Speaker

　　Title

　　Time

　　Venue

N219

　　Abstract

In this work, we show the intrinsic relations between optimal transportation and convex geometry, especially the variational approach to solve Alexandrov problem: constructing a convex polytope with prescribed face normals and volumes. This leads to a geometric interpretation to generative models, and leads to a novel framework for generative models. By using the optimal transportation view of GAN model, we show that the discriminator computes the Kantorovich potential, the generator calculates the transportation map. For a large class of transportation costs, the Kantorovich potential can give the optimal transportation map by a close-form formula. Therefore, it is sufficient to solely optimize the discriminator. This shows the adversarial competition can be avoided, and the computational architecture can be simplified. Preliminary experimental results show the geometric method outperforms WGAN for approximating probability measures with multiple clusters in low dimensional space. 

　　Affiliation

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。
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（与胡事民教授合作），“华人菲尔茨奖”: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。目前已经发表二百篇余篇国际论文，学术专著包括“Computational Conformal Geometry”（计算共形几何）， “Ricci Flow for Surface Registration and Shape Analysis”等。