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Wasserstein of Wasserstein Loss for Learning Generative Models

Yonatan Dukler · Wuchen Li · Alex Lin · Guido Montufar

Pacific Ballroom #15

Keywords: [ Unsupervised and Semi-supervised Learning ] [ Generative Adversarial Networks ] [ Deep Learning Theory ] [ Deep Generative Models ] [ Computer Vision ]

Abstract: The Wasserstein distance serves as a loss function for unsupervised learning which depends on the choice of a ground metric on sample space. We propose to use the Wasserstein distance itself as the ground metric on the sample space of images. This ground metric is known as an effective distance for image retrieval, that correlates with human perception. We derive the Wasserstein ground metric on pixel space and define a Riemannian Wasserstein gradient penalty to be used in the Wasserstein Generative Adversarial Network (WGAN) framework. The new gradient penalty is computed efficiently via convolutions on the $L^2$ gradients with negligible additional computational cost. The new formulation is more robust to the natural variability of the data and provides for a more continuous discriminator in sample space.

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