Neural Optimal Transport

TL;DR

This paper introduces a neural network-based algorithm for computing optimal transport maps and plans, demonstrating its universality and effectiveness on toy examples and image translation tasks.

Contribution

It proposes a new neural network approach for optimal transport, with theoretical proof of universality and practical evaluation on diverse tasks.

Findings

Neural networks can approximate optimal transport plans universally.

The algorithm performs well on toy examples.

Effective in unpaired image-to-image translation.

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.