip modeling because it is time-consuming and demands scarce expertise. We address this barrier by investigating whether open-weight large language models, adapted via instruction tuning, can generate high-quality BPMN process models directly from natural language descriptions in a cost-effective and privacy-preserving way. We introduce InstruBPM, a reproducible approach that prepares paired text-diagram data and instruction tunes an open source large language model with parameter-efficient fine-tuning and quantization for on-prem deployment. We evaluate the tuned model through complementary perspectives: (i) text/code similarity using BLEU, ROUGE-L, and METEOR, (ii) structural fidelity using Relative Graph Edit Distance, (iii) guidelines conformance using external tool checks, and (iv) a small expert review. Using a curated subset of a multi-domain BPMN dataset, we compare the tuned model with untuned open-weight baselines and strong proprietary models under consistent prompting regimes. Our compact tuned model outperforms all baselines across sequence and structural metrics while requiring substantially fewer resources; guideline analysis and expert feedback further indicate that the generated diagrams largely follow BPMN best practices and are useful starting points that reduce modeling effort. Overall, instruction tuning improves structural accuracy and robustness compared to untuned baselines and reduces reliance on heavy prompt scaffolding. We publicly share the trained models and scripts to support reproducibility and further research.

The Archives Unleashed project aims to improve scholarly access to web archives through a multi-pronged strategy involving tool creation, process modeling, and community building - all proceeding concurrently in mutually-reinforcing efforts. As we near the end of our initially-conceived three-year project, we report on our progress and share lessons learned along the way. The main contribution articulated in this paper is a process model that decomposes scholarly inquiries into four main activities: filter, extract, aggregate, and visualize. Based on the insight that these activities can be disaggregated across time, space, and tools, it is possible to generate "derivative products", using our Archives Unleashed Toolkit, that serve as useful starting points for scholarly inquiry. Scholars can download these products from the Archives Unleashed Cloud and manipulate them just like any other dataset, thus providing access to web archives without requiring any specialized knowledge. Over the past few years, our platform has processed over a thousand different collections from about two hundred users, totaling over 280 terabytes of web archives.

This paper explores the use of large language models (LLMs) as research tools in the history, philosophy, and sociology of science (HPSS). LLMs are remarkably effective at processing unstructured text and inferring meaning from context, offering new affordances that challenge long-standing divides between computational and interpretive methods. This raises both opportunities and challenges for HPSS, which emphasizes interpretive methodologies and understands meaning as context-dependent, ambiguous, and historically situated. We argue that HPSS is uniquely positioned not only to benefit from LLMs' capabilities but also to interrogate their epistemic assumptions and infrastructural implications. To this end, we first offer a concise primer on LLM architectures and training paradigms tailored to non-technical readers. We frame LLMs not as neutral tools but as epistemic infrastructures that encode assumptions about meaning, context, and similarity, conditioned by their training data, architecture, and patterns of use. We then examine how computational techniques enhanced by LLMs, such as structuring data, detecting patterns, and modeling dynamic processes, can be applied to support interpretive research in HPSS. Our analysis compares full-context and generative models, outlines strategies for domain and task adaptation (e.g., continued pretraining, fine-tuning, and retrieval-augmented generation), and evaluates their respective strengths and limitations for interpretive inquiry in HPSS. We conclude with four lessons for integrating LLMs into HPSS: (1) model selection involves interpretive trade-offs; (2) LLM literacy is foundational; (3) HPSS must define its own benchmarks and corpora; and (4) LLMs should enhance, not replace, interpretive methods.

A theoretical approach to describing transport of an entire ensemble of clusters with different sizes as a single species in gas has been developed. The major assumption is an existence of local partial chemical equilibrium between the clusters. It is shown that thermal diffusion emerges in the collective description as a significant factor even if it is negligible when transport of the original molecular species is considered. Analytical expressions for the effective diffusion and thermal diffusion coefficients at temperature, pressure, and chemical composition gradients have been derived. The theory has been applied to a technology of H2S conversion in a centrifugal plasma-chemical reactor and has made it possible to account for sulfur clusters in numerical process modeling.

We propose two approaches to extend the notion of knowledge distillation to Gaussian Process Regression (GPR) and Gaussian Process Classification (GPC); data-centric and distribution-centric. The data-centric approach resembles most current distillation techniques for machine learning, and refits a model on deterministic predictions from the teacher, while the distribution-centric approach, re-uses the full probabilistic posterior for the next iteration. By analyzing the properties of these approaches, we show that the data-centric approach for GPR closely relates to known results for self-distillation of kernel ridge regression and that the distribution-centric approach for GPR corresponds to ordinary GPR with a very particular choice of hyperparameters. Furthermore, we demonstrate that the distribution-centric approach for GPC approximately corresponds to data duplication and a particular scaling of the covariance and that the data-centric approach for GPC requires redefining the model from a Binomial likelihood to a continuous Bernoulli likelihood to be well-specified. To the best of our knowledge, our proposed approaches are the first to formulate knowledge distillation specifically for Gaussian Process models.

Agentic assistants capable of proactive, personalized interactions require structured models of user intent and workflow. However, building these models from raw, unstructured screen activity remains an open challenge. We present SERUM, a multi-pass framework that extracts finite-state behavioral models directly from unstructured egocentric video using hierarchical VLM annotation. Processing screen recordings through a sliding window, SERUM alternates between activity-recognition and intent-inference passes, with each pass refining labels using accumulated prior context to reduce hallucination and temporal conflation seen in single-pass annotation. Synonymous states are then merged via sentence embeddings and human-calibrated thresholds into a compact, coherent taxonomy. We evaluate behavioral structure by fitting first-order Markov models over the resulting label sequences (both actions and intents) and measuring predictive accuracy against frequency baselines. Across 61 egocentric videos in four domains (coding, cooking, physical activities, and daily life), we find: (1) iterative label refinement converges to a stable state vocabulary, which we term schematic equilibrium, after several passes; (2) normalized Markov models achieve substantially lower perplexity and higher action predictions than frequency baselines, with the largest gains on structured tasks like coding; and (3) human annotators rate final-pass labels as accurate and meaningfully improved over first-pass labels. To our knowledge, SERUM is the first system to produce interpretable process models from unstructured egocentric screen video without manual annotation, opening a scalable pathway for user modeling and behavioral understanding in the wild. Our demo, code, and results are publicly available

Similar to conventional video generation, current deep learning-based weather prediction frameworks often lack explicit physical constraints, leading to unphysical outputs that limit their reliability for operational forecasting. Among various physical processes requiring proper representation, radiation plays a fundamental role as it drives Earth's weather and climate systems. However, accurate simulation of radiative transfer processes remains challenging for traditional numerical weather prediction (NWP) models due to their inherent complexity and high computational costs. Here, we propose FuXi-RTM, a hybrid physics-guided deep learning framework designed to enhance weather forecast accuracy while enforcing physical consistency. FuXi-RTM integrates a primary forecasting model (FuXi) with a fixed deep learning-based radiative transfer model (DLRTM) surrogate that efficiently replaces conventional radiation parameterization schemes. This represents the first deep learning-based weather forecasting framework to explicitly incorporate physical process modeling. Evaluated over a comprehensive 5-year dataset, FuXi-RTM outperforms its unconstrained counterpart in 88.51% of 3320 variable and lead time combinations, with improvements in radiative flux predictions. By incorporating additional physical processes, FuXi-RTM paves the way for next-generation weather forecasting systems that are both accurate and physically consistent.

Real-world datasets often exhibit temporal dynamics characterized by evolving data distributions. Disregarding this phenomenon, commonly referred to as concept drift, can significantly diminish a model's predictive accuracy. Furthermore, the presence of hyperparameters in online models exacerbates this issue. These parameters are typically fixed and cannot be dynamically adjusted by the user in response to the evolving data distribution. Gaussian Process (GP) models offer powerful non-parametric regression capabilities with uncertainty quantification, making them ideal for modeling complex data relationships in an online setting. However, conventional online GP methods face several critical limitations, including a lack of drift-awareness, reliance on fixed hyperparameters, vulnerability to data snooping, absence of a principled decay mechanism, and memory inefficiencies. In response, we propose DAO-GP (Drift-Aware Online Gaussian Process), a novel, fully adaptive, hyperparameter-free, decayed, and sparse non-linear regression model. DAO-GP features a built-in drift detection and adaptation mechanism that dynamically adjusts model behavior based on the severity of drift. Extensive empirical evaluations confirm DAO-GP's robustness across stationary conditions, diverse drift types (abrupt, incremental, gradual), and varied data characteristics. Analyses demonstrate its dynamic adaptation, efficient in-memory and decay-based management, and evolving inducing points. Compared with state-of-the-art parametric and non-parametric models, DAO-GP consistently achieves superior or competitive performance, establishing it as a drift-resilient solution for online non-linear regression.

Existing human motion generation methods with trajectory and pose inputs operate global processing on both modalities, leading to suboptimal outputs. In this paper, we propose IKMo, an image-keyframed motion generation method based on the diffusion model with trajectory and pose being decoupled. The trajectory and pose inputs go through a two-stage conditioning framework. In the first stage, the dedicated optimization module is applied to refine inputs. In the second stage, trajectory and pose are encoded via a Trajectory Encoder and a Pose Encoder in parallel. Then, motion with high spatial and semantic fidelity is guided by a motion ControlNet, which processes the fused trajectory and pose data. Experiment results based on HumanML3D and KIT-ML datasets demonstrate that the proposed method outperforms state-of-the-art on all metrics under trajectory-keyframe constraints. In addition, MLLM-based agents are implemented to pre-process model inputs. Given texts and keyframe images from users, the agents extract motion descriptions, keyframe poses, and trajectories as the optimized inputs into the motion generation model. We conducts a user study with 10 participants. The experiment results prove that the MLLM-based agents pre-processing makes generated motion more in line with users' expectation. We believe that the proposed method improves both the fidelity and controllability of motion generation by the diffusion model.

Video-based large language models (Video-LLMs) have been recently introduced, targeting both fundamental improvements in perception and comprehension, and a diverse range of user inquiries. In pursuit of the ultimate goal of achieving artificial general intelligence, a truly intelligent Video-LLM model should not only see and understand the surroundings, but also possess human-level commonsense, and make well-informed decisions for the users. To guide the development of such a model, the establishment of a robust and comprehensive evaluation system becomes crucial. To this end, this paper proposes Video-Bench, a new comprehensive benchmark along with a toolkit specifically designed for evaluating Video-LLMs. The benchmark comprises 10 meticulously crafted tasks, evaluating the capabilities of Video-LLMs across three distinct levels: Video-exclusive Understanding, Prior Knowledge-based Question-Answering, and Comprehension and Decision-making. In addition, we introduce an automatic toolkit tailored to process model outputs for various tasks, facilitating the calculation of metrics and generating convenient final scores. We evaluate 8 representative Video-LLMs using Video-Bench. The findings reveal that current Video-LLMs still fall considerably short of achieving human-like comprehension and analysis of real-world videos, offering valuable insights for future research directions. The benchmark and toolkit are available at: https://github.com/PKU-YuanGroup/Video-Bench.

Emotional dialogue research includes two influential strategy traditions. Empathetic dialogue prioritizes understanding a speaker's emotional experience. Emotional support conversation selects and sequences support for the seeker's current needs. Sustained use introduces a further goal. Effective support should sustain users' capacities for emotion regulation, coping, self-endorsed decisions, and social connection across the interaction lifecycle. We propose capability-sustaining emotional dialogue (CSED) as a longitudinal research paradigm that aligns supportive strategy with this goal and organizes data, models, system design, evaluation, and governance around repeated use, non-use, transition, and termination. A targeted literature-and-corpus audit motivates this position. In a PRISMA-ScR-guided sample, 95% of 60 system-building papers pursue relief-oriented goals. None evaluates capability or longitudinal outcomes, and only 1 considers dependency, autonomy, or termination risk. In 300 ESConv supporter turns, capability-relevant functions appear in 43.0%, while generic suggestions account for 22.0%, compared with 4.0% reappraisal, 6.7% self-efficacy support, and 0.3% boundary behavior. We release a protocol for extending the audit to model behavior. An illustrative process model connects latent user capability to six design commitments, four evaluation timescales, and lifecycle constraints. The resulting agenda makes CSED testable across data, policy design, training, evaluation, and governance.

