Subsampling Generative Adversarial Networks: Density Ratio Estimation in Feature Space with Softplus Loss

Subsampling Generative Adversarial Networks: Density Ratio Estimation in Feature Space with Softplus Loss Xin Ding 1 1 University of British Columbia September 25, 2019 Abstract Filtering out unrealistic images from trained generative adversarial networks (GANs) starts attracting people's attention recently. Two density ratio based subsampling methods--Discriminator Rejection Sampling (DRS) and Metropolis-Hastings GAN (MH-GAN)--are recently proposed, and their effectiveness in improving GANs are demonstrated on multiple datasets. However, DRS and MH-GAN are developed based on discriminator based density ratio estimation (DRE) methods so they may not work well if the discriminator in the trained GAN is far away from its optimality. Moreover, they do not apply to some GANs (e.g., MMD-GAN). In this paper, we propose a novel Softplus (SP) loss for DRE based on which we develop a sample-based DRE method in a feature space learned by a specially designed and pre-trained ResNet-34 (DRE-F-SP). We derive the rate of convergence of a density ratio model trained under the SP loss. Then, we introduce three different density ratio based subsampling methods (DRE-F-SP RS, DRE-F-SP MH, and DRE-F-SP SIR) for GANs based on DRE-F-SP. Our subsampling methods do not rely on the optimality of the discriminator and are suitable for all types of GANs. We empirically show our subsampling approach can substantially outperform DRS and MH-GAN on a synthetic dataset and the CIF AR-10 dataset, using multiple GANs. 1 Introduction Generative adversarial networks (GANs) first introduced by [1] are well-known and powerful generative models for image synthesis and have been applied to various types of image-related tasks [2, 3, 4, 5, 6, 7]. The vanilla GANs proposed by [1] consist of two neural networks: a generator and a discriminator. The generator is trained to generate fake images to fool the discriminator while the discriminator is trained to distinguish fake images from real ones. To enhance the quality of fake images generated from the vanilla GANs, many subsequent works have been done on improving the training procedure of GANs, such as adopting large scale training schemes (e.g., BigGAN [8]), novel normalization methods (e.g., SN-GAN [9]), advanced GAN architectures (e.g., SAGAN [10]), and different loss functions (e.g., WGAN [11, 12] and MMD-GAN [13]). Instead of improving the training procedure, we are more interested in post-processing fake images from a trained GAN (i.e., subsampling fake images to filter out unrealistic images).