title: AE-OT: A NEW GENERATIVE MODEL BASED ON EXTENDED SEMI-DISCRETE OPTIMAL TRANSPORT
abstract: Generative adversarial networks (GANs) have attracted huge attention due to
  its capability to generate visual realistic images. However, most of the existing
  models suffer from the mode collapse or mode mixture problems. In this work, we
  give a theoretic explanation of the both problems by Figalli’s regularity theory of
  optimal transportation maps. Basically, the generator compute the transportation
  maps between the white noise distributions and the data distributions, which are
  in general discontinuous. However, DNNs can only represent continuous maps.
  This intrinsic conflict induces mode collapse and mode mixture. In order to
  tackle the both problems, we explicitly separate the manifold embedding and the
  optimal transportation; the first part is carried out using an autoencoder to map the
  images onto the latent space; the second part is accomplished using a GPU-based
  convex optimization to find the discontinuous transportation maps. Composing the
  extended OT map and the decoder, we can finally generate new images from the
  white noise. This AE-OT model avoids representing discontinuous maps by DNNs,
  therefore effectively prevents mode collapse and mode mixture.
authors: Dongsheng An Yang Guo Na Lei Zhongxuan Luo Shing-Tung Yau Xianfeng Gu
hIndex: Shing-Tung Yau 103