This paper presents multi- and interdisciplinary approaches for finding the appropriate AI technologies for research information. Professional research information management (RIM) is becoming increasingly important as an expressly data-driven tool for researchers. It is not only the basis of scientific knowledge processes, but also related to other data. A concept and a process model of the elementary phases from the start of the project to the ongoing operation of the AI methods in the RIM is presented, portraying the implementation of an AI project, meant to enable universities and research institutions to support their researchers in dealing with incorrect and incomplete research information, while it is being stored in their RIMs. Our aim is to show how research information harmonizes with the challenges of data literacy and data quality issues, related to AI, also wanting to underline that any project can be successful if the research institutions and various departments of universities, involved work together and appropriate support is offered to improve research information and data management.

Asynchronous events on the continuous time domain, e.g., social media actions and stock transactions, occur frequently in the world. The ability to recognize occurrence patterns of event sequences is crucial to predict which typeof events will happen next and when. A de facto standard mathematical framework to do this is the Hawkes process. In order to enhance expressivity of multivariate Hawkes processes, conventional statistical methods and deep recurrent networks have been employed to modify its intensity function. The former is highly interpretable and requires small size of training data but relies on correct model design while the latter has less dependency on prior knowledge and is more powerful in capturing complicated patterns. We leverage pros and cons of these models and propose a self-attentive Hawkes process(SAHP). The proposed method adapts self-attention to fit the intensity function of Hawkes processes. This design has two benefits:(1) compared with conventional statistical methods, the SAHP is more powerful to identify complicated dependency relationships between temporal events; (2)compared with deep recurrent networks, the self-attention mechanism is able to capture longer historical information, and is more interpretable because the learnt attention weight tensor shows contributions of each historical event. Experiments on four real-world datasets demonstrate the effectiveness of the proposed method.

We present Turn, a compiled, actor-based programming language -- statically typed for schema inference, dynamically typed at the value level -- for agentic software: programs that reason and act autonomously by delegating inference to large language models (LLMs). Existing approaches augment general-purpose languages with frameworks, encoding critical invariants (bounded context, typed inference output, credential isolation, durable state) as application-level conventions rather than language guarantees. Turn introduces five language-level constructs that address this gap. Cognitive Type Safety makes LLM inference a typed primitive: the compiler generates a JSON Schema from a struct definition and the VM validates model output before binding. The confidence operator enables deterministic control flow gated on model certainty. Turn's actor-based process model, derived from Erlang, gives each agent an isolated context window, persistent memory, and mailbox. A capability-based identity system returns opaque, unforgeable handles from the VM host, ensuring raw credentials never enter agent memory. Finally, compile-time schema absorption (use schema::<protocol>) synthesizes typed API bindings from external specifications at compile time; the openapi adapter is shipped with graphql, fhir, and mcp in active development. We describe the language design, type rules, schema semantics, and a Rust-based bytecode VM, and evaluate Turn against representative agentic workloads. Turn is open source at https://github.com/ekizito96/Turn.

Neural processes (NPs) are a class of models that learn stochastic processes directly from data and can be used for inference, sampling and conditional sampling. We introduce a new NP model based on flow matching, a generative modeling paradigm that has demonstrated strong performance on various data modalities. Following the NP training framework, the model provides amortized predictions of conditional distributions over any arbitrary points in the data. Compared to previous NP models, our model is simple to implement and can be used to sample from conditional distributions using an ODE solver, without requiring auxiliary conditioning methods. In addition, the model provides a controllable tradeoff between accuracy and running time via the number of steps in the ODE solver. We show that our model outperforms previous state-of-the-art neural process methods on various benchmarks including synthetic 1D Gaussian processes data, 2D images, and real-world weather data.

Computational efficiency and robustness are essential in process modeling, optimization, and control for real-world engineering applications. While neural network-based approaches have gained significant attention in recent years, conventional neural networks often fail to address these two critical aspects simultaneously or even independently. Inspired by natural physical systems and established literature, input convex architectures are known to enhance computational efficiency in optimization tasks, whereas Lipschitz-constrained architectures improve robustness. However, combining these properties within a single model requires careful review, as inappropriate methods for enforcing one property can undermine the other. To overcome this, we introduce a novel network architecture, termed Input Convex Lipschitz Recurrent Neural Networks (ICLRNNs). This architecture seamlessly integrates the benefits of convexity and Lipschitz continuity, enabling fast and robust neural network-based modeling and optimization. The ICLRNN outperforms existing recurrent units in both computational efficiency and robustness. Additionally, it has been successfully applied to practical engineering scenarios, such as modeling and control of chemical process and the modeling and real-world solar irradiance prediction for solar PV system planning at LHT Holdings in Singapore. Source code is available at https://github.com/killingbear999/ICLRNN.

In this work, we consider the problem of deriving and incorporating accurate dynamic models for model predictive control (MPC) with an application to quadrotor control. MPC relies on precise dynamic models to achieve the desired closed-loop performance. However, the presence of uncertainties in complex systems and the environments they operate in poses a challenge in obtaining sufficiently accurate representations of the system dynamics. In this work, we make use of a deep learning tool, knowledge-based neural ordinary differential equations (KNODE), to augment a model obtained from first principles. The resulting hybrid model encompasses both a nominal first-principle model and a neural network learnt from simulated or real-world experimental data. Using a quadrotor, we benchmark our hybrid model against a state-of-the-art Gaussian Process (GP) model and show that the hybrid model provides more accurate predictions of the quadrotor dynamics and is able to generalize beyond the training data. To improve closed-loop performance, the hybrid model is integrated into a novel MPC framework, known as KNODE-MPC. Results show that the integrated framework achieves 60.2% improvement in simulations and more than 21% in physical experiments, in terms of trajectory tracking performance.

Machine Unlearning (MU) aims to remove target training data from a trained model so that the removed data no longer influences the model's behavior, fulfilling "right to be forgotten" obligations under data privacy laws. Yet, we observe that researchers in this rapidly emerging field face challenges in analyzing and understanding the behavior of different MU methods, especially in terms of three fundamental principles in MU: accuracy, efficiency, and privacy. Consequently, they often rely on aggregate metrics and ad-hoc evaluations, making it difficult to accurately assess the trade-offs between methods. To fill this gap, we introduce a visual analytics system, Unlearning Comparator, designed to facilitate the systematic evaluation of MU methods. Our system supports two important tasks in the evaluation process: model comparison and attack simulation. First, it allows the user to compare the behaviors of two models, such as a model generated by a certain method and a retrained baseline, at class-, instance-, and layer-levels to better understand the changes made after unlearning. Second, our system simulates membership inference attacks (MIAs) to evaluate the privacy of a method, where an attacker attempts to determine whether specific data samples were part of the original training set. We evaluate our system through a case study visually analyzing prominent MU methods and demonstrate that it helps the user not only understand model behaviors but also gain insights that can inform the improvement of MU methods.

Emotion regulation is a crucial element in dealing with emotional events and has positive effects on mental health. This paper aims to provide a more comprehensive understanding of emotional events by introducing a new French corpus of emotional narratives collected using a questionnaire for emotion regulation. We follow the theoretical framework of the Component Process Model which considers emotions as dynamic processes composed of four interrelated components (behavior, feeling, thinking and territory). Each narrative is related to a discrete emotion and is structured based on all emotion components by the writers. We study the interaction of components and their impact on emotion classification with machine learning methods and pre-trained language models. Our results show that each component improves prediction performance, and that the best results are achieved by jointly considering all components. Our results also show the effectiveness of pre-trained language models in predicting discrete emotion from certain components, which reveal differences in how emotion components are expressed.

For decades, classical point process models, such as the epidemic-type aftershock sequence (ETAS) model, have been widely used for forecasting the event times and locations of earthquakes. Recent advances have led to Neural Point Processes (NPPs), which promise greater flexibility and improvements over such classical models. However, the currently-used benchmark for NPPs does not represent an up-to-date challenge in the seismological community, since it contains data leakage and omits the largest earthquake sequence from the region. Additionally, initial earthquake forecasting benchmarks fail to compare NPPs with state-of-the-art forecasting models commonly used in seismology. To address these gaps, we introduce EarthquakeNPP: a benchmarking platform that curates and standardizes existing public resources: globally available earthquake catalogs, the ETAS model, and evaluation protocols from the seismology community. The datasets cover a range of small to large target regions within California, dating from 1971 to 2021, and include different methodologies for dataset generation. Benchmarking experiments, using both log-likelihood and generative evaluation metrics widely recognised in seismology, show that none of the five NPPs tested outperform ETAS. These findings suggest that current NPP implementations are not yet suitable for practical earthquake forecasting. Nonetheless, EarthquakeNPP provides a platform to foster future collaboration between the seismology and machine learning communities.

Weather forecasting is critical for a range of human activities including transportation, agriculture, industry, as well as the safety of the general public. Machine learning models have the potential to transform the complex weather prediction pipeline, but current approaches still rely on numerical weather prediction (NWP) systems, limiting forecast speed and accuracy. Here we demonstrate that a machine learning model can replace the entire operational NWP pipeline. Aardvark Weather, an end-to-end data-driven weather prediction system, ingests raw observations and outputs global gridded forecasts and local station forecasts. Further, it can be optimised end-to-end to maximise performance over quantities of interest. Global forecasts outperform an operational NWP baseline for multiple variables and lead times. Local station forecasts are skillful up to ten days lead time and achieve comparable and often lower errors than a post-processed global NWP baseline and a state-of-the-art end-to-end forecasting system with input from human forecasters. These forecasts are produced with a remarkably simple neural process model using just 8% of the input data and three orders of magnitude less compute than existing NWP and hybrid AI-NWP methods. We anticipate that Aardvark Weather will be the starting point for a new generation of end-to-end machine learning models for medium-range forecasting that will reduce computational costs by orders of magnitude and enable the rapid and cheap creation of bespoke models for users in a variety of fields, including for the developing world where state-of-the-art local models are not currently available.

This paper presents a modeling effort to explore the underlying physics of temperature evolution during additive friction stir deposition (AFSD) by a human-AI teaming approach. AFSD is an emerging solid-state additive manufacturing technology that deposits materials without melting. However, both process modeling and modeling of the AFSD tool are at an early stage. In this paper, a human-AI teaming approach is proposed to combine models based on first principles with AI. The resulting human-informed machine learning method, denoted as AFSD-Physics, can effectively learn the governing equations of temperature evolution at the tool and the build from in-process measurements. Experiments are designed and conducted to collect in-process measurements for the deposition of aluminum 7075 with a total of 30 layers. The acquired governing equations are physically interpretable models with low computational cost and high accuracy. Model predictions show good agreement with the measurements. Experimental validation with new process parameters demonstrates the model's generalizability and potential for use in tool temperature control and process optimization.

Latent Gaussian process (GP) models are widely used in neuroscience to uncover hidden state evolutions from sequential observations, mainly in neural activity recordings. While latent GP models provide a principled and powerful solution in theory, the intractable posterior in non-conjugate settings necessitates approximate inference schemes, which may lack scalability. In this work, we propose cvHM, a general inference framework for latent GP models leveraging Hida-Mat\'ern kernels and conjugate computation variational inference (CVI). With cvHM, we are able to perform variational inference of latent neural trajectories with linear time complexity for arbitrary likelihoods. The reparameterization of stationary kernels using Hida-Mat\'ern GPs helps us connect the latent variable models that encode prior assumptions through dynamical systems to those that encode trajectory assumptions through GPs. In contrast to previous work, we use bidirectional information filtering, leading to a more concise implementation. Furthermore, we employ the Whittle approximate likelihood to achieve highly efficient hyperparameter learning.

