We study in this paper the rate of convergence for learning distributions with the Generative Adversarial Networks (GAN) framework, which subsumes Wasserstein, Sobolev and MMD GANs as special cases. We study a wide range of parametric and nonparametric target distributions, under a collection of objective evaluation metrics. On the nonparametric end, we investigate the minimax optimal rates and fundamental difficulty of the density estimation under the adversarial framework. On the parametric end, we establish theory for neural network classes, that characterizes the interplay between the choice of generator and discriminator. We investigate how to improve the GAN framework with better theoretical guarantee through the lens of regularization. We discover and isolate a new notion of regularization, called the \textit{generator/discriminator pair regularization}, that sheds light on the advantage of GAN compared to classic parametric and nonparametric approaches for density estimation.

Recently, a series of algorithms have been explored for GAN compression, which aims to reduce tremendous computational overhead and memory usages when deploying GANs on resource-constrained edge devices. However, most of the existing GAN compression work only focuses on how to compress the generator, while fails to take the discriminator into account. In this work, we revisit the role of discriminator in GAN compression and design a novel generator-discriminator cooperative compression scheme for GAN compression, termed GCC. Within GCC, a selective activation discriminator automatically selects and activates convolutional channels according to a local capacity constraint and a global coordination constraint, which help maintain the Nash equilibrium with the lightweight generator during the adversarial training and avoid mode collapse. The original generator and discriminator are also optimized from scratch, to play as a teacher model to progressively refine the pruned generator and the selective activation discriminator.

In this paper, we show that the approximation for distributions by Wasserstein GAN depends on both the width/depth (capacity) of generators and discriminators, as well as the number of samples in training. A quantified generalization bound is developed for Wasserstein distance between the generated distribution and the target distribution. It implies that with sufficient training samples, for generators and discriminators with proper number of width and depth, the learned Wasserstein GAN can approximate distributions well. We discover that discriminators suffer a lot from the curse of dimensionality, meaning that GANs have higher requirement for the capacity of discriminators than generators, which is consistent with the theory in arXiv:1703.00573v5 [cs.LG]. More importantly, overly deep (high capacity) generators may cause worse results (after training) than low capacity generators if discriminators are not strong enough. Different from Wasserstein GAN in arXiv:1701.07875v3 [stat.ML], we adopt GroupSort neural networks arXiv:1811.05381v2 [cs.LG] in the model for their better approximation to 1-Lipschitz functions. Compared to some existing generalization (convergence) analysis of GANs, we expect our work are more applicable.

Traditional GANs use a deterministic generator function (typically a neural network) to transform a random noise input $z$ to a sample $\mathbf{x}$ that the discriminator seeks to distinguish. We propose a new GAN called Bayesian Conditional Generative Adversarial Networks (BC-GANs) that use a random generator function to transform a deterministic input $y'$ to a sample $\mathbf{x}$. Our BC-GANs extend traditional GANs to a Bayesian framework, and naturally handle unsupervised learning, supervised learning, and semi-supervised learning problems. Experiments show that the proposed BC-GANs outperforms the state-of-the-arts.

Recently, a series of algorithms have been explored for GAN compression, which aims to reduce tremendous computational overhead and memory usages when deploying GANs on resource-constrained edge devices. However, most of the existing GAN compression work only focuses on how to compress the generator, while fails to take the discriminator into account. In this work, we revisit the role of discriminator in GAN compression and design a novel generator-discriminator cooperative compression scheme for GAN compression, termed GCC. Within GCC, a selective activation discriminator automatically selects and activates convolutional channels according to a local capacity constraint and a global coordination constraint, which help maintain the Nash equilibrium with the lightweight generator during the adversarial training and avoid mode collapse. The original generator and discriminator are also optimized from scratch, to play as a teacher model to progressively refine the pruned generator and the selective activation discriminator. A novel online collaborative distillation scheme is designed to take full advantage of the intermediate feature of the teacher generator and discriminator to further boost the performance of the lightweight generator. Extensive experiments on various GAN-based generation tasks demonstrate the effectiveness and generalization of GCC. Among them, GCC contributes to reducing 80% computational costs while maintains comparable performance in image translation tasks. Our code and models are available at: https://github.com/SJLeo/GCC