Kernel Neural Optimal Transport

TL;DR

This paper improves Neural Optimal Transport by introducing kernel weak quadratic costs, which enhance theoretical guarantees and practical performance, especially in unpaired image translation tasks.

Contribution

The paper proposes kernel weak quadratic costs for Neural Optimal Transport, addressing issues of non-optimal plans and improving both theory and practice.

Findings

Kernel costs lead to more accurate transport plans.

Improved theoretical guarantees for NOT.

Enhanced performance in image translation tasks.

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.