Eight percent of global carbon dioxide emissions can be attributed to the production of cement, the main component of concrete, which is also the dominant source of CO2 emissions in the construction of data centers. The discovery of lower-carbon concrete formulae is therefore of high significance for sustainability. However, experimenting with new concrete formulae is time consuming and labor intensive, as one usually has to wait to record the concrete's 28-day compressive strength, a quantity whose measurement can by its definition not be accelerated. This provides an opportunity for experimental design methodology like Bayesian Optimization (BO) to accelerate the search for strong and sustainable concrete formulae. Herein, we 1) propose modeling steps that make concrete strength amenable to be predicted accurately by a Gaussian process model with relatively few measurements, 2) formulate the search for sustainable concrete as a multi-objective optimization problem, and 3) leverage the proposed model to carry out multi-objective BO with real-world strength measurements of the algorithmically proposed mixes. Our experimental results show improved trade-offs between the mixtures' global warming potential (GWP) and their associated compressive strengths, compared to mixes based on current industry practices. Our methods are open-sourced at github.com/facebookresearch/SustainableConcrete.

Active learning is able to reduce the amount of labelling effort by using a machine learning model to query the user for specific inputs. While there are many papers on new active learning techniques, these techniques rarely satisfy the constraints of a real-world project. In this paper, we analyse the main drawbacks of current active learning techniques and we present approaches to alleviate them. We do a systematic study on the effects of the most common issues of real-world datasets on the deep active learning process: model convergence, annotation error, and dataset imbalance. We derive two techniques that can speed up the active learning loop such as partial uncertainty sampling and larger query size. Finally, we present our open-source Bayesian active learning library, BaaL.

Flowcharts are indispensable tools in software design and business-process analysis, yet current vision-language models (VLMs) frequently misinterpret the directional arrows and graph topology that set these diagrams apart from natural images. We introduce a seven-stage pipeline grouped into three broader processes: (1) arrow-aware detection of nodes and arrow endpoints; (2) optical character recognition (OCR) to extract node text; and (3) construction of a structured prompt that guides the VLMs. Tested on a 90-question benchmark distilled from 30 annotated flowcharts, the method raises overall accuracy from 80 % to 89 % (+9 percentage points) without any task-specific fine-tuning. The gain is most pronounced for next-step queries (25/30 -> 30/30; 100 %, +17 pp); branch-result questions improve more modestly, and before-step questions remain difficult. A parallel evaluation with an LLM-as-a-Judge protocol shows the same trends, reinforcing the advantage of explicit arrow encoding. Limitations include dependence on detector and OCR precision, the small evaluation set, and residual errors at nodes with multiple incoming edges. Future work will enlarge the benchmark with synthetic and handwritten flowcharts and assess the approach on Business Process Model and Notation (BPMN) and Unified Modeling Language (UML).

Existing benchmarks for scientific data analysis evaluate LLMs primarily on code execution or workflow completion, overlooking that scientific analysis serves to support distinct types of scientific claims: hypothesis exploration, statistical inference, mechanistic explanation, each with different assumptions and validity criteria. We introduce SDABench, a benchmark that reorganizes evaluation around six capabilities (descriptive, exploratory, inferential, predictive, causal, and mechanistic) across five domains (Biology, Chemistry, Environment, Geography, Physics). SDABench comprises 527 real-data instances (SDA-Real) and 6000 synthetic instances (SDA-Synth), each in both multiple-choice and open-ended formats, constructed through an automated pipeline. Evaluating 15 representative LLMs, we find that models handle descriptive analysis well but degrade sharply on tasks requiring assumption selection, latent-process modeling, or mechanistic reasoning. SDABench further provides a five-stage error analysis framework that locates where LLMs fail: more advanced models more reliably identify the relevant scope and variables, but still struggle to select appropriate analytical procedures, model variable relationships, and draw valid conclusions.

Assessing learner competency in clinical simulation requires expert observation that is time-intensive, difficult to scale, and subject to inter-rater variability. Vision-language models have emerged as a promising tool for understanding complex visual behavior. In this work, we investigate whether visual observations can provide educationally meaningful signals for competency assessment through a three-stage framework that (1) extracts action timelines from egocentric nursing simulation video using frozen visual encoders and few-shot learning, (2) derives sequence-level features and per-session recognition metrics, and (3) relates these to instructor-rated competency. Across 22 densely annotated sessions (3.8 hours, 493 actions), a frozen DINOv2 backbone with HMM Viterbi decoding achieves 57.4% MOF in leave-one-out 1-shot recognition. Surprisingly, we observe a negative trend between recognition accuracy and competency (rho = -0.524, p = 0.012 for mIoU), robust to six confound controls: more competent students produce diverse, harder-to-classify workflows, while simple sequence features show no such relationship. Per-item analysis identifies patient safety protocols and team communication as the expected behaviors most reflected in this pattern, and process model comparisons reveal that higher-competency students exhibit more protocol-consistent action transitions. These findings suggest that recognition accuracy may complement predicted action timelines as a pedagogically informative signal in automated competency assessment.

3D Gaussian Splatting has emerged as an efficient photorealistic novel view synthesis method. However, its reliance on sparse Structure-from-Motion (SfM) point clouds consistently compromises the scene reconstruction quality. To address these limitations, this paper proposes a novel 3D reconstruction framework Gaussian Processes Gaussian Splatting (GP-GS), where a multi-output Gaussian Process model is developed to achieve adaptive and uncertainty-guided densification of sparse SfM point clouds. Specifically, we propose a dynamic sampling and filtering pipeline that adaptively expands the SfM point clouds by leveraging GP-based predictions to infer new candidate points from the input 2D pixels and depth maps. The pipeline utilizes uncertainty estimates to guide the pruning of high-variance predictions, ensuring geometric consistency and enabling the generation of dense point clouds. The densified point clouds provide high-quality initial 3D Gaussians to enhance reconstruction performance. Extensive experiments conducted on synthetic and real-world datasets across various scales validate the effectiveness and practicality of the proposed framework.

Generating synthetic data through generative models is gaining interest in the ML community and beyond, promising a future where datasets can be tailored to individual needs. Unfortunately, synthetic data is usually not perfect, resulting in potential errors in downstream tasks. In this work we explore how the generative process affects the downstream ML task. We show that the naive synthetic data approach -- using synthetic data as if it is real -- leads to downstream models and analyses that do not generalize well to real data. As a first step towards better ML in the synthetic data regime, we introduce Deep Generative Ensemble (DGE) -- a framework inspired by Deep Ensembles that aims to implicitly approximate the posterior distribution over the generative process model parameters. DGE improves downstream model training, evaluation, and uncertainty quantification, vastly outperforming the naive approach on average. The largest improvements are achieved for minority classes and low-density regions of the original data, for which the generative uncertainty is largest.

Large language models (LLMs) are probabilistic in nature and perform more reliably when augmented with external information. As complex queries often require multi-step reasoning over the retrieved information, with no clear or predetermined reasoning path, they remain challenging. Recent approaches train models using reinforcement learning on the model's outcome, showing promise in improving how models handle complex information. We introduce SubSearch, a specialized framework that shifts from outcome-only supervision to intermediate reward signals that incentivize planning high-quality reasoning. Unlike previous work on process reward modeling, which focuses on training a separate reward model with annotated trajectories by either human annotators or large LLM judges, SubSearch directly optimizes the generator using intrinsic process rewards, which we define as internally-derived rewards, eliminating the need for external supervision, and moving towards autonomous information-intensive reasoning. Experiments on seven benchmarks show that rewarding intermediate reasoning steps with intrinsic rewards leads to more robust reasoning traces in both QA and multi-hop QA datasets over using only outcome rewards. SubSearch can help in building reasoning traces that allow agents to better integrate search engines for complex query answering, while offering a data-efficient alternative to supervised process modeling.

Integrated autoregressive conditional duration (ACD) models serve as natural counterparts to the well-known integrated GARCH models used for financial returns. However, despite their resemblance, asymptotic theory for ACD is challenging and also not complete, in particular for integrated ACD. Central challenges arise from the facts that (i) integrated ACD processes imply durations with infinite expectation, and (ii) even in the non-integrated case, conventional asymptotic approaches break down due to the randomness in the number of durations within a fixed observation period. Addressing these challenges, we provide here unified asymptotic theory for the (quasi-) maximum likelihood estimator for ACD models; a unified theory which includes integrated ACD models. Based on the new results, we also provide a novel framework for hypothesis testing in duration models, enabling inference on a key empirical question: whether durations possess a finite or infinite expectation. We apply our results to high-frequency cryptocurrency ETF trading data. Motivated by parameter estimates near the integrated ACD boundary, we assess whether durations between trades in these markets have finite expectation, an assumption often made implicitly in the literature on point process models. Our empirical findings indicate infinite-mean durations for all the five cryptocurrencies examined, with the integrated ACD hypothesis rejected -- against alternatives with tail index less than one -- for four out of the five cryptocurrencies considered.

Pretext training followed by task-specific fine-tuning has been a successful approach in vision and language domains. This paper proposes a self-supervised pretext training framework tailored to event sequence data. We introduce a novel alignment verification task that is specialized to event sequences, building on good practices in masked reconstruction and contrastive learning. Our pretext tasks unlock foundational representations that are generalizable across different down-stream tasks, including next-event prediction for temporal point process models, event sequence classification, and missing event interpolation. Experiments on popular public benchmarks demonstrate the potential of the proposed method across different tasks and data domains.

Continuous-time event sequences play a vital role in real-world domains such as healthcare, finance, online shopping, social networks, and so on. To model such data, temporal point processes (TPPs) have emerged as the most natural and competitive models, making a significant impact in both academic and application communities. Despite the emergence of many powerful models in recent years, there hasn't been a central benchmark for these models and future research endeavors. This lack of standardization impedes researchers and practitioners from comparing methods and reproducing results, potentially slowing down progress in this field. In this paper, we present EasyTPP, the first central repository of research assets (e.g., data, models, evaluation programs, documentations) in the area of event sequence modeling. Our EasyTPP makes several unique contributions to this area: a unified interface of using existing datasets and adding new datasets; a wide range of evaluation programs that are easy to use and extend as well as facilitate reproducible research; implementations of popular neural TPPs, together with a rich library of modules by composing which one could quickly build complex models. All the data and implementation can be found at https://github.com/ant-research/EasyTemporalPointProcess. We will actively maintain this benchmark and welcome contributions from other researchers and practitioners. Our benchmark will help promote reproducible research in this field, thus accelerating research progress as well as making more significant real-world impacts.

Conditional Neural Processes (CNPs) are a class of metalearning models popular for combining the runtime efficiency of amortized inference with reliable uncertainty quantification. Many relevant machine learning tasks, such as in spatio-temporal modeling, Bayesian Optimization and continuous control, inherently contain equivariances -- for example to translation -- which the model can exploit for maximal performance. However, prior attempts to include equivariances in CNPs do not scale effectively beyond two input dimensions. In this work, we propose Relational Conditional Neural Processes (RCNPs), an effective approach to incorporate equivariances into any neural process model. Our proposed method extends the applicability and impact of equivariant neural processes to higher dimensions. We empirically demonstrate the competitive performance of RCNPs on a large array of tasks naturally containing equivariances.

