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We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent variable models of the data distribution based on the primal and the dual formulations of the optimal transport (OT) problem. We utilize the primal…

Generative Adversarial Networks (GANs) have shown great promise in modeling high dimensional data. The learning objective of GANs usually minimizes some measure discrepancy, \textit{e.g.}, $f$-divergence~($f$-GANs) or Integral Probability…

GANs involve training two networks in an adversarial game, where each network's task depends on its adversary. Recently, several works have framed GAN training as an online or continual learning problem. We focus on the discriminator, which…

We consider the problem of optimizing the discriminator in generative adversarial networks (GANs) subject to higher-order gradient regularization. We show analytically, via the least-squares (LSGAN) and Wasserstein (WGAN) GAN variants, that…

Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress toward stable training of GANs, but sometimes can still generate only…

Generative Adversarial Networks (GANs) have been used to model the underlying probability distribution of sample based datasets. GANs are notoriuos for training difficulties and their dependence on arbitrary hyperparameters. One recent…

This paper explores the problem of generative modeling, aiming to simulate diverse examples from an unknown distribution based on observed examples. While recent studies have focused on quantifying the statistical precision of popular…

This paper proposes a new theoretical lens to view Wasserstein generative adversarial networks (WGANs). To minimize the Wasserstein-1 distance between the true data distribution and our estimate of it, we derive a distribution-dependent…

In the paper, we offer a method for studying an extremal in the classical calculus of variation in the presence of various degenerations. This method is based on introduction of Weierstrass type variations characterized by a numerical…

Mutual information maximization has emerged as a powerful learning objective for unsupervised representation learning obtaining state-of-the-art performance in applications such as object recognition, speech recognition, and reinforcement…

One of the challenges in the study of Generative Adversarial Networks (GANs) is the difficulty of its performance control. Lipschitz constraint is essential in guaranteeing training stability for GANs. Although heuristic methods such as…

We provide non asymptotic rates of convergence of the Wasserstein Generative Adversarial networks (WGAN) estimator. We build neural networks classes representing the generators and discriminators which yield a GAN that achieves the minimax…

Generative modelling is often cast as minimizing a similarity measure between a data distribution and a model distribution. Recently, a popular choice for the similarity measure has been the Wasserstein metric, which can be expressed in the…

We introduce a test for the conditional independence of random variables $X$ and $Y$ given a random variable $Z$, specifically by sampling from the joint distribution $(X,Y,Z)$, binning the support of the distribution of $Z$, and conducting…

Generative Adversarial Networks (GANs) have been promising in the field of image generation, however, they have been hard to train for language generation. GANs were originally designed to output differentiable values, so discrete language…

The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…

Generative adversarial networks (GANs) are an exciting alternative to algorithms for solving density estimation problems---using data to assess how likely samples are to be drawn from the same distribution. Instead of explicitly computing…

Generative models and in particular Generative Adversarial Networks (GANs) have become very popular and powerful data generation tool. In recent years, major progress has been made in extending this concept into the quantum realm. However,…

Stability results for extremum seeking control in $\mathbb{R}^n$ have predominantly been restricted to local or, at best, semi-global practical stability. Extending semi-global stability results of extremum-seeking systems to unbounded sets…

In many domains of computer vision, generative adversarial networks (GANs) have achieved great success, among which the family of Wasserstein GANs (WGANs) is considered to be state-of-the-art due to the theoretical contributions and…