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.
Yonatan Dukler (UCLA)
lwc2017 Li (UCLA)
Alex Lin (University of California, Los Angeles)
Guido Montufar (UCLA)
Related Events (a corresponding poster, oral, or spotlight)
2019 Poster: Wasserstein of Wasserstein Loss for Learning Generative Models »
Tue Jun 11th 06:30 -- 09:00 PM Room Pacific Ballroom