Neural Optimal Transport

TL;DR

A novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs is presented and it is proved that they are universal approximators of transport plans between probability distributions.

Abstract

We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans between probability distributions. We evaluate the performance of our optimal transport algorithm on toy examples and on the unpaired image-to-image translation.