A Geometric View of Optimal Transport for Generative Models
科研大讨论系列报告
报告题目(Title)：A Geometric View of Optimal Transport for Generative Models
报告人(Speaker)：Xianfeng David Gu（State University of New York at Stony Brook）
地点(Place)：#腾讯会议：812241833
时间(Time)：2024年6月28日 20:30-21:30
邀请人(Inviter)：王发强
报告摘要
According to the manifold distribution law, a data set can be treated as a distribution on a low dimensional data manifold embedded in the high dimensional ambient space. Therefore, the main tasks for a deep learning system are to learn the manifold structure and the distribution. The later can be achieved using optimal transport maps.
This talk introduces a geometric view of optimal transport: the Brenier theorem for L^2 cost optimal transport map is equivalent to the Alexandrov theorem in differential geometry. This view leads to a geometric variational approach to solve the optimal transport problem, and the regularity property of the Monge-Ampère equation. The results are directly applied for generative models to explain and solve the mode collapsing issue and the physical mistakes made by Sora.
主讲人简介
Dr. David Xianfeng Gu got his bachelor degree in computer science from Tsinghua university, his master and PhD from Harvard university, supervised by the world famous differential geometer: Prof. Shing-Tung Yau. Dr. Gu is currently an empire innovation professor in the computer science department and applied mathematics department in the State University of New York at Stony Brook. Prof. Yau and Dr. Gu founded an interdisciplinary field: Computational Conformal Geometry, and applied it for many fields in engineering and medical sciences. Dr. Gu got NSF Career award in 2005, NSFC Outstanding Overseas Young Scholar award in 2006, Morningside gold medal in applied mathematics in ICCM 2013.
