报告题目：A Geometric Understanding of Deep Learning

主 讲 人：雷娜

单 位：大连理工大学

时 间：11月5日14:00

腾 讯 ID：851 623 324

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：

雷娜，教授，博士生导师，大连理工大学国际信息与软件学院党总支书记，北京成像技术高精尖创新中心研究员；美国数学会Mathematical Review评论员；纽约州立大学石溪分校计算机系访问教授；德克萨斯大学奥斯汀分校计算工程与科学研究所JTO research fellow。多个国际TOP期刊审稿人,国际顶会的PC member。研究方向为：应用现代微分几何和代数几何的理论与方法解决工程及医学领域的问题，主要聚焦于计算共形几何、计算拓扑、符号计算及其在人工智能、计算机图形学、几何建模和医学图像中的应用。主持国家自然科学基金重点项目、面上项目以及国家部委等重要项目多项；多次受邀在国际、国内重要会议上做大会报告及会前课程。注重科研结合应用，所取得的科研成果在企业进行了超过百万的知识产权转化。