About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Publication
AISTATS 2019
Conference paper
Sobolev descent
Abstract
We study a simplification of GAN training: the problem of transporting particles from a source to a target distribution. Starting from the Sobolev GAN critic, part of the gradient regularized GAN family, we show a strong relation with Optimal Transport (OT). Specifically with the less popular dynamic formulation of OT that finds a path of distributions from source to target minimizing a “kinetic energy”. We introduce Sobolev descent that constructs similar paths by following gradient flows of a critic function in a kernel space or parametrized by a neural network. In the kernel version, we show convergence to the target distribution in the MMD sense. We show in theory and experiments that regularization has an important role in favoring smooth transitions between distributions, avoiding large gradients from the critic. This analysis in a simplified particle setting provides insight in paths to equilibrium in GANs.