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Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in rare event simulation. In this article, we discuss the asymptotic efficiency of a self-normalized importance sampler of the tilted distribution. We provide a sharp characterization of its accuracy, given the number of samples and the degree of tilt. Our findings reveal a surprising dichotomy: while the number of samples needed to accurately tilt a bounded random vector increases polynomially in the tilt amount, it increases at a super polynomial rate for unbounded distributions.

Automating radiology report generation with Large Vision-Language Models (LVLMs) holds great potential, yet these models often produce clinically critical hallucinations, posing serious risks. Existing hallucination detection methods frequently lack the necessary sentence-level granularity or robust generalization across different LVLM generators. We introduce a novel approach: a sentence-level Process Reward Model (PRM) adapted for this vision-language task. Our PRM predicts the factual correctness of each generated sentence, conditioned on clinical context and preceding text. When fine-tuned on MIMIC-CXR with weakly-supervised labels, a lightweight 0.5B-parameter PRM outperforms existing verification techniques, demonstrating, for instance, relative improvements of 7.5% in Matthews Correlation Coefficient and 1.8% in AUROC over strong white-box baselines on outputs from one LVLM. Unlike methods reliant on internal model states, our PRM demonstrates strong generalization to an unseen LVLM. We further show its practical utility: PRM scores effectively filter low-quality reports, improving F1-CheXbert scores by 4.5% (when discarding the worst 10% of reports). Moreover, when guiding a novel weighted best-of-N selection process on the MIMIC-CXR test set, our PRM show relative improvements in clinical metrics of 7.4% for F1-CheXbert and 0.6% for BERTScore. These results demonstrate that a lightweight, context-aware PRM provides a model-agnostic safety layer for clinical LVLMs without access to internal activations

Reinforcement learning (RL) algorithms struggle with learning optimal policies for tasks where reward feedback is sparse and depends on a complex sequence of events in the environment. Probabilistic reward machines (PRMs) are finite-state formalisms that can capture temporal dependencies in the reward signal, along with nondeterministic task outcomes. While special RL algorithms can exploit this finite-state structure to expedite learning, PRMs remain difficult to modify and design by hand. This hinders the already difficult tasks of utilizing high-level causal knowledge about the environment, and transferring the reward formalism into a new domain with a different causal structure. This paper proposes a novel method to incorporate causal information in the form of Temporal Logic-based Causal Diagrams into the reward formalism, thereby expediting policy learning and aiding the transfer of task specifications to new environments. Furthermore, we provide a theoretical result about convergence to optimal policy for our method, and demonstrate its strengths empirically.

Vision-Language-Action (VLA) models have become a prominent paradigm for embodied intelligence, yet further performance improvements typically rely on scaling up training data and model size -- an approach that is prohibitively expensive for robotics and fundamentally limited by data collection costs. We address this limitation with $\mathbf{RoVer}$, an embodied test-time scaling framework that uses a $\mathbf{Ro}$bot Process Reward Model (PRM) as a Test-Time $\mathbf{Ver}$ifier to enhance the capabilities of existing VLA models without modifying their architectures or weights. Specifically, RoVer (i) assigns scalar-based process rewards to evaluate the reliability of candidate actions, and (ii) predicts an action-space direction for candidate expansion/refinement. During inference, RoVer generates multiple candidate actions concurrently from the base policy, expands them along PRM-predicted directions, and then scores all candidates with PRM to select the optimal action for execution. Notably, by caching shared perception features, it can amortize perception cost and evaluate more candidates under the same test-time computational budget. Essentially, our approach effectively transforms available computing resources into better action decision-making, realizing the benefits of test-time scaling without extra training overhead. Our contributions are threefold: (1) a general, plug-and-play test-time scaling framework for VLAs; (2) a PRM that jointly provides scalar process rewards and an action-space direction to guide exploration; and (3) an efficient direction-guided sampling strategy that leverages a shared perception cache to enable scalable candidate generation and selection during inference.

Achieving both accuracy and diverse reasoning remains challenging for Large Language Models (LLMs) in complex domains like mathematics. A key bottleneck is evaluating intermediate reasoning steps to guide generation without costly human annotations. To address this, we first introduce a novel Process Reward Model (PRM) trained automatically using Monte Carlo Tree Search coupled with a similarity-based data augmentation technique, effectively capturing step-level reasoning quality. Leveraging this PRM, we then adapt Generative Flow Networks (GFlowNets) to operate at the reasoning step level. Unlike traditional reinforcement learning focused on maximizing a single reward, GFlowNets naturally sample diverse, high-quality solutions proportional to their rewards, as measured by our PRM. Empirical evaluation shows strong improvements in both accuracy and solution diversity on challenging mathematical benchmarks (e.g., +2.59% absolute accuracy on MATH Level 5 for Llama3.2-3B), with effective generalization to unseen datasets (+9.4\% absolute on SAT MATH). Furthermore, we benchmark our PRM against existing open-source reward models, demonstrating superior alignment with reasoning quality and more consistent guidance for downstream generation. Our work demonstrates the potential of PRM-guided, step-level GFlowNets for developing more robust and versatile mathematical reasoning in LLMs.