We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning probability measures to the spatial domain, which allows us to treat collocation grids probabilistically as random variables to be marginalised out. Adapting this spatial statistics view, we solve forward and inverse problems for parametric PDEs in a way that leads to the construction of Gaussian process models of solution fields. The implementation of these random grids poses a unique set of challenges for inverse physics informed deep learning frameworks and we propose a new architecture called Grid Invariant Convolutional Networks (GICNets) to overcome these challenges. We further show how to incorporate noisy data in a principled manner into our physics informed model to improve predictions for problems where data may be available but whose measurement location does not coincide with any fixed mesh or grid. The proposed method is tested on a nonlinear Poisson problem, Burgers equation, and Navier-Stokes equations, and we provide extensive numerical comparisons. We demonstrate significant computational advantages over current physics informed neural learning methods for parametric PDEs while improving the predictive capabilities and flexibility of these 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.

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.

Process Reward Models (PRMs) have emerged as a promising framework for supervising intermediate reasoning in large language models (LLMs), yet existing PRMs are primarily trained on general or Science, Technology, Engineering, and Mathematics (STEM) domains and fall short in domain-specific contexts such as finance, where reasoning is more structured, symbolic, and sensitive to factual and regulatory correctness. We introduce Fin-PRM, a domain-specialized, trajectory-aware PRM tailored to evaluate intermediate reasoning steps in financial tasks. Fin-PRM integrates step-level and trajectory-level reward supervision, enabling fine-grained evaluation of reasoning traces aligned with financial logic. We apply Fin-PRM in both offline and online reward learning settings, supporting three key applications: (i) selecting high-quality reasoning trajectories for distillation-based supervised fine-tuning, (ii) providing dense process-level rewards for reinforcement learning, and (iii) guiding reward-informed Best-of-N inference at test time. Experimental results on financial reasoning benchmarks, including CFLUE and FinQA, demonstrate that Fin-PRM consistently outperforms general-purpose PRMs and strong domain baselines in trajectory selection quality. Downstream models trained with Fin-PRM yield substantial improvements with baselines, with gains of 12.9\% in supervised learning, 5.2\% in reinforcement learning, and 5.1\% in test-time performance. These findings highlight the value of domain-specialized reward modeling for aligning LLMs with expert-level financial reasoning. Our project resources will be available at https://github.com/aliyun/qwen-dianjin.

Process reward models (PRMs) have proven effective for test-time scaling of Large Language Models (LLMs) on challenging reasoning tasks. However, reward hacking issues with PRMs limit their successful application in reinforcement fine-tuning. In this paper, we identify the main cause of PRM-induced reward hacking: the canonical summation-form credit assignment in reinforcement learning (RL), which defines the value as cumulative gamma-decayed future rewards, easily induces LLMs to hack steps with high rewards. To address this, we propose PURE: Process sUpervised Reinforcement lEarning. The key innovation of PURE is a min-form credit assignment that formulates the value function as the minimum of future rewards. This method significantly alleviates reward hacking by limiting the value function range and distributing advantages more reasonably. Through extensive experiments on 3 base models, we show that PRM-based approaches enabling min-form credit assignment achieve comparable reasoning performance to verifiable reward-based methods within only 30% steps. In contrast, the canonical sum-form credit assignment collapses training even at the beginning! Additionally, when we supplement PRM-based fine-tuning with just 10% verifiable rewards, we further alleviate reward hacking and produce the best fine-tuned model based on Qwen2.5-Math-7B in our experiments, achieving 82.5% accuracy on AMC23 and 53.3% average accuracy across 5 benchmarks. Moreover, we summarize the observed reward hacking cases and analyze the causes of training collapse. Code and models are available at https://github.com/CJReinforce/PURE.

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 GR-Ben, a process-level benchmark specifically designed for assessing PRM's performance across two primary reasoning domains (science and logic) 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, PRMs are less adept at identifying knowledge-based errors, whereas LLMs exhibit poorer performance in detecting computational errors. We hope GR-Ben can foster future researches on PRMs for general domains, thereby enhancing the reasoning capabilities of LLMs.

Process Reward Model (PRM) is widely used in the post-training of Large Language Model (LLM) because it can perform fine-grained evaluation of the reasoning steps of generated content. However, most PRMs lack long-term reasoning and deep thinking capabilities. On the other hand, although a few works have tried to introduce Chain-of-Thought capability into PRMs, the annotation cost of CoT-PRM data is too expensive to play a stable role in various tasks. To address the above challenges, we propose VRPRM, a process reward model via visual reasoning, and design an efficient two-stage training strategy. Experimental results show that using only 3.6K CoT-PRM SFT data and 50K non-CoT PRM RL training data, VRPRM can surpass the non-thinking PRM with a total data volume of 400K and achieved a relative performance improvement of up to 118\% over the base model in the BoN experiment. This result confirms that the proposed combined training strategy can achieve higher quality reasoning capabilities at a lower data annotation cost, thus providing a new paradigm for PRM training with more efficient data utilization.

Process Reward Models (PRMs) have emerged as a promising approach to enhance the reasoning quality of Large Language Models (LLMs) by assigning fine-grained scores to intermediate reasoning steps within a solution trajectory. However, existing PRMs predominantly adopt a unidirectional left-to-right (L2R) evaluation paradigm, which limits their ability to leverage global context, making it challenging to verify the consistency of earlier steps based on later ones. In light of these challenges, we propose a novel bidirectional evaluation paradigm, named Bidirectional Process Reward Model (BiPRM). BiPRM seamlessly incorporates a parallel right-to-left (R2L) evaluation stream alongside the conventional L2R flow, enabling later reasoning steps to help assess earlier ones in real time. Notably, the built-in R2L evaluation is implemented solely through prompt modifications that reverse the original reasoning trajectory, without any additional parameters or inference latency introduced. This ensures BiPRM remains both efficient and broadly compatible with existing PRM studies. We conduct extensive experiments on two mathematical reasoning benchmarks using samples generated by three different policy models. Our method, BiPRM, is evaluated across three backbones and three distinct PRM objectives. Across all settings, BiPRM consistently outperforms unidirectional baselines, achieving up to a 31.9% improvement in stepwise reward evaluation. Generally, our results highlight BiPRM's effectiveness, robustness, and general applicability, offering a promising new direction for process-based reward modeling.

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.

We introduce Agent Process Reward Models (AgentPRM), a simple and scalable framework for training LLM agents to continually improve through interactions. AgentPRM follows a lightweight actor-critic paradigm, using Monte Carlo rollouts to compute reward targets and optimize policies. It requires minimal modifications to existing RLHF pipelines, making it easy to integrate at scale. Beyond AgentPRM, we propose InversePRM, which learns process rewards directly from demonstrations without explicit outcome supervision. We also explore key challenges and opportunities, including exploration, process reward shaping, and model-predictive reasoning. We evaluate on ALFWorld benchmark, show that small 3B models trained with AgentPRM and InversePRM outperform strong GPT-4o baselines, and analyze test-time scaling, reward hacking, and more. Our code is available at: https://github.com/sanjibanc/agent_prm.

Process Reward Models (PRMs) have proven effective at enhancing mathematical reasoning for Large Language Models (LLMs) by leveraging increased inference-time computation. However, they are predominantly trained on mathematical data and their generalizability to non-mathematical domains has not been rigorously studied. In response, this work first shows that current PRMs have poor performance in other domains. To address this limitation, we introduce VersaPRM, a multi-domain PRM trained on synthetic reasoning data generated using our novel data generation and annotation method. VersaPRM achieves consistent performance gains across diverse domains. For instance, in the MMLU-Pro category of Law, VersaPRM via weighted majority voting, achieves a 7.9% performance gain over the majority voting baseline -- surpassing Qwen2.5-Math-PRM's gain of 1.3%. We further contribute to the community by open-sourcing all data, code and models for VersaPRM.

Process Reward Modeling (PRM) is critical for complex reasoning and decision-making tasks where the accuracy of intermediate steps significantly influences the overall outcome. Existing PRM approaches, primarily framed as classification problems, employ cross-entropy loss to independently evaluate each step's correctness. This method can lead to suboptimal reward distribution and does not adequately address the interdependencies among steps. To address these limitations, we introduce the Process Q-value Model (PQM), a novel framework that redefines PRM in the context of a Markov Decision Process. PQM optimizes Q-value rankings based on a novel comparative loss function, enhancing the model's ability to capture the intricate dynamics among sequential decisions. This approach provides a more granular and theoretically grounded methodology for process rewards. Our extensive empirical evaluations across various sampling policies, language model backbones, and multi-step reasoning benchmarks show that PQM outperforms classification-based PRMs. The effectiveness of the comparative loss function is highlighted in our comprehensive ablation studies, confirming PQM's practical efficacy and theoretical advantage.

Process Reward Models (PRMs) emerge as a promising approach for process supervision in mathematical reasoning of Large Language Models (LLMs), which aim to identify and mitigate intermediate errors in the reasoning processes. However, the development of effective PRMs faces significant challenges, particularly in data annotation and evaluation methodologies. In this paper, through extensive experiments, we demonstrate that commonly used Monte Carlo (MC) estimation-based data synthesis for PRMs typically yields inferior performance and generalization compared to LLM-as-a-judge and human annotation methods. MC estimation relies on completion models to evaluate current-step correctness, leading to inaccurate step verification. Furthermore, we identify potential biases in conventional Best-of-N (BoN) evaluation strategies for PRMs: (1) The unreliable policy models generate responses with correct answers but flawed processes, leading to a misalignment between the evaluation criteria of BoN and the PRM objectives of process verification. (2) The tolerance of PRMs of such responses leads to inflated BoN scores. (3) Existing PRMs have a significant proportion of minimum scores concentrated on the final answer steps, revealing the shift from process to outcome-based assessment in BoN Optimized PRMs. To address these challenges, we develop a consensus filtering mechanism that effectively integrates MC estimation with LLM-as-a-judge and advocates a more comprehensive evaluation framework that combines response-level and step-level metrics. Based on the mechanisms, we significantly improve both model performance and data efficiency in the BoN evaluation and the step-wise error identification task. Finally, we release a new state-of-the-art PRM that outperforms existing open-source alternatives and provides practical guidelines for future research in building process supervision models.

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.

Step-by-step verifiers -- also known as process reward models (PRMs) -- are a key ingredient for test-time scaling. PRMs require step-level supervision, making them expensive to train. This work aims to build data-efficient PRMs as verbalized step-wise reward models that verify every step in the solution by generating a verification chain-of-thought (CoT). We propose ThinkPRM, a long CoT verifier fine-tuned on orders of magnitude fewer process labels than those required by discriminative PRMs. Our approach capitalizes on the inherent reasoning abilities of long CoT models, and outperforms LLM-as-a-Judge and discriminative verifiers -- using only 1% of the process labels in PRM800K -- across several challenging benchmarks. Specifically, ThinkPRM beats the baselines on ProcessBench, MATH-500, and AIME '24 under best-of-N selection and reward-guided search. In an out-of-domain evaluation on a subset of GPQA-Diamond and LiveCodeBench, our PRM surpasses discriminative verifiers trained on the full PRM800K by 8% and 4.5%, respectively. Lastly, under the same token budget, ThinkPRM scales up verification compute more effectively compared to LLM-as-a-Judge, outperforming it by 7.2% on a subset of ProcessBench. Our work highlights the value of generative, long CoT PRMs that can scale test-time compute for verification while requiring minimal supervision for training. Our code, data, and models will be released at https://github.com/mukhal/thinkprm.

