Solving inverse problems -- recovering signals from incomplete or noisy measurements -- is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main paradigms have formed: unsupervised approaches that adapt pretrained generative models to inverse problems, and supervised bridge methods that train stochastic processes conditioned on paired clean and corrupted data. While the former typically assume knowledge of the measurement model, the latter have largely overlooked this structural information. We introduce System embedded Diffusion Bridge Models (SDBs), a new class of supervised bridge methods that explicitly embed the known linear measurement system into the coefficients of a matrix-valued SDE. This principled integration yields consistent improvements across diverse linear inverse problems and demonstrates robust generalization under system misspecification between training and deployment, offering a promising solution to real-world applications.

-- Human activity intensity prediction is crucial to many location - based services. Despite tremendous p rogress in modeling d ynamics of human activity, most existing methods overlook physical constraints of spatial interaction, leading to uninterpretable spatial correlations and over - smoothing phenomenon . To address these limitations, this work proposes a physics - informed deep learning framework, namely Gravity - informed Spatiotemporal Transformer (Gravityformer) by integrat ing the universal law of gravitation to refin e transformer attention. Specifically, it (1) estimates two spatially explicit mass parameters based on spatiotemporal embedding feature, (2) models the spatial interaction in end - to - end neural network using proposed adaptive gravity model to learn the physic al constrain t, and (3) utilizes the learned spatial interaction to guide and mitigate the over - smoothing phenomenon in transformer attention. Moreover, a parallel spatiotemporal graph convolution transformer is proposed for achieving a balance between coupled spatial and temporal learning. Systematic experiments on six real - world large - scale activity datasets demonstrate the quantitative and qualitative superiority of our model over state - of - the - art benchmarks. Additionally, the learned gravity attention matrix can be not only disentangled and interpreted based on geographical laws, but also improved the generalization in zero - shot cross - region inference . This work provides a novel insight into integrating physical laws with deep learning for spatiotemporal prediction . Index Terms -- Human activity intensity prediction; Gravity model; Spatial interaction; Physics - informed machine learning; Over - smoothing phenomenon; Spatiotemporal graph neural network . This work is supported by the National Natural Science Foundation of China ( Grant # 42430106, 42371468, 424B2013) . Y i Wang, Zhenghong Wang, Fan Zhang, Chengling Tang, Weiyu Zhang and Yu Liu are with Institute of Remote Sensing and Geographic Information System, School of Earth and Space Sciences, Peking University, Beijing 100871, China. Chaogui Kang is with National Engineering Research Center of Geographic Information System, China University of Geosciences (Wuhan) 430074, China. Sijie Ruan is with School of Computer Science and Technology, Beijing Institute of Technology, Beijing 100081, China . Di Zhu and Zhongfu Ma are with Department of Geography, Environment and Society, University of Minnesota, Twin Cities, Minneapolis, MN 55455, USA . Y u Zheng is with JD iCity, JD Technology, Beijing 100176, China . P hilip S. Yu is with Department of Computer Science, University of Illinois Chicago, Chicago 60607, USA .

A challenge in human-AI decision-making is to balance three factors: the correctness of predictions, the cost of knowledge and reasoning complexity, and the confidence about whether to abstain from automated answers or escalate to human experts. In this work, we present a cascaded LLM decision framework that adaptively delegates tasks across multiple tiers of expertise -- a base model for initial candidate answers, a more capable and knowledgeable (but costlier) large model, and a human expert for when the model cascade abstains. Our method proceeds in two stages. First, a deferral policy determines whether to accept the base model's answer or regenerate it with the large model based on the confidence score. Second, an abstention policy decides whether the cascade model response is sufficiently certain or requires human intervention. Moreover, to overcome static policies and accommodate changing task difficulty, we incorporate an online learning mechanism which uses human feedback. We demonstrate this approach to general question-answering (ARC-Easy, ARC-Challenge, and MMLU) and medical question-answering (MedQA and MedMCQA). Our results demonstrate that our cascaded strategy outperforms single-model baselines in most cases, achieving higher accuracy while reducing costs and providing a principled approach to handling abstentions.

