报告题目:A Geometric Understanding of Deep Learning

主 讲 人：顾 险 峰

单 位：美国纽约州立大学

时 间：3月3日8:30

ZOOM ID：210 089 8623

密 码：123456

摘 要：

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.

简 介：

顾险峰，美国纽约州立大学石溪分校计算机系帝国创新教授，美国哈佛大学数学与应用中心客座教授，清华大学丘成桐数学中心客座教授。师从微分几何大师丘成桐先生，与丘先生共同创立了跨领域学科“计算共形几何”，将现代拓扑与几何应用于工程和医疗等领域。曾获美国国家自然科学基金CAREER奖、中国国家自然科学基金海外杰出青年奖、“华人菲尔茨奖”：晨兴应用数学金奖。