Process Reward Models (PRMs) provide step-level supervision that improves the reliability of reasoning in large language models. While PRMs have been extensively studied in text-based domains, their extension to Vision Language Models (VLMs) remains limited. Existing Vision-Language PRMs (VL-PRMs) rely on Monte Carlo Tree Search (MCTS) for data construction, which can often produce noisy supervision signals and limit generalization across tasks. In this work, we aim to elucidate the design space of VL-PRMs by exploring diverse strategies for dataset construction, training, and test-time scaling. First, we introduce a hybrid data synthesis framework that combines MCTS with judgments from a strong VLM, producing more accurate step-level labels. Second, we propose perception-focused supervision, enabling our PRM to explicitly detect errors at the visual grounding stage of reasoning. Third, we systematically evaluate multiple test-time scaling strategies, showing that our PRMs can reliably guide VLMs toward more accurate solutions. Our experiments covering five diverse multimodal benchmarks (MMMU, PuzzleVQA, AlgoPuzzleVQA, MathVista, and MathVision) reveal several key insights: (i) VL-PRMs when used as Outcome Reward Models (ORMs) during test-time scaling (TTS) can outperform VL-PRM guided process step selection, (ii) smaller VL-PRMs can match or even surpass larger ones in detecting process errors, (iii) VL-PRMs uncover latent reasoning abilities in stronger VLM backbones, (iv) perception-level supervision leads to significant gains in test-time scaling, and (v) TTS performance of different policies improve on advanced math reasoning datasets despite not training VL-PRMs on such datasets. We hope our work will motivate further research and support the advancement of VLMs.

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.

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

Process Reward Models (PRMs) are crucial for guiding Large Language Models (LLMs) in complex scenarios by providing dense reward signals. However, existing PRMs primarily rely on heuristic approaches, which struggle with cross-domain generalization. While LLM-as-judge has been proposed to provide generalized rewards, current research has focused mainly on feedback results, overlooking the meaningful guidance embedded within the text. Additionally, static and coarse-grained evaluation criteria struggle to adapt to complex process supervision. To tackle these challenges, we propose Dynamic and Generalizable Process Reward Modeling (DG-PRM), which features a reward tree to capture and store fine-grained, multi-dimensional reward criteria. DG-PRM dynamically selects reward signals for step-wise reward scoring. To handle multifaceted reward signals, we pioneeringly adopt Pareto dominance estimation to identify discriminative positive and negative pairs. Experimental results show that DG-PRM achieves stunning performance on prevailing benchmarks, significantly boosting model performance across tasks with dense rewards. Further analysis reveals that DG-PRM adapts well to out-of-distribution scenarios, demonstrating exceptional generalizability.

Process reward models (PRMs) play a central role in guiding inference-time scaling algorithms for large language models (LLMs). However, we observe that even state-of-the-art PRMs can be poorly calibrated and often overestimate success probabilities. To address this, we present a calibration approach, performed via quantile regression, that adjusts PRM outputs to better align with true success probabilities. Leveraging these calibrated success estimates and their associated confidence bounds, we introduce an instance-adaptive scaling (IAS) framework that dynamically adjusts the inference budget based on the estimated likelihood that a partial reasoning trajectory will yield a correct final answer. Unlike conventional methods that allocate a fixed number of reasoning trajectories per query, this approach successfully adapts to each instance and reasoning step when using our calibrated PRMs. Experiments on mathematical reasoning benchmarks show that (i) our PRM calibration method successfully achieves small calibration error, outperforming the baseline methods, (ii) calibration is crucial for enabling effective adaptive scaling, and (iii) the proposed IAS strategy reduces inference costs while maintaining final answer accuracy, utilizing less compute on more confident problems as desired.

Process Reward Models (PRMs) are crucial in complex reasoning and problem-solving tasks (e.g., LLM agents with long-horizon decision-making) by verifying the correctness of each intermediate reasoning step. In real-world scenarios, LLMs may apply various reasoning patterns (e.g., decomposition) to solve a problem, potentially suffering from errors under various reasoning patterns. Therefore, PRMs are required to identify errors under various reasoning patterns during the reasoning process. However, existing benchmarks mainly focus on evaluating PRMs with stepwise correctness, ignoring a systematic evaluation of PRMs under various reasoning patterns. To mitigate this gap, we introduce Socratic-PRMBench, a new benchmark to evaluate PRMs systematically under six reasoning patterns, including Transformation, Decomposition, Regather, Deduction, Verification, and Integration. Socratic-PRMBench}comprises 2995 reasoning paths with flaws within the aforementioned six reasoning patterns. Through our experiments on both PRMs and LLMs prompted as critic models, we identify notable deficiencies in existing PRMs. These observations underscore the significant weakness of current PRMs in conducting evaluations on reasoning steps under various reasoning patterns. We hope Socratic-PRMBench can serve as a comprehensive testbed for systematic evaluation of PRMs under diverse reasoning patterns and pave the way for future development of PRMs.

Large language models (LLMs) inevitably make mistakes when performing step-by-step mathematical reasoning. Process Reward Models (PRMs) have emerged as a promising solution by evaluating each reasoning step. However, existing PRMs typically output evaluation scores directly, limiting both learning efficiency and evaluation accuracy, which is further exacerbated by the scarcity of annotated data. To address these issues, we propose Reasoning-Driven Process Reward Modeling (R-PRM). First, we leverage stronger LLMs to generate seed data from limited annotations, effectively bootstrapping our model's reasoning capabilities and enabling comprehensive step-by-step evaluation. Second, we further enhance performance through preference optimization, without requiring additional annotated data. Third, we introduce inference-time scaling to fully harness the model's reasoning potential. Extensive experiments demonstrate R-PRM's effectiveness: on ProcessBench and PRMBench, it surpasses strong baselines by 11.9 and 8.5 points in F1 scores, respectively. When applied to guide mathematical reasoning, R-PRM achieves consistent accuracy improvements of over 8.5 points across six challenging datasets. Further analysis reveals that R-PRM exhibits more comprehensive evaluation and stronger generalization capabilities, thereby highlighting its significant potential.

We introduce VisualPRM, an advanced multimodal Process Reward Model (PRM) with 8B parameters, which improves the reasoning abilities of existing Multimodal Large Language Models (MLLMs) across different model scales and families with Best-of-N (BoN) evaluation strategies. Specifically, our model improves the reasoning performance of three types of MLLMs and four different model scales. Even when applied to the highly capable InternVL2.5-78B, it achieves a 5.9-point improvement across seven multimodal reasoning benchmarks. Experimental results show that our model exhibits superior performance compared to Outcome Reward Models and Self-Consistency during BoN evaluation. To facilitate the training of multimodal PRMs, we construct a multimodal process supervision dataset VisualPRM400K using an automated data pipeline. For the evaluation of multimodal PRMs, we propose VisualProcessBench, a benchmark with human-annotated step-wise correctness labels, to measure the abilities of PRMs to detect erroneous steps in multimodal reasoning tasks. We hope that our work can inspire more future research and contribute to the development of MLLMs. Our model, data, and benchmark are released in https://internvl.github.io/blog/2025-03-13-VisualPRM/.

Process-supervised reward models serve as a fine-grained function that provides detailed step-wise feedback to model responses, facilitating effective selection of reasoning trajectories for complex tasks. Despite its advantages, evaluation on PRMs remains less explored, especially in the multimodal domain. To address this gap, this paper first benchmarks current vision large language models (VLLMs) as two types of reward models: output reward models (ORMs) and process reward models (PRMs) on multiple vision-language benchmarks, which reveal that neither ORM nor PRM consistently outperforms across all tasks, and superior VLLMs do not necessarily yield better rewarding performance. To further advance evaluation, we introduce ViLBench, a vision-language benchmark designed to require intensive process reward signals. Notably, OpenAI's GPT-4o with Chain-of-Thought (CoT) achieves only 27.3% accuracy, indicating the benchmark's challenge for current VLLMs. Lastly, we preliminarily showcase a promising pathway towards bridging the gap between general VLLMs and reward models -- by collecting 73.6K vision-language process reward data using an enhanced tree-search algorithm, our 3B model is able to achieve an average improvement of 3.3% over standard CoT and up to 2.5% compared to its untrained counterpart on ViLBench by selecting OpenAI o1's generations. We release the implementations at https://ucsc-vlaa.github.io/ViLBench with our code, model, and data.

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.

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.

Large language models (LLMs) have shown strong performance in many reasoning benchmarks. However, recent studies have pointed to memorization, rather than generalization, as one of the leading causes for such performance. LLMs, in fact, are susceptible to content variations, demonstrating a lack of robust planning or symbolic abstractions supporting their reasoning process. To improve reliability, many attempts have been made to combine LLMs with symbolic methods. Nevertheless, existing approaches fail to effectively leverage symbolic representations due to the challenges involved in developing reliable and scalable verification mechanisms. In this paper, we propose to overcome such limitations by synthesizing high-quality symbolic reasoning trajectories with stepwise pseudo-labels at scale via Monte Carlo estimation. A Process Reward Model (PRM) can be efficiently trained based on the synthesized data and then used to select more symbolic trajectories. The trajectories are then employed with Direct Preference Optimization (DPO) and Supervised Fine-Tuning (SFT) to improve logical reasoning and generalization. Our results on benchmarks (i.e., FOLIO and LogicAsker) show the effectiveness of the proposed method with gains on frontier and open-weight models. Moreover, additional experiments on claim verification data reveal that fine-tuning on the generated symbolic reasoning trajectories enhances out-of-domain generalizability, suggesting the potential impact of the proposed method in enhancing planning and logical reasoning.

Large language models (LLMs) have shown promise in performing complex multi-step reasoning, yet they continue to struggle with mathematical reasoning, often making systematic errors. A promising solution is reinforcement learning (RL) guided by reward models, particularly those focusing on process rewards, which score each intermediate step rather than solely evaluating the final outcome. This approach is more effective at guiding policy models towards correct reasoning trajectories. In this work, we propose an entropy-regularized process reward model (ER-PRM) that integrates KL-regularized Markov Decision Processes (MDP) to balance policy optimization with the need to prevent the policy from shifting too far from its initial distribution. We derive a novel reward construction method based on the theoretical results. Our theoretical analysis shows that we could derive the optimal reward model from the initial policy sampling. Our empirical experiments on the MATH and GSM8K benchmarks demonstrate that ER-PRM consistently outperforms existing process reward models, achieving 1% improvement on GSM8K and 2-3% improvement on MATH under best-of-N evaluation, and more than 1% improvement under RLHF. These results highlight the efficacy of entropy-regularization in enhancing LLMs' reasoning capabilities.

Multimodal Large Language Models (MLLMs) demonstrate remarkable capabilities but often struggle with complex, multi-step mathematical reasoning, where minor errors in visual perception or logical deduction can lead to complete failure. While Process Reward Models (PRMs) offer step-by-step supervision, existing multimodal PRMs are limited to being binary verifiers that can identify but not correct errors, offering little explanatory power. To address these deficiencies, we introduce the Generative Multimodal Process Reward Model (GM-PRM), a novel paradigm that transforms the PRM from a passive judge into an active reasoning collaborator. Instead of a simple scalar score, GM-PRM provides a fine-grained, interpretable analysis of each reasoning step, evaluating its step intent, visual alignment, and logical soundness. More critically, GM-PRM is trained to generate a corrected version of the first erroneous step it identifies. This unique corrective capability enables our new test-time inference strategy, Refined Best-of-N (Refined-BoN). This framework actively enhances solution quality by using the PRM's generated correction to guide the policy model toward a more promising reasoning trajectory, thereby improving the diversity and correctness of the solution pool. We demonstrate that GM-PRM achieves state-of-the-art results on multiple multimodal math benchmarks, significantly boosting policy model performance with remarkable data efficiency, requiring only a 20K-sample training dataset. Our code will be released upon acceptance.