Synthetic data generation is increasingly used in machine learning for training and data augmentation. Yet, current strategies often rely on external foundation models or datasets, whose usage is restricted in many scenarios due to policy or legal constraints. We propose ScoreMix, a self-contained synthetic generation method to produce hard synthetic samples for recognition tasks by leveraging the score compositionality of diffusion models. The approach mixes class-conditioned scores along reverse diffusion trajectories, yielding domain-specific data augmentation without external resources. We systematically study class-selection strategies and find that mixing classes distant in the discriminator's embedding space yields larger gains, providing up to 3% additional average improvement, compared to selection based on proximity. Interestingly, we observe that condition and embedding spaces are largely uncorrelated under standard alignment metrics, and the generator's condition space has a negligible effect on downstream performance. Across 8 public face recognition benchmarks, ScoreMix improves accuracy by up to 7 percentage points, without hyperparameter search, highlighting both robustness and practicality. Our method provides a simple yet effective way to maximize discriminator performance using only the available dataset, without reliance on third-party resources. Paper website: https://parsa-ra.github.io/scoremix/.

Anomaly Detection (AD) and Anomaly Localization (AL) are crucial in fields that demand high reliability, such as medical imaging and industrial monitoring. However, current AD and AL approaches are often susceptible to adversarial attacks due to limitations in training data, which typically include only normal, unlabeled samples. This study introduces PatchGuard, an adversarially robust AD and AL method that incorporates pseudo anomalies with localization masks within a Vision Transformer (ViT)-based architecture to address these vulnerabilities. We begin by examining the essential properties of pseudo anomalies, and follow it by providing theoretical insights into the attention mechanisms required to enhance the adversarial robustness of AD and AL systems. We then present our approach, which leverages Foreground-Aware Pseudo-Anomalies to overcome the deficiencies of previous anomaly-aware methods. Our method incorporates these crafted pseudo-anomaly samples into a ViT-based framework, with adversarial training guided by a novel loss function designed to improve model robustness, as supported by our theoretical analysis. Experimental results on well-established industrial and medical datasets demonstrate that PatchGuard significantly outperforms previous methods in adversarial settings, achieving performance gains of $53.2\%$ in AD and $68.5\%$ in AL, while also maintaining competitive accuracy in non-adversarial settings. The code repository is available at https://github.com/rohban-lab/PatchGuard .

Recent advances in Chain-of-Thought (CoT) reasoning have improved complex video understanding, but existing methods often struggle to adapt to domain-specific skills (e.g., event detection, spatial relation understanding, emotion understanding) over various video content. To address this, we propose Video-Skill-CoT (a.k.a. Video-SKoT), a framework that automatically constructs and leverages skill-aware CoT supervisions for domain-adaptive video reasoning. First, we construct skill-based CoT annotations: we extract domain-relevant reasoning skills from training questions, cluster them into a shared skill taxonomy, and create detailed multi-step CoT rationale tailored to each video-question pair for training. Second, we introduce a skill-specific expert learning framework. Each expert module specializes in a subset of reasoning skills and is trained with lightweight adapters using the collected CoT supervision. We demonstrate the effectiveness of the proposed approach on three video understanding benchmarks, where Video-SKoT consistently outperforms strong baselines. We also provide in-depth analyses on comparing different CoT annotation pipelines and learned skills over multiple video domains.

Learning efficient visual representations across heterogeneous unlabeled datasets remains a central challenge in federated learning. Effective federated representations require features that are jointly informative across clients while disentangling domain-specific factors without supervision. We introduce FORLA, a novel framework for federated object-centric representation learning and feature adaptation across clients using unsupervised slot attention. At the core of our method is a shared feature adapter, trained collaboratively across clients to adapt features from foundation models, and a shared slot attention module that learns to reconstruct the adapted features. To optimize this adapter, we design a two-branch student-teacher architecture. In each client, a student decoder learns to reconstruct full features from foundation models, while a teacher decoder reconstructs their adapted, low-dimensional counterpart. The shared slot attention module bridges cross-domain learning by aligning object-level representations across clients. Experiments in multiple real-world datasets show that our framework not only outperforms centralized baselines on object discovery but also learns a compact, universal representation that generalizes well across domains. This work highlights federated slot attention as an effective tool for scalable, unsupervised visual representation learning from cross-domain data with distributed concepts.