Inference scaling helps LLMs solve complex reasoning problems through extended runtime computation. On top of long chain-of-thought (long-CoT) models, purely inference-time techniques such as best-of-N (BoN) sampling, majority voting, or more generally, minimum Bayes risk decoding (MBRD), can further improve LLM accuracy by generating multiple candidate solutions and aggregating over them. These methods typically leverage additional signals in the form of reward models and risk/similarity functions that compare generated samples, e.g., exact match in some normalized space or standard similarity metrics such as Rouge. Here we present a novel method for incorporating reward and risk/similarity signals into MBRD. Based on the concept of optimal policy in KL-controlled reinforcement learning, our framework provides a simple and well-defined mechanism for leveraging such signals, offering several advantages over traditional inference-time methods: higher robustness, improved accuracy, and well-understood asymptotic behavior. In addition, it allows for the development of a sample-efficient variant of MBRD that can adjust the number of samples to generate according to the difficulty of the problem, without relying on majority vote counts. We empirically demonstrate the advantages of our approach on math (MATH-$500$) and coding (HumanEval) tasks using recent open-source models. We also present a comprehensive analysis of its accuracy-compute trade-offs.

Autonomous agents for long-sequence Graphical User Interface tasks are hindered by sparse rewards and the intractable credit assignment problem. To address these challenges, we introduce GUI-Shepherd, a Process Reward Model that provides dense, step-by-step feedback to guide agents. GUI-Shepherd is trained on a diverse large-scale data set of $52$k interactions that features human-annotated scores and GPT-4o generated rationales, enabling it to serve both as a reward provider for RL training and as a verifier for inference. As far as we know, we are the first to conduct a systematic study of process supervision in GUI agents, across diverse settings from online long-horizon tasks to offline single-step prediction. On the online AndroidWorld benchmark, GUI-Shepherd improves success rate by $7.7$ points via multi-turn online PPO, significantly outperforming Outcome Reward Model based competitors. When used as an inference verifier, it brings $5.1$ points improvements. The benefits generalize to the offline AndroidControl benchmark, with gains of $2.2$ points as a reward provider and $4.3$ points as a verifier. Collectively, our results establish that high-fidelity process supervision is critical for building more capable GUI agents and present a generalizable solution.

Reward models are central to both reinforcement learning (RL) with language models and inference-time verification. However, existing reward models often lack temporal consistency, leading to ineffective policy updates and unstable RL training. We introduce TDRM, a method for learning smoother and more reliable reward models by minimizing temporal differences (TD) for training-time reinforcement learning and inference-time verification. Experiments show that TD-trained process reward models (PRMs) improve performance across Best-of-N (up to 6.6%) and tree-search (up to 23.7%) settings. When combined with Reinforcement Learning with Verifiable Rewards (RLVR), TD-trained PRMs lead to more data-efficient RL -- achieving comparable performance with just 2.5k data to what baseline methods require 50.1k data to attain -- and yield higher-quality language model policies in 8 model variants (5 series), e.g., Qwen2.5-(0.5B, 1,5B), GLM4-9B-0414, GLM-Z1-9B-0414, Qwen2.5-Math-(1.5B, 7B), and DeepSeek-R1-Distill-Qwen-(1.5B, 7B). We release all code at https://github.com/THUDM/TDRM.

Autonomous motion planning is critical for efficient and safe underwater manipulation in dynamic marine environments. Current motion planning methods often fail to effectively utilize prior motion experiences and adapt to real-time uncertainties inherent in underwater settings. In this paper, we introduce an Adaptive Heuristic Motion Planner framework that integrates a Heuristic Motion Space (HMS) with Bayesian Networks to enhance motion planning for autonomous underwater manipulation. Our approach employs the Probabilistic Roadmap (PRM) algorithm within HMS to optimize paths by minimizing a composite cost function that accounts for distance, uncertainty, energy consumption, and execution time. By leveraging HMS, our framework significantly reduces the search space, thereby boosting computational performance and enabling real-time planning capabilities. Bayesian Networks are utilized to dynamically update uncertainty estimates based on real-time sensor data and environmental conditions, thereby refining the joint probability of path success. Through extensive simulations and real-world test scenarios, we showcase the advantages of our method in terms of enhanced performance and robustness. This probabilistic approach significantly advances the capability of autonomous underwater robots, ensuring optimized motion planning in the face of dynamic marine challenges.