Multimodal Process Reward Models (MPRMs) are central to step-level supervision for visual reasoning in MLLMs. Training MPRMs typically requires large-scale Monte Carlo (MC)-annotated corpora, incurring substantial training cost. This paper studies the data efficiency for MPRM training.Our preliminary experiments reveal that MPRM training quickly saturates under random subsampling of the training data, indicating substantial redundancy within existing MC-annotated corpora.To explain this, we formalize a theoretical framework and reveal that informative gradient updates depend on two factors: label mixtures of positive/negative steps and label reliability (average MC scores of positive steps). Guided by these insights, we propose the Balanced-Information Score (BIS), which prioritizes both mixture and reliability based on existing MC signals at the rollout level, without incurring any additional cost. Across two backbones (InternVL2.5-8B and Qwen2.5-VL-7B) on VisualProcessBench, BIS-selected subsets consistently match and even surpass the full-data performance at small fractions. Notably, the BIS subset reaches full-data performance using only 10% of the training data, improving over random subsampling by a relative 4.1%.

Recent work on reinforcement learning with verifiable rewards (RLVR) has shown that large language models (LLMs) can be substantially improved using outcome-level verification signals, such as unit tests for code or exact-match checks for mathematics. In parallel, process supervision has long been explored as a way to shape the intermediate reasoning behaviour of LLMs, but existing approaches rely on neural judges to score chain-of-thought steps, leaving them vulnerable to opacity, bias, and reward hacking. To address this gap, we introduce Verifiable Process Reward Models (VPRMs), a reinforcement-learning framework in which intermediate reasoning steps are checked by deterministic, rule-based verifiers. We apply VPRMs to risk-of-bias assessment for medical evidence synthesis, a domain where guideline-defined criteria and rule-based decision paths enable programmatic verification of reasoning traces. Across multiple datasets, we find that VPRMs generate reasoning that adheres closely to domain rules and achieve substantially higher coherence between step-level decisions and final labels. Results show that VPRMs achieve up to 20% higher F1 than state-of-the-art models and 6.5% higher than verifiable outcome rewards, with substantial gains in evidence grounding and logical coherence.

We study how Large Language Models (LLMs) process negation mechanistically. First, we establish that even though open-weight models often provide wrong answers to questions involving negation, they do possess internal components that process negation correctly. Their poor accuracy is due to late-layer attention behavior that promotes simple shortcuts; ablating those attention modules greatly improves accuracy on negation-related questions. Second, we uncover how models process negation. We consider two hypotheses: models could use attention heads that attend to the phrase being negated and suppress related concepts, or they could directly construct a representation of the entire negative phrase (e.g., representing "not gas" as a vector that promotes liquids and solids). We apply a range of observational and causal interpretability techniques on Mistral-7B and Llama-3.1-8B to show that models implement both mechanisms, with the "constructive" mechanism being more prominent. Combined, our work deepens the understanding of LLMs' internals, highlighting construction-dominant computations and the coexistence of competing mechanisms within LLMs.

Large language models (LLMs) are designed to perform a wide range of tasks. To improve their ability to solve complex problems requiring multi-step reasoning, recent research leverages process reward modeling to provide fine-grained feedback at each step of the reasoning process for reinforcement learning (RL), but it predominantly focuses on English. In this paper, we tackle the critical challenge of extending process reward models (PRMs) to multilingual settings. To achieve this, we train multilingual PRMs on a dataset spanning seven languages, which is translated from English. Through comprehensive evaluations on two widely used reasoning benchmarks across 11 languages, we demonstrate that multilingual PRMs not only improve average accuracy but also reduce early-stage reasoning errors. Furthermore, our results highlight the sensitivity of multilingual PRMs to both the number of training languages and the volume of English data, while also uncovering the benefits arising from more candidate responses and trainable parameters. This work opens promising avenues for robust multilingual applications in complex, multi-step reasoning tasks. In addition, we release the code to foster research along this line.

DEEPTHINK methods improve reasoning by generating, refining, and aggregating populations of candidate solutions, which enables strong performance on complex mathematical and scientific tasks. However, existing frameworks often lack reliable correctness signals during inference, which creates a population-enhancement bottleneck where deeper deliberation amplifies errors, suppresses correct minority solutions, and yields weak returns to additional compute. In this paper, we introduce a functional decomposition of DEEPTHINK systems and propose PRISM, a Process Reward Model (PRM)-guided inference algorithm that uses step-level verification to guide both population refinement and solution aggregation. During refinement, PRISM treats candidate solutions as particles in a PRM-defined energy landscape and reshapes the population through score-guided resampling and stochastic refinement, which concentrates probability mass on higher-quality reasoning while preserving diversity. Across mathematics and science benchmarks, PRISM is competitive with or outperforms existing DEEPTHINK methods, reaching 90.0%, 75.4%, and 71.4% with gpt-oss-20b on AIME25, HMMT25, and GPQA Diamond, respectively, while matching or exceeding gpt-oss-120b. Additionally, our analysis shows that PRISM produces consistent net-directional correction during refinement, remains reliable when the initial population contains few correct candidates, and often lies on the compute-accuracy Pareto frontier.

The primary obstacle for applying reinforcement learning (RL) to real-world robotics is the design of effective reward functions. While recently learning-based Process Reward Models (PRMs) are a promising direction, they are often hindered by two fundamental limitations: their reward models lack step-aware understanding and rely on single-view perception, leading to unreliable assessments of fine-grained manipulation progress; and their reward shaping procedures are theoretically unsound, often inducing a semantic trap that misguides policy optimization. To address these, we introduce Dopamine-Reward, a novel reward modeling method for learning a general-purpose, step-aware process reward model from multi-view inputs. At its core is our General Reward Model (GRM), trained on a vast 3,400+ hour dataset, which leverages Step-wise Reward Discretization for structural understanding and Multi-Perspective Reward Fusion to overcome perceptual limitations. Building upon Dopamine-Reward, we propose Dopamine-RL, a robust policy learning framework that employs a theoretically-sound Policy-Invariant Reward Shaping method, which enables the agent to leverage dense rewards for efficient self-improvement without altering the optimal policy, thereby fundamentally avoiding the semantic trap. Extensive experiments across diverse simulated and real-world tasks validate our approach. GRM achieves state-of-the-art accuracy in reward assessment, and Dopamine-RL built on GRM significantly improves policy learning efficiency. For instance, after GRM is adapted to a new task in a one-shot manner from a single expert trajectory, the resulting reward model enables Dopamine-RL to improve the policy from near-zero to 95% success with only 150 online rollouts (approximately 1 hour of real robot interaction), while retaining strong generalization across tasks. Project website: https://robo-dopamine.github.io

Training multimodal process reward models (PRMs) is challenged by distribution shifts and noisy data. We introduce DreamPRM-1.5, an instance-reweighted framework that adaptively adjusts the importance of each training example via bi-level optimization. We design two complementary strategies: Instance Table, effective for smaller datasets, and Instance Net, scalable to larger ones. Integrated into test-time scaling, DreamPRM-1.5 achieves 84.6 accuracy on the MMMU benchmark, surpassing GPT-5.

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.

Reasoning has improved the performance of large language models (LLMs) on complicated tasks. Central to the current reasoning studies, Process Reward Models (PRMs) offer a fine-grained evaluation of intermediate reasoning steps and guide the reasoning process. However, extending PRMs to multimodal large language models (MLLMs) introduces challenges. Since multimodal reasoning covers a wider range of tasks compared to text-only scenarios, the resulting distribution shift from the training to testing sets is more severe, leading to greater generalization difficulty. Training a reliable multimodal PRM, therefore, demands large and diverse datasets to ensure sufficient coverage. However, current multimodal reasoning datasets suffer from quality imbalance, which degrades PRM performance and highlights the need for data selection strategy. To address the issues, we introduce DreamPRM, a domain-reweighted training framework for multimodal PRMs which employs bi-level optimization. In the lower-level optimization, DreamPRM performs fine-tuning on multiple datasets with domain weights, allowing the PRM to prioritize high-quality reasoning signals and alleviating the impact of dataset quality imbalance. In the upper-level optimization, the PRM is evaluated on a separate meta-learning dataset; this feedback updates the domain weights through an aggregation loss function, thereby improving the generalization capability of trained PRM. Extensive experiments on multiple multimodal reasoning benchmarks covering both mathematical and general reasoning show that test-time scaling with DreamPRM consistently improves performance of state-of-the-art MLLMs. Further comparisons reveal that DreamPRM's domain-reweighting strategy surpasses data selection methods and yields higher accuracy gains than existing test-time scaling approaches. Codes are available at https://github.com/coder-qicao/DreamPRM.

Recent advances in language models have demonstrated their capability to solve mathematical reasoning problems, achieving near-perfect accuracy on grade-school level math benchmarks like GSM8K. In this paper, we formally study how language models solve these problems. We design a series of controlled experiments to address several fundamental questions: (1) Can language models truly develop reasoning skills, or do they simply memorize templates? (2) What is the model's hidden (mental) reasoning process? (3) Do models solve math questions using skills similar to or different from humans? (4) Do models trained on GSM8K-like datasets develop reasoning skills beyond those necessary for solving GSM8K problems? (5) What mental process causes models to make reasoning mistakes? (6) How large or deep must a model be to effectively solve GSM8K-level math questions? Our study uncovers many hidden mechanisms by which language models solve mathematical questions, providing insights that extend beyond current understandings of LLMs.

Large Language Models (LLMs) are prone to hallucination, especially during multi-hop and reasoning-intensive tasks such as mathematical problem solving. While Outcome Reward Models verify only final answers, Process Reward Models (PRMs) score each intermediate step to steer generation toward coherent solutions. We introduce PathFinder-PRM, a novel hierarchical, error-aware discriminative PRM that first classifies math and consistency errors at each step, then combines these fine-grained signals to estimate step correctness. To train PathFinder-PRM, we construct a 400K-sample dataset by enriching the human-annotated PRM800K corpus and RLHFlow Mistral traces with three-dimensional step-level labels. On PRMBench, PathFinder-PRM achieves a new state-of-the-art PRMScore of 67.7, outperforming the prior best (65.5) while using 3 times less data. When applied to reward guided greedy search, our model yields prm@8 48.3, a +1.5 point gain over the strongest baseline. These results demonstrate that decoupled error detection and reward estimation not only boost fine-grained error detection but also substantially improve end-to-end, reward-guided mathematical reasoning with greater data efficiency.

Vision-language process reward models (VL-PRMs) are increasingly used to score intermediate reasoning steps and rerank candidates under test-time scaling. However, they often function as black-box judges: a low step score may reflect a genuine reasoning mistake or simply the verifier's misperception of the image. This entanglement between perception and reasoning leads to systematic false positives (rewarding hallucinated visual premises) and false negatives (penalizing correct grounded statements), undermining both reranking and error localization. We introduce Explicit Visual Premise Verification (EVPV), a lightweight verification interface that conditions step scoring on the reliability of the visual premises a step depends on. The policy is prompted to produce a step-wise visual checklist that makes required visual facts explicit, while a constraint extractor independently derives structured visual constraints from the input image. EVPV matches checklist claims against these constraints to compute a scalar visual reliability signal, and calibrates PRM step rewards via reliability gating: rewards for visually dependent steps are attenuated when reliability is low and preserved when reliability is high. This decouples perceptual uncertainty from logical evaluation without per-step tool calls. Experiments on VisualProcessBench and six multimodal reasoning benchmarks show that EVPV improves step-level verification and consistently boosts Best-of-N reranking accuracy over strong baselines. Furthermore, injecting controlled corruption into the extracted constraints produces monotonic performance degradation, providing causal evidence that the gains arise from constraint fidelity and explicit premise verification rather than incidental prompt effects. Code is available at: https://github.com/Qwen-Applications/EVPV-PRM

Modern language models can imitate complex patterns through few-shot learning, enabling them to complete challenging tasks without fine-tuning. However, imitation can also lead models to reproduce inaccuracies or harmful content if present in the context. We study harmful imitation through the lens of a model's internal representations, and identify two related phenomena: "overthinking" and "false induction heads". The first phenomenon, overthinking, appears when we decode predictions from intermediate layers, given correct vs. incorrect few-shot demonstrations. At early layers, both demonstrations induce similar model behavior, but the behavior diverges sharply at some "critical layer", after which the accuracy given incorrect demonstrations progressively decreases. The second phenomenon, false induction heads, are a possible mechanistic cause of overthinking: these are heads in late layers that attend to and copy false information from previous demonstrations, and whose ablation reduces overthinking. Beyond scientific understanding, our results suggest that studying intermediate model computations could be a promising avenue for understanding and guarding against harmful model behaviors.