Efficiently solving constrained optimization problems is crucial for numerous real-world applications, yet traditional solvers are often computationally prohibitive for real-time use. Machine learning-based approaches have emerged as a promising alternative to provide approximate solutions at faster speeds, but they struggle to strictly enforce constraints, leading to infeasible solutions in practice. To address this, we propose the Feasibility-Seeking Neural Network (FSNet), which integrates a feasibility-seeking step directly into its solution procedure to ensure constraint satisfaction. This feasibility-seeking step solves an unconstrained optimization problem that minimizes constraint violations in a differentiable manner, enabling end-to-end training and providing guarantees on feasibility and convergence. Our experiments across a range of different optimization problems, including both smooth/nonsmooth and convex/nonconvex problems, demonstrate that FSNet can provide feasible solutions with solution quality comparable to (or in some cases better than) traditional solvers, at significantly faster speeds.

Autonomy is a hallmark of animal intelligence, enabling adaptive and intelligent behavior in complex environments without relying on external reward or task structure. Existing reinforcement learning approaches to exploration in reward-free environments, including a class of methods known as model-based intrinsic motivation, exhibit inconsistent exploration patterns and do not converge to an exploratory policy, thus failing to capture robust autonomous behaviors observed in animals. Moreover, systems neuroscience has largely overlooked the neural basis of autonomy, focusing instead on experimental paradigms where animals are motivated by external reward rather than engaging in ethological, naturalistic and task-independent behavior. To bridge these gaps, we introduce a novel model-based intrinsic drive explicitly designed after the principles of autonomous exploration in animals. Our method (3M-Progress) achieves animal-like exploration by tracking divergence between an online world model and a fixed prior learned from an ecological niche. To the best of our knowledge, we introduce the first autonomous embodied agent that predicts brain data entirely from self-supervised optimization of an intrinsic goal -- without any behavioral or neural training data -- demonstrating that 3M-Progress agents capture the explainable variance in behavioral patterns and whole-brain neural-glial dynamics recorded from autonomously behaving larval zebrafish, thereby providing the first goal-driven, population-level model of neural-glial computation. Our findings establish a computational framework connecting model-based intrinsic motivation to naturalistic behavior, providing a foundation for building artificial agents with animal-like autonomy.

Retrieval-Augmented Generation (RAG) integrates external knowledge with Large Language Models (LLMs) to enhance factual correctness and mitigate hallucination. However, dense retrievers often become the bottleneck of RAG systems due to their limited parameters compared to LLMs and their inability to perform step-by-step reasoning. While prompt-based iterative RAG attempts to address these limitations, it is constrained by human-designed workflows. To address these limitations, we propose $\textbf{R3-RAG}$, which uses $\textbf{R}$einforcement learning to make the LLM learn how to $\textbf{R}$eason and $\textbf{R}$etrieve step by step, thus retrieving comprehensive external knowledge and leading to correct answers. R3-RAG is divided into two stages. We first use cold start to make the model learn the manner of iteratively interleaving reasoning and retrieval. Then we use reinforcement learning to further harness its ability to better explore the external retrieval environment. Specifically, we propose two rewards for R3-RAG: 1) answer correctness for outcome reward, which judges whether the trajectory leads to a correct answer; 2) relevance-based document verification for process reward, encouraging the model to retrieve documents that are relevant to the user question, through which we can let the model learn how to iteratively reason and retrieve relevant documents to get the correct answer. Experimental results show that R3-RAG significantly outperforms baselines and can transfer well to different retrievers. We release R3-RAG at https://github.com/Yuan-Li-FNLP/R3-RAG.