Generative Adversarial Networks (GANs) have been successful in producing outstanding results in areas as diverse as image, video, and text generation. Building on these successes, a large number of empirical studies have validated the benefits of the cousin approach called Wasserstein GANs (WGANs), which brings stabilization in the training process. In the present paper, we add a new stone to the edifice by proposing some theoretical advances in the properties of WGANs. First, we properly define the architecture of WGANs in the context of integral probability metrics parameterized by neural networks and highlight some of their basic mathematical features. We stress in particular interesting optimization properties arising from the use of a parametric 1-Lipschitz discriminator. Then, in a statistically-driven approach, we study the convergence of empirical WGANs as the sample size tends to infinity, and clarify the adversarial effects of the generator and the discriminator by underlining some trade-off properties. These features are finally illustrated with experiments using both synthetic and real-world datasets.

翻译：在图象、视频和文字生成等不同领域,产生出杰出成果的工作取得了成功。在这些成功的基础上,大量经验研究证实了表亲方法 " 瓦西尔斯坦-GANs " (WGANs)的好处,使培训过程趋于稳定。在本文件中,我们通过提议在WGANs特性方面取得一些理论进步,为版面增添了新的石块。首先,我们在神经网络综合概率参数参数参数范围内适当界定了WGANs的结构,并突出了它们的一些基本数学特征。我们特别强调了使用参数1-Lipschitz区分器所产生的最优化性能。然后,我们以统计学驱动的方法,研究实验性WGANs在样本大小趋于无限时的趋同性,并通过强调某些交易特性来澄清生成者和歧视者的对抗性影响。这些特征最后通过使用合成和现实世界数据集进行实验加以说明。