{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/generative-adversarial-learning-of-sinkhorn","title":"Universal Neural Optimal Transport","arxiv_id":"2212.00133","date":"2022-11-30","proceeding":null,"authors":["Jonathan Geuter","Gregor Kornhardt","Ingimar Tomasson","Vaios Laschos"],"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. 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