Despite their empirical success, however, two very basic questions on how well they can approximate the target distribution remain unanswered. First, it is not known how restricting the discriminator family affects the approximation quality. Second, while a number of different objective functions have been proposed, we do not understand when convergence to the global minima of the objective function leads to convergence to the target distribution under various notions of distributional convergence. In this paper, we address these questions in a broad and unified setting by defining a notion of adversarial divergences that includes a number of recently proposed objective functions. We show that if the objective function is an adversarial divergence with some additional conditions, then using a restricted discriminator family has a moment-matching effect. Additionally, we show that for objective functions that are strict adversarial divergences, convergence in the objective function implies weak convergence, thus generalizing previous results.

In our opinion, the existing GAN models are fundamentally two-sample test problems.

Correctness: I like the ideas and concepts of'diversity' and'realness' on the sphere (which is projected by simple L2-normalization), but it is non-trivial to say that proposed objective function actually minimizes some'distance' between real and fake probability distribution. SphereGAN implements IPMs as their objective function and shows the equivalence relation between minimizing Wasserstein distance in hyper-sphere and minimizing objective functions, but this kind of analysis is not dealt in proposed method even if SphereGAN is main baseline method. Thus authors needs to clarify what to minimize. The proposed method uses L2-normalization as a projection onto hyper-sphere which induces information loss as it is not one-to-one (All the conventional features lying in same lay started at origin is projected to same point in hyper-sphere). The stereo-graphic projection not only admits single fixed point where north pole ('center' in the paper) can be rotated transitively on the hyper-sphere.

This paper proposes a new GAN training technique based on intuition about the hypersphere. It attains state-of-the-art IS and FID scores on a few datasets. Reviewers were initially confused and concerned about its similarity to SphereGAN but were convinced it should be accepted after the rebuttal.

We present a novel discriminator for GANs that improves realness and diversity of generated samples by learning a structured hypersphere embedding space using spherical circles. The proposed discriminator learns to populate realistic samples around the longest spherical circle, i.e., a great circle, while pushing unrealistic samples toward the poles perpendicular to the great circle. Since longer circles occupy larger area on the hypersphere, they encourage more diversity in representation learning, and vice versa. Discriminating samples based on their corresponding spherical circles can thus naturally induce diversity to generated samples. We also extend the proposed method for conditional settings with class labels by creating a hypersphere for each category and performing class-wise discrimination and update.

The authors present a formal analysis to characterize general adversarial learning. The analysis shows that under certain conditions on the objective function the adversarial process has a moment-matching effect. They also show results on convergence properties. The writing is quite dense and may not be accessible to most of the NIPS audience. I did not follow the full details myself.

Quantum Generative Adversarial Networks (QGANs), an intersection of quantum computing and machine learning, have attracted widespread attention due to their potential advantages over classical analogs. However, in the current era of Noisy Intermediate-Scale Quantum (NISQ) computing, it is essential to investigate whether QGANs can perform learning tasks on near-term quantum devices usually affected by noise and even defects. In this Letter, using a programmable silicon quantum photonic chip, we experimentally demonstrate the QGAN model in photonics for the first time, and investigate the effects of noise and defects on its performance. Our results show that QGANs can generate high-quality quantum data with a fidelity higher than 90\%, even under conditions where up to half of the generator's phase shifters are damaged, or all of the generator and discriminator's phase shifters are subjected to phase noise up to 0.04$\pi$. Our work sheds light on the feasibility of implementing QGANs on NISQ-era quantum hardware.

In recent years, generative adversarial networks (GANs) have demonstrated impressive experimental results while there are only a few works that foster statistical learning theory for GANs. In this work, we propose an infinite dimensional theoretical framework for generative adversarial learning. We assume that the probability density functions of the underlying measure are uniformly bounded, $k$-times $\alpha$-H\"{o}lder differentiable ($C^{k,\alpha}$) and uniformly bounded away from zero. Under these assumptions, we show that the Rosenblatt transformation induces an optimal generator, which is realizable in the hypothesis space of $C^{k,\alpha}$-generators. With a consistent definition of the hypothesis space of discriminators, we further show that the Jensen-Shannon divergence between the distribution induced by the generator from the adversarial learning procedure and the data generating distribution converges to zero. Under certain regularity assumptions on the density of the data generating process, we also provide rates of convergence based on chaining and concentration.

The Sinkhorn algorithm (arXiv:1306.0895) is the state-of-the-art to compute approximations of optimal transport distances between discrete probability distributions, making use of an entropically regularized formulation of the problem. The algorithm is guaranteed to converge, no matter its initialization. This lead to little attention being paid to initializing it, and simple starting vectors like the n-dimensional one-vector are common choices. We train a neural network to compute initializations for the algorithm, which significantly outperform standard initializations. The network predicts a potential of the optimal transport dual problem, where training is conducted in an adversarial fashion using a second, generating network. The network is universal in the sense that it is able to generalize to any pair of distributions of fixed dimension after training, and we prove that the generating network is universal in the sense that it is capable of producing any pair of distributions during training. Furthermore, we show that for certain applications the network can be used independently.

Modeling the risk of extreme weather events in a changing climate is essential for developing effective adaptation and mitigation strategies. Although the available low-resolution climate models capture different scenarios, accurate risk assessment for mitigation and adaption often demands detail that they typically cannot resolve. Here, we develop a dynamic data-driven downscaling (super-resolution) method that incorporates physics and statistics in a generative framework to learn the fine-scale spatial details of rainfall. Our method transforms coarse-resolution ($0.25^{\circ} \times 0.25^{\circ}$) climate model outputs into high-resolution ($0.01^{\circ} \times 0.01^{\circ}$) rainfall fields while efficaciously quantifying uncertainty. Results indicate that the downscaled rainfall fields closely match observed spatial fields and their risk distributions.