A Geometric Understanding of Deep Learning 136



Xianfeng Gu, Stony Brook University, USA


2020.07.03 09:00-10:00





Meeting ID: 928-919-26806

Password: 519613


This work introduces an optimal transportation (OT) view of generative adversarial networks (GANs). Natural datasets have intrinsic patterns, which can be summarized as the manifold distribution principle: the distribution of a class of data is close to a low-dimensional manifold. GANs mainly accomplish two tasks: manifold learning and probability distribution transformation. The latter can be carried out using the classical OT method. From the OT perspective, the generator computes the OT map, while the discriminator computes the Wasserstein distance between the generated data distribution and the real data distribution; both can be reduced to a convex geometric optimization process. Furthermore, OT theory discovers the intrinsic collaborative—instead of competitive—relation between the generator and the discriminator, and the fundamental reason for mode collapse. We also propose a novel generative model, which uses an autoencoder (AE) for manifold learning and OT map for probability distribution transformation. This AE–OT model improves the theoretical rigor and transparency, as well as the computational stability and efficiency; in particular, it eliminates the mode collapse. The experimental results validate our hypothesis, and demonstrate the advantages of our proposed model.


A Geometric Understanding of Deep Learning


Dr. Xianfeng Gu got his bachelor’s degree from Tsinghua university, PhD in computer science from Harvard university, supervised by the Fields medalist, Prof. Shing-Tung Yau. Currently, Dr. Gu is a New York State Empire Innovation Professor in the Computer Science Department, Stony Brook university. Dr. Gu’s research focuses on applying modern geometry in engineering and medicine fields. Together with Prof. Shing-Tung Yau, Dr. Gu and other collaborators have founded an interdisciplinary field: Computational Conformal Geometry. Dr. Gu has won NSF Career award, Morningside Gold medal in applied Mathematics.