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学术报告

Global well posedness of Score-Based Generative model via Sharp Lipschitz estimate

王中剑 助理教授

新加坡南洋理工大学

报告时间： 2024年6月3日 (星期一) 下午3：00-4：00

报告地点 ：沙河主E706

报告摘要：We establish global well-posedness and convergence of the score-based generative models (SGM) under minimal general assumptions of initial data for score estimation. For the smooth case, we start from a Lipschitz bound of the score function with optimal time length. The optimality is validated by an example whose Lipschitz constant of scores is bounded at initial but blows up in finite time. This necessitates the separation of time scales in conventional bounds for non-log-concave distributions. In contrast, our follow up analysis only relies on a local Lipschitz condition and is valid globally in time. This leads to the convergence of numerical scheme without time separation. For the non-smooth case, we show that the optimal Lipschitz bound is O(1/t) in the point-wise sense for distributions supported on a compact, smooth and low-dimensional manifold with boundary.

报告人简介：Zhongjian WANG joined the division of mathematics (SPMS) at Nanyang Technological University as an Assistant Professor since 2023. Prior to that, he got a math PhD degree from the University of Hong Kong and worked as a William H. Kruskal Instructor at the University of Chicago. His research interests lie broadly in the applied and computational mathematics, some recent topics include generative models, reduced order methods, particle methods in the computation of PDEs.

邀请人：罗雪