A Wasserstein perspective of Vanilla GANs


arXiv:2403.15312v1 Announce Sort: cross
Summary: The empirical success of Generative Adversarial Networks (GANs) induced an rising curiosity in theoretical analysis. The statistical literature is especially targeted on Wasserstein GANs and generalizations thereof, which particularly permit for good dimension discount properties. Statistical outcomes for Vanilla GANs, the unique optimization drawback, are nonetheless relatively restricted and require assumptions equivalent to easy activation features and equal dimensions of the latent house and the ambient house. To bridge this hole, we draw a connection from Vanilla GANs to the Wasserstein distance. By doing so, present outcomes for Wasserstein GANs will be prolonged to Vanilla GANs. Particularly, we acquire an oracle inequality for Vanilla GANs in Wasserstein distance. The assumptions of this oracle inequality are designed to be happy by community architectures generally utilized in observe, equivalent to feedforward ReLU networks. By offering a quantitative consequence for the approximation of a Lipschitz perform by a feedforward ReLU community with bounded H”older norm, we conclude a fee of convergence for Vanilla GANs in addition to Wasserstein GANs as estimators of the unknown likelihood distribution.

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