Kernel Neural Optimal Transport

Abstract

We study the Neural Optimal Transport (NOT) algorithm which uses the general optimal transport formulation and learns stochastic transport plans. We show that NOT with the weak quadratic cost might learn fake plans which are not optimal. To resolve this issue, we introduce kernel weak quadratic costs. We show that they provide improved theoretical guarantees and practical performance. We test NOT with kernel costs on the unpaired image-to-image translation task.

Alexander Korotin

Assistant professor,
senior research scientist

My research interests include generative modeling, unpaired learning, optimal transport and Schrodinger bridges.