On the Gradient Formula for learning Generative Models with Regularized Optimal Transport Costs
Langue
en
Article de revue
Ce document a été publié dans
Transactions on Machine Learning Research Journal. 2023-07-14
[Amherst Massachusetts]: OpenReview.net, 2022
Résumé en anglais
The use of optimal transport costs for learning generative models has become popular with Wasserstein Generative Adversarial Networks (WGANs). Training a WGAN requires the computation of the differentiation of the optimal ...Lire la suite >
The use of optimal transport costs for learning generative models has become popular with Wasserstein Generative Adversarial Networks (WGANs). Training a WGAN requires the computation of the differentiation of the optimal transport cost with respect to the parameters of the generative model. In this work, we provide sufficient conditions for the existence of a gradient formula in two different frameworks: the case of semi-discrete optimal transport (i.e. with a discrete target distribution) and the case of regularized optimal transport (i.e. with an entropic penalty). Both cases are based on the dual formulation of the transport cost, and the gradient formula involves a solution of the dual problem. The learning problem is addressed with an alternate algorithm, whose behavior is examined for the problem of MNIST digits generation. In particular, we analyze the impact of entropic regularization both on visual results and convergence speed.< Réduire
Project ANR
Models, Inference and Synthesis for Texture In Color - ANR-19-CE40-0005
Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010
Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010
Origine
Importé de halUnités de recherche