Title：A Geometric Understanding of Deep Learning
Speaker：An, Dongsheng（安东生）
Affiliation：Stony Brook University
Time：9:00 am - 10: 00 am， 26/10/2021，Tuesday
Tencent Meeting ID：140 539 605
Inviter：Shuliang Bai (103200068@seu.edu.cn)
Abstract：Our work introduces an optimal transport (OT) view of the generative models, including the GANs and VAEs. 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. The generative models 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 from a simple distribution to the complex distribution defined by the dataset. Furthermore, OT theory can help explain the problems encountered by nearly all of the generative models, like mode collapse and mode mixture. 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 and mode mixture problem. The experimental results validate our hypothesis, and demonstrate the advantages of our proposed model.
Bio： Dongsheng An is currently a PhD candidate at the Department of Computer Science, Stony Brook University, supervised by Prof. Xianfeng Gu. Prior to that, he obtained his M.S. and B.S. from Tsinghua University, China. His main research interests include computational optimal transport, generative modeling and computational conformal geometry.