Terminally constrained flow-based generative models from an optimal control perspective
School of Mathematical Sciences, Fudan University（复旦大学数学学院）；Shanghai Key Laboratory of Contemporary Applied Mathematics（上海当代应用数学重点实验室）；Department of Mathematics and Institute for Functional Intelligent Materials（数学系和功能智能材料研究所）；National University of Singapore（新加坡国立大学）
We address the problem of sampling from terminally constrained distributions with pre-trained flow-based generative models through an optimal control formulation. Theoretically, we characterize the value function by a Hamilton-Jacobi-Bellman equation and derive the optimal feedback control as the minimizer of the associated Hamiltonian. We show that as the control penalty increases, the controlled process recovers the reference distribution, while as the penalty vanishes, the terminal law converges to a generalized Wasserstein projection onto the constraint manifold. Algorithmically, we introduce Terminal Optimal Control with Flow-based models (TOCFlow), a geometry-aware sampling-time guidance method for pre-trained flows. Solving the control problem in a terminal co-moving frame that tracks reference trajectories yields a closed-form scalar damping factor along the Riemannian gradient, capturing second-order curvature effects without matrix inversions. TOCFlow therefore matches the geometric consistency of Gauss-Newton updates at the computational cost of standard gradient guidance. We evaluate TOCFlow on three high-dimensional scientific tasks spanning equality, inequality, and global statistical constraints, namely Darcy flow, constrained trajectory planning, and turbulence snapshot generation with Kolmogorov spectral scaling. Across all settings, TOCFlow improves constraint satisfaction over Euclidean guidance and projection baselines while preserving the reference model's generative quality.
A Variational Inequality Perspective on Generative Adversarial Networks
Mila & DIRO, University of Montreal（蒙特利尔大学 Mila 与 DIRO）；Facebook Artificial Intelligence Research（Facebook 人工智能研究院）；Canada CIFAR AI Chair（加拿大 CIFAR 人工智能教席）
On the Robustness of Generative Retrieval Models: An Out-of-Distribution Perspective
CAS Key Lab of Network Data Science and Technology, ICT, CAS（中国科学院计算技术研究所网络数据科学与技术重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；University of Amsterdam（阿姆斯特丹大学）
Introduction to Stochastic Differential Equations for Generative Machine Learning: A Variational Perspective
Department of Biology, University of Copenhagen（哥本哈根大学生物系）；Department of Applied Mathematics and Computer Science, Technical University of Denmark（丹麦技术大学应用数学与计算机科学系）；Google DeepMind（谷歌DeepMind）；Technical University of Berlin (TU Berlin)（柏林工业大学）；Technical University of Munich（慕尼黑工业大学）
Revisit and Outstrip Entity Alignment: A Perspective of Generative Models
College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；Zhejiang University - Ant Group Joint Laboratory of Knowledge Graph（浙江大学-蚂蚁集团知识图谱联合实验室）；Donghai Laboratory（东海实验室）；Department of Computer Science, The University of Manchester（曼彻斯特大学计算机科学系）；School of Software Technology, Zhejiang University（浙江大学软件学院）
ProGen: Revisiting Probabilistic Spatial-Temporal Time Series Forecasting from a Continuous Generative Perspective Using Stochastic Differential Equations
Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
Revisiting Generative Policies: A Simpler Reinforcement Learning Algorithmic Perspective
Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；Xi’an Jiaotong University（西安交通大学）；SenseTime Research（商汤科技研究院）；Peking University（北京大学）；The Chinese University of Hong Kong（香港中文大学）
Generative Adversarial Nets for Robust Scatter Estimation: A Proper Scoring Rule Perspective
University of Chicago（芝加哥大学）；Hong Kong University of Science and Technology（香港科技大学）
稳健散布估计是统计学中的一项基本任务。Gao et al.（2018）最近关于鲁棒估计和生成对抗网络（GANs）之间的联系的发现表明，可以使用优化GANs的类似技术来计算类似深度的鲁棒估计器。在本文中，我们介绍了一个一般的学习通过分类框架的基础上适当的评分规则的概念。这个框架允许我们通过$f$的变分近似的透镜来理解矩阵深度函数和各种GANs-由适当的评分规则引起的发散。然后，我们提出了一类新的强大的散布估计在这个框架中仔细构造鉴别器与适当的神经网络结构。在Huber污染模型下，证明了这些估计量能达到极小极大散布率估计.我们的数值结果表明，在各种设置下对文献中的竞争对手的良好性能。
Copyright Protection in Generative AI: A Technical Perspective
Michigan State University（密歇根州立大学）；School of Artificial Intelligence, Jilin University（吉林大学人工智能学院）；International Center of Future Science, Jilin University（吉林大学未来科学国际中心）；Stanford University（斯坦福大学）；Sony AI（索尼人工智能）；Engineering Research Center of Knowledge-Driven Human-Machine Intelligence, MOE（教育部知识驱动人机智能工程研究中心）
Generative Modeling through Koopman Spectral Analysis: An Operator-Theoretic Perspective
Center for Science Adventure；Collaborative Research Advancement, Graduate School of Science, Kyoto University, Kyoto, Japan；Massachusetts Institute of Technology, Cambridge, MA；LinkedIn Corporation, Sunnyvale, CA；Dynamic Systems Lab, University College London, London, UK；Graduate School of Information Science；Technology, The University of Osaka, Osaka, Japan；RIKEN Center for Advanced Intelligence Project, Tokyo, Japan
Generative and Nonparametric Approaches for Conditional Distribution Estimation: Methods, Perspectives, and Comparative Evaluations
Institute of Statistical Science, Academia Sinica（学术院统计科学研究所）；Department of Mathematics, National Taiwan University（台湾大学数学系）；Data Science Degree Program, National Taiwan University and Academia Sinica（台湾大学数据科学学士学位计划）；Department of Statistics, University of Michigan（密歇根大学统计学系）
A Bayesian Perspective of Convolutional Neural Networks through a Deconvolutional Generative Model
Rice University（莱斯大学）；University of California at Berkeley（加州大学伯克利分校）；Baylor College of Medicine（贝勒医学院）；California Institute of Technology（加州理工学院）；NVIDIA（英伟达）
