Some Theoretical Insights into Wasserstein GANs

Abstract

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.

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Cited by in corpus (6)

• Ten Years of Generative Adversarial Nets (GANs): A survey of the state-of-the-art
• Statistical guarantees for generative models without domination
• Rates of convergence for density estimation with generative adversarial networks
• Statistical analysis of Wasserstein GANs with applications to time series forecasting
• Optimal 1-Wasserstein Distance for WGANs
• Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution