Ae-OT: a New Generative Model based on Extended Semi-discrete Optimal transport
Ae-OT: a New Generative Model based on Extended Semi-discrete Optimal transport
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发表时间：
2020-04
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通讯作者：
Dongsheng An;Yang Guo;Na Lei;Zhongxuan Luo;S. Yau;X. Gu
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作者：
Dongsheng An;Yang Guo;Na Lei;Zhongxuan Luo;S. Yau;X. Gu
生成对抗网络（GAN）由于其生成视觉逼真图像的能力而引起了人们的极大关注。然而，现有的模型大多存在模式崩溃或模式混合问题。在这项工作中，我们给出了理论解释的最优运输地图的Figalli的正则性理论的两个问题。基本上，生成器计算白色噪声分布和数据分布之间的传输映射，其通常是不连续的。然而，DNN只能表示连续映射。这种内在的冲突导致了模式崩溃和模式混合。为了解决这两个问题，我们显式地分离流形嵌入和最优传输;第一部分使用自动编码器将图像映射到潜在空间;第二部分使用基于GPU的凸优化来找到不连续的传输映射。通过扩展OT映射和解码器的组合，我们最终可以从白色噪声中生成新的图像。该AE-OT模型避免了用DNN表示不连续映射，有效地防止了模式崩溃和模式混合。
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.