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

We prove theoretically that the GRPO RL algorithm induces a non-trivial process reward model (PRM), under certain assumptions regarding within-group overlap of token sequences across completions. We then show empirically that these assumptions are met under real-world conditions: GRPO does in fact induce a non-trivial PRM. Leveraging the framework of GRPO-as-a-PRM, we identify a flaw in the GRPO objective: non-uniformly distributed process steps hinder both exploration and exploitation (under different conditions). We propose a simple modification to the algorithm to mitigate this defect (lambda-GRPO), and show that LLMs trained with lambda-GRPO achieve higher validation accuracy and performance on downstream reasoning tasks-and reach peak performance more rapidly-than LLMs trained with standard GRPO. Our results call into question the advantage of costly, explicitly-defined PRMs for GRPO: we show that it is possible to instead leverage the hidden, built-in PRM structure within the vanilla GRPO algorithm to boost model performance with a negligible impact on training time and cost.

Code generation is a core application of large language models (LLMs), yet LLMs still frequently fail on complex programming tasks. Given its success in mathematical reasoning, test-time scaling approaches such as Process Reward Model (PRM)-based Best-of-N selection offer a promising way to improve performance. However, existing PRMs remain ineffective for code generation due to the lack of meaningful step decomposition in code and the noise of Monte Carlo-estimated partial-solution correctness scores (rewards). To address these challenges, we propose FunPRM. FunPRM prompts LLMs to encourage modular code generation organized into functions, with functions treated as PRM reasoning steps. Furthermore, FunPRM introduces a novel meta-learning-based reward correction mechanism that leverages clean final-solution rewards obtained via a unit-test-based evaluation system to purify noisy partial-solution rewards. Experiments on LiveCodeBench and BigCodeBench demonstrate that FunPRM consistently outperforms existing test-time scaling methods across five base LLMs, notably achieving state-of-the-art performance on LiveCodeBench when combined with O4-mini. Furthermore, FunPRM produces code that is more readable and reusable for developers.

Reward-guided search methods have demonstrated strong potential in enhancing tool-using agents by effectively guiding sampling and exploration over complex action spaces. As a core design, those search methods utilize process reward models (PRMs) to provide step-level rewards, enabling more fine-grained monitoring. However, there is a lack of systematic and reliable evaluation benchmarks for PRMs in tool-using settings. In this paper, we introduce ToolPRMBench, a large-scale benchmark specifically designed to evaluate PRMs for tool-using agents. ToolPRMBench is built on top of several representative tool-using benchmarks and converts agent trajectories into step-level test cases. Each case contains the interaction history, a correct action, a plausible but incorrect alternative, and relevant tool metadata. We respectively utilize offline sampling to isolate local single-step errors and online sampling to capture realistic multi-step failures from full agent rollouts. A multi-LLM verification pipeline is proposed to reduce label noise and ensure data quality. We conduct extensive experiments across large language models, general PRMs, and tool-specialized PRMs on ToolPRMBench. The results reveal clear differences in PRM effectiveness and highlight the potential of specialized PRMs for tool-using. Code and data will be released at https://github.com/David-Li0406/ToolPRMBench.

Recent advancements in Large Language Models (LLMs) have shown that it is promising to utilize Process Reward Models (PRMs) as verifiers to enhance the performance of LLMs. However, current PRMs face three key challenges: (1) limited process supervision and generalization capabilities, (2) dependence on scalar value prediction without leveraging the generative abilities of LLMs, and (3) inability to scale the test-time compute of PRMs. In this work, we introduce GenPRM, a generative process reward model that performs explicit Chain-of-Thought (CoT) reasoning with code verification before providing judgment for each reasoning step. To obtain high-quality process supervision labels and rationale data, we propose Relative Progress Estimation (RPE) and a rationale synthesis framework that incorporates code verification. Experimental results on ProcessBench and several mathematical reasoning tasks show that GenPRM significantly outperforms prior PRMs with only 23K training data from MATH dataset. Through test-time scaling, a 1.5B GenPRM outperforms GPT-4o, and a 7B GenPRM surpasses Qwen2.5-Math-PRM-72B on ProcessBench. Additionally, GenPRM demonstrates strong abilities to serve as a critic model for policy model refinement. This work establishes a new paradigm for process supervision that bridges the gap between PRMs and critic models in LLMs. Our code, model, and data will be available in https://ryanliu112.github.io/GenPRM.

Complex multi-step reasoning tasks, such as solving mathematical problems or generating code, remain a significant hurdle for even the most advanced large language models (LLMs). Verifying LLM outputs with an Outcome Reward Model (ORM) is a standard inference-time technique aimed at enhancing the reasoning performance of LLMs. However, this still proves insufficient for reasoning tasks with a lengthy or multi-hop reasoning chain, where the intermediate outcomes are neither properly rewarded nor penalized. Process supervision addresses this limitation by assigning intermediate rewards during the reasoning process. To date, the methods used to collect process supervision data have relied on either human annotation or per-step Monte Carlo estimation, both prohibitively expensive to scale, thus hindering the broad application of this technique. In response to this challenge, we propose a novel divide-and-conquer style Monte Carlo Tree Search (MCTS) algorithm named OmegaPRM for the efficient collection of high-quality process supervision data. This algorithm swiftly identifies the first error in the Chain of Thought (CoT) with binary search and balances the positive and negative examples, thereby ensuring both efficiency and quality. As a result, we are able to collect over 1.5 million process supervision annotations to train a Process Reward Model (PRM). Utilizing this fully automated process supervision alongside the weighted self-consistency algorithm, we have enhanced the instruction tuned Gemini Pro model's math reasoning performance, achieving a 69.4\% success rate on the MATH benchmark, a 36\% relative improvement from the 51\% base model performance. Additionally, the entire process operates without any human intervention, making our method both financially and computationally cost-effective compared to existing methods.

Web agents hold great potential for automating complex computer tasks, yet their interactions involve long-horizon, sequential decision-making with irreversible actions. In such settings, outcome-based supervision is sparse and delayed, often rewarding incorrect trajectories and failing to support inference-time scaling. This motivates the use of Process Reward Models (WebPRMs) for web navigation, but existing approaches remain limited: scalar WebPRMs collapse progress into coarse, weakly grounded signals, while checklist-based WebPRMs rely on brittle template matching that fails under layout or semantic changes and often mislabels superficially correct actions as successful, providing little insight or interpretability. To address these challenges, we introduce WebArbiter, a reasoning-first, principle-inducing WebPRM that formulates reward modeling as text generation, producing structured justifications that conclude with a preference verdict and identify the action most conducive to task completion under the current context. Training follows a two-stage pipeline: reasoning distillation equips the model with coherent principle-guided reasoning, and reinforcement learning corrects teacher biases by directly aligning verdicts with correctness, enabling stronger generalization. To support systematic evaluation, we release WebPRMBench, a comprehensive benchmark spanning four diverse web environments with rich tasks and high-quality preference annotations. On WebPRMBench, WebArbiter-7B outperforms the strongest baseline, GPT-5, by 9.1 points. In reward-guided trajectory search on WebArena-Lite, it surpasses the best prior WebPRM by up to 7.2 points, underscoring its robustness and practical value in real-world complex web tasks.

The reasoning capabilities of advanced large language models (LLMs) like o1 have revolutionized artificial intelligence applications. Nevertheless, evaluating and optimizing complex reasoning processes remain significant challenges due to diverse policy distributions and the inherent limitations of human effort and accuracy. In this paper, we present AURORA, a novel automated framework for training universal process reward models (PRMs) using ensemble prompting and reverse verification. The framework employs a two-phase approach: First, it uses diverse prompting strategies and ensemble methods to perform automated annotation and evaluation of processes, ensuring robust assessments for reward learning. Second, it leverages practical reference answers for reverse verification, enhancing the model's ability to validate outputs and improving training accuracy. To assess the framework's performance, we extend beyond the existing ProcessBench benchmark by introducing UniversalBench, which evaluates reward predictions across full trajectories under diverse policy distribtion with long Chain-of-Thought (CoT) outputs. Experimental results demonstrate that AURORA enhances process evaluation accuracy, improves PRMs' accuracy for diverse policy distributions and long-CoT responses. The project will be open-sourced at https://auroraprm.github.io/. The Universal-PRM-7B is available at https://huggingface.co/infly/Universal-PRM-7B.

Vision-language-action (VLA) models aim to understand natural language instructions and visual observations and to execute corresponding actions as an embodied agent. Recent work integrates future images into the understanding-acting loop, yielding unified VLAs that jointly understand, generate, and act -- reading text and images and producing future images and actions. However, these models either rely on external experts for modality unification or treat image generation and action prediction as separate processes, limiting the benefits of direct synergy between these tasks. Our core philosophy is to optimize generation and action jointly through a synchronous denoising process, where the iterative refinement enables actions to evolve from initialization, under constant and sufficient visual guidance. We ground this philosophy in our proposed Unified Diffusion VLA and Joint Discrete Denoising Diffusion Process (JD3P), which is a joint diffusion process that integrates multiple modalities into a single denoising trajectory to serve as the key mechanism enabling understanding, generation, and acting to be intrinsically synergistic. Our model and theory are built on a unified tokenized space of all modalities and a hybrid attention mechanism. We further propose a two-stage training pipeline and several inference-time techniques that optimize performance and efficiency. Our approach achieves state-of-the-art performance on benchmarks such as CALVIN, LIBERO, and SimplerEnv with 4times faster inference than autoregressive methods, and we demonstrate its effectiveness through in-depth analysis and real-world evaluations. Our project page is available at https://irpn-eai.github.io/UD-VLA.github.io/.

Large language models have shown promise in clinical decision making, but current approaches struggle to localize and correct errors at specific steps of the reasoning process. This limitation is critical in medicine, where identifying and addressing reasoning errors is essential for accurate diagnosis and effective patient care. We introduce Med-PRM, a process reward modeling framework that leverages retrieval-augmented generation to verify each reasoning step against established medical knowledge bases. By verifying intermediate reasoning steps with evidence retrieved from clinical guidelines and literature, our model can precisely assess the reasoning quality in a fine-grained manner. Evaluations on five medical QA benchmarks and two open-ended diagnostic tasks demonstrate that Med-PRM achieves state-of-the-art performance, with improving the performance of base models by up to 13.50% using Med-PRM. Moreover, we demonstrate the generality of Med-PRM by integrating it in a plug-and-play fashion with strong policy models such as Meerkat, achieving over 80\% accuracy on MedQA for the first time using small-scale models of 8 billion parameters. Our code and data are available at: https://med-prm.github.io/

Small language models (SLMs) are more efficient, cost-effective, and customizable than large language models (LLMs), though they often underperform in specific areas like reasoning. Past methods for enhancing SLMs' reasoning, such as supervised fine-tuning and distillation, often depend on costly external signals, resulting in SLMs being overly confident with limited supervision signals, thus limiting their abilities. Therefore, this study enables SLMs to learn to reason from self-iterative feedback. By combining odds ratio preference optimization (ORPO), we fine-tune and align SLMs using positive and negative signals generated by themselves. Additionally, we introduce process supervision for rewards in preference alignment by sampling-based inference simulation and process reward models. Compared to Supervised Fine-Tuning (SFT), our method improves the performance of Gemma-2B by 12.43 (Acc) on GSM8K and 3.95 (Pass@1) on MBPP. Furthermore, the proposed method also demonstrated superior out-of-domain generalization capabilities on MMLU_Math and HumanEval.

