“最优运输问题、PDE及其在图像处理中的应用”系列学术报告(五)

发布单位:数学与统计学院编辑:朱亚宾发布时间:2020-09-11浏览量:14

题目(Title):A  Geometric  Understanding  of  Deep  Learning

报告人(Speaker):顾险峰 教授(纽约州立大学石溪分校)

报告时间(Time):2020年9月15日上午 9:00(北京时间)

方式(Online):ZOOM ID:645 9082 6194 (密码:062071)

摘要(Abstract):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.

报告人简介:顾险峰,美国纽约州立大学石溪分校计算机系终身教授。1989年考入清华大学计算机科学与技术系,攻读基础理论方向,1992年获得清华大学特等奖学金,后于美国哈佛大学获得计算机博士学位,师从国际著名微分几何大师丘成桐先生。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,晨兴应用数学金奖。丘成桐先生和顾险峰博士团队,将微分几何,代数拓扑,黎曼面理论,偏微分方程与计算机科学相结合,创立跨领域学科“计算共形几何”,并广泛应用于计算机图形学,计算机视觉,几何建模,无线传感器网络,医学图像等领域。

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 数学与统计学院

2020年9月11日