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论文类型：期刊论文

发表时间：2019-01-01

发表刊物：COMPUTER AIDED GEOMETRIC DESIGN

收录刊物：SCIE、EI

卷号：68

页面范围：1-21

ISSN号：0167-8396

关键字：Optimal Mass Transportation; Monge-Ampere; GAN; Wasserstein distance

摘要：In this work, we give a geometric interpretation to the Generative Adversarial Networks (GANs). The geometric view is based on the intrinsic relation between Optimal Mass Transportation (OMT) theory and convex geometry, and leads to a variational approach to solve the Alexandrov problem: constructing a convex polytope with prescribed face normals and volumes.
   By using the optimal transportation view of GAN model, we show that the discriminator computes the Wasserstein distance via 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 the traditional Wasserstein GAN for approximating probability measures with multiple clusters in low dimensional space. (C) 2018 Elsevier B.V. All rights reserved.