Large Language Models (LLMs) have shown promising capabilities for solving Operations Research (OR) problems. While reinforcement learning serves as a powerful paradigm for LLM training on OR problems, existing works generally face two key limitations. First, outcome reward suffers from the credit assignment problem, where correct final answers can reinforce flawed reasoning. Second, conventional discriminative process supervision is myopic, failing to evaluate the interdependent steps of OR modeling holistically. To this end, we introduce StepORLM, a novel self-evolving framework with generative process supervision. At its core, StepORLM features a co-evolutionary loop where a policy model and a generative process reward model (GenPRM) iteratively improve on each other. This loop is driven by a dual-feedback mechanism: definitive, outcome-based verification from an external solver, and nuanced, holistic process evaluation from the GenPRM. The combined signal is used to align the policy via Weighted Direct Preference Optimization (W-DPO) and simultaneously refine the GenPRM. Our resulting 8B-parameter StepORLM establishes a new state-of-the-art across six benchmarks, significantly outperforming vastly larger generalist models, agentic methods, and specialized baselines. Moreover, the co-evolved GenPRM is able to act as a powerful and universally applicable process verifier, substantially boosting the inference scaling performance of both our own model and other existing LLMs.

Resolving real-world software engineering (SWE) issues with autonomous agents requires complex, long-horizon reasoning. Current pipelines are bottlenecked by unoptimized demonstration data, sparse execution rewards, and computationally prohibitive inference scaling, which collectively exacerbate token bloat, reward hacking, and policy degradation. We present SWE-TRACE (Trajectory Reduction and Agentic Criteria Evaluation), a unified framework optimizing the SWE agent lifecycle across data curation, reinforcement learning (RL), and test-time inference. First, we introduce an LLM multi-task cascading method, utilizing stepwise oracle verification to distill a 60K-instance Supervised Fine-Tuning (SFT) corpus strictly biased toward token-efficient, shortest-path trajectories. Second, to overcome the instability of sparse outcome rewards, we design a MemoryAugmented Agentic RL pipeline featuring a Rubric-Based Process Reward Model (PRM). An auxiliary Rubric-Agent provides dense, fine-grained heuristic feedback on intermediate steps, guiding the model through long-horizon tasks. Finally, we bridge training and inference by repurposing the PRM for heuristic-guided Test-Time Scaling (TTS). By dynamically evaluating and pruning action candidates at each step, SWE-TRACE achieves superior search efficiency without the latency overhead of standard parallel sampling. Extensive experiments on standard SWE benchmarks demonstrate that SWE-TRACE significantly advances the state-of-the-art, maximizing resolution rates while drastically reducing both token consumption and inference latency.

Process Reward Models (PRMs) provide step-level feedback for reasoning, but current PRMs usually output only a single reward score for each step. Downstream methods must therefore treat imperfect step-level reward predictions as reliable decision signals, with no indication of when these predictions should be trusted. We propose BetaPRM, a distributional PRM that predicts both a step-level success probability and the reliability of that prediction. Given step-success supervision from Monte Carlo continuations, BetaPRM learns a Beta belief that explains the observed number of successful continuations through a Beta-Binomial likelihood, rather than regressing to the finite-sample success ratio as a point target. This learned reliability signal indicates when a step reward should be trusted, enabling downstream applications to distinguish reliable rewards from uncertain ones. As one application, we introduce Adaptive Computation Allocation (ACA) for PRM-guided Best-of-N reasoning. ACA uses the learned reliability signal to stop when a high-reward solution is reliable and to spend additional computation on uncertain candidate prefixes. Experiments across four backbones and four reasoning benchmarks show that BetaPRM improves PRM-guided Best-of-N selection while preserving standard step-level error detection. Built on this signal, ACA improves the accuracy--token tradeoff over fixed-budget Best-of-16, reducing token usage by up to 33.57% while improving final-answer accuracy.

Process reward models (PRMs) that provide dense, step-level feedback have shown promise for reinforcement learning, yet their adoption remains limited by the need for expensive step-level annotations or ground truth references. We propose SPARK: a three-stage framework where in the first stage a generator model produces diverse solutions and a verifier model evaluates them using parallel scaling (self-consistency) and sequential scaling (meta-critique). In the second stage, we use these verification outputs as synthetic training data to fine-tune generative process reward models, which subsequently serve as reward signals during training. We show that aggregating multiple independent verifications at the step level produces training data for process reward models that surpass ground-truth outcome supervision, achieving 67.5 F1 on ProcessBench (a benchmark for identifying erroneous steps in mathematical reasoning) compared to 66.4 for reference-guided training and 61.9 for GPT-4o. In the final stage, we apply our generative PRM with chain-of-thought verification (PRM-CoT) as the reward model in RL experiments on mathematical reasoning, and introduce format constraints to prevent reward hacking. Using Qwen2.5-Math-7B, we achieve 47.4% average accuracy across six mathematical reasoning benchmarks, outperforming ground-truth-based RLVR (43.9%). Our work enables reference-free RL training that exceeds ground-truth methods, opening new possibilities for domains lacking verifiable answers or accessible ground truth.

Reinforcement learning (RL) has emerged as a powerful framework for improving the reasoning capabilities of large language models (LLMs). However, most existing RL approaches rely on sparse outcome rewards, which fail to credit correct intermediate steps in partially successful solutions. Process reward models (PRMs) offer fine-grained step-level supervision, but their scores are often noisy and difficult to evaluate. As a result, recent PRM benchmarks focus on a more objective capability: detecting the first incorrect step in a reasoning path. However, this evaluation target is misaligned with how PRMs are typically used in RL, where their step-wise scores are treated as raw rewards to maximize. To bridge this gap, we propose Verifiable Prefix Policy Optimization (VPPO), which uses PRMs only to localize the first error during RL. Given an incorrect rollout, VPPO partitions the trajectory into a verified correct prefix and an erroneous suffix based on the first error, rewarding the former while applying targeted penalties only after the detected mistake. This design yields stable, interpretable learning signals and improves credit assignment. Across multiple reasoning benchmarks, VPPO consistently outperforms sparse-reward RL and prior PRM-guided baselines on both Pass@1 and Pass@K.

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. To improve a base policy by running search against a PRM or using it as dense rewards for reinforcement learning (RL), we ask: "How should we design process rewards?". Our key insight is that, to be effective, the process reward for a step should measure progress: a change in the likelihood of producing a correct response in the future, before and after taking the step, corresponding to the notion of step-level advantages in RL. Crucially, this progress should be measured under a prover policy distinct from the base policy. We theoretically characterize the set of good provers and our results show that optimizing process rewards from such provers improves exploration during test-time search and online RL. In fact, our characterization shows that weak prover policies can substantially improve a stronger base policy, which we also observe empirically. We validate our claims by training process advantage verifiers (PAVs) to predict progress under such provers, and show that compared to ORMs, test-time search against PAVs is >8% more accurate, and 1.5-5times more compute-efficient. Online RL with dense rewards from PAVs enables one of the first results with 5-6times gain in sample efficiency, and >6% gain in accuracy, over ORMs.

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.

Reinforcement Learning (RL) with unit test feedback has enhanced large language models (LLMs) code generation, but relies on sparse rewards provided only after complete code evaluation, limiting learning efficiency and incremental improvements. When generated code fails all unit tests, no learning signal is received, hindering progress on complex tasks. To address this, we propose a Process Reward Model (PRM) that delivers dense, line-level feedback on code correctness during generation, mimicking human code refinement and providing immediate guidance. We explore various strategies for training PRMs and integrating them into the RL framework, finding that using PRMs both as dense rewards and for value function initialization significantly boosts performance. Our approach increases our in-house LLM's pass rate from 28.2% to 29.8% on LiveCodeBench and from 31.8% to 35.8% on our internal benchmark. Our experimental results highlight the effectiveness of PRMs in enhancing RL-driven code generation, especially for long-horizon scenarios.

Recent advancements in Large Language Models (LLMs) have significantly enhanced their ability to process long contexts, yet a notable gap remains in generating long, aligned outputs. This limitation stems from a training gap where pre-training lacks effective instructions for long-text generation, and post-training data primarily consists of short query-response pairs. Current approaches, such as instruction backtranslation and behavior imitation, face challenges including data quality, copyright issues, and constraints on proprietary model usage. In this paper, we introduce an innovative iterative training framework called Self-Lengthen that leverages only the intrinsic knowledge and skills of LLMs without the need for auxiliary data or proprietary models. The framework consists of two roles: the Generator and the Extender. The Generator produces the initial response, which is then split and expanded by the Extender. This process results in a new, longer response, which is used to train both the Generator and the Extender iteratively. Through this process, the models are progressively trained to handle increasingly longer responses. Experiments on benchmarks and human evaluations show that Self-Lengthen outperforms existing methods in long-text generation, when applied to top open-source LLMs such as Qwen2 and LLaMA3. Our code is publicly available at https://github.com/QwenLM/Self-Lengthen.

Information-seeking is a core capability for AI agents, requiring them to gather and reason over tool-generated information across long trajectories. However, such multi-step information-seeking tasks remain challenging for agents backed by language models. While process reward models (PRMs) can guide agents by ranking candidate steps at test-time, existing PRMs, designed for short reasoning with binary judgment, cannot capture richer dimensions of information-seeking steps, such as tool interactions and reasoning over tool outputs, nor handle the rapidly growing context in long-horizon tasks. To address these limitations, we introduce PRInTS, a generative PRM trained with dual capabilities: (1) dense scoring based on the PRM's reasoning across multiple step quality dimensions (e.g., interpretation of tool outputs, tool call informativeness) and (2) trajectory summarization that compresses the growing context while preserving essential information for step evaluation. Extensive evaluations across FRAMES, GAIA (levels 1-3), and WebWalkerQA (easy-hard) benchmarks on multiple models, along with ablations, reveal that best-of-n sampling with PRInTS enhances information-seeking abilities of open-source models as well as specialized agents, matching or surpassing the performance of frontier models with a much smaller backbone agent and outperforming other strong reward modeling baselines.

Different from its counterpart outcome reward models (ORMs), which evaluate the entire responses, a process reward model (PRM) scores a reasoning trajectory step by step, providing denser and more fine grained rewards. However, training a PRM requires labels annotated at every intermediate step, presenting significant challenges for both manual and automatic data collection. This paper aims to address this challenge. Both theoretically and empirically, we show that an implicit PRM can be obtained at no additional cost, by simply training an ORM on the cheaper response-level labels. The only assumption is to parameterize the outcome reward as the log-likelihood ratios of the policy and reference models, which can be optimized regardless of the specific choice of loss objectives. In experiments, we instantiate our implicit PRMs with various objectives and evaluate their performance on MATH. We show that our implicit PRM outperforms a strong MCTS-based baseline \'a la Math-Shepherd using less than 1/38 of the training data. Its performance can be further improved with majority voting. We further find that scaling up instructions and responses benefits our implicit PRM, and the latter brings a larger gain. Particularly, we find that our implicit PRM, when instantiated with the cross-entropy (CE) loss, is more data-efficient and can keep improving generation models even when trained with only one response per instruction, the setup that suffers from extreme data scarcity and imbalance. Further, instructions should be relevant to downstream tasks while the diversity of responses does not bring gains. Surprisingly, training on extra Math-Shepherd step labels brings no further improvements to our implicit PRM trained on only outcome data. We hope that our work will encourage a rethinking of PRM training approaches and contribute to making training PRMs more accessible.

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.