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arXiv · 2212.00133

Universal Neural Optimal Transport

Jonathan Geuter·Gregor Kornhardt·Ingimar Tomasson·Vaios Laschos
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Abstract

Optimal Transport (OT) problems are a cornerstone of many applications, but solving them is computationally expensive. To address this problem, we propose UNOT (Universal Neural Optimal Transport), a novel framework capable of accurately predicting (entropic) OT distances and plans between discrete measures for a given cost function. UNOT builds on Fourier Neural Operators, a universal class of neural networks that map between function spaces and that are discretization-invariant, which enables our network to process measures of variable resolutions. The network is trained adversarially using a second, generating network and a self-supervised bootstrapping loss. We ground UNOT in an extensive theoretical framework. Through experiments on Euclidean and non-Euclidean domains, we show that our network not only accurately predicts OT distances and plans across a wide range of datasets, but also captures the geometry of the Wasserstein space correctly. Furthermore, we show that our network can be used as a state-of-the-art initialization for the Sinkhorn algorithm with speedups of up to $7.4\times$, significantly outperforming existing approaches.

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Jonathan Geuter, Gregor Kornhardt, Ingimar Tomasson, Vaios Laschos. 2022-11-30. Universal Neural Optimal Transport. https://arxiv.org/abs/2212.00133

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