Connections between Support Vector Machines, Wasserstein distance and gradient-penalty GANs
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We generalize the concept of maximum-margin classifiers (MMCs) to arbitrary norms and non-linear functions. Support Vector Machines (SVMs) are a special case of MMC. We find that MMCs can be formulated as Integral Probability Metrics (IPMs) or classifiers with some form of gradient norm penalty. This implies a direct link to a class of Generative adversarial networks (GANs) which penalize a gradient norm. We show that the Discriminator in Wasserstein, Standard, Least-Squares, and Hinge GAN with Gradient Penalty is an MMC. We explain why maximizing a margin may be helpful in GANs. We hypothesize and confirm experimentally that L^∞-norm penalties with Hinge loss produce better GANs than L^2-norm penalties (based on common evaluation metrics). We derive the margins of Relativistic paired (Rp) and average (Ra) GANs.
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