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| Format: | Preprint |
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2022
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| Online-Zugang: | https://arxiv.org/abs/2212.00133 |
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| _version_ | 1866918328961859584 |
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| author | Geuter, Jonathan Kornhardt, Gregor Tomasson, Ingimar Laschos, Vaios |
| author_facet | Geuter, Jonathan Kornhardt, Gregor Tomasson, Ingimar Laschos, Vaios |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_00133 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Universal Neural Optimal Transport Geuter, Jonathan Kornhardt, Gregor Tomasson, Ingimar Laschos, Vaios Machine Learning Optimization and Control 68T07 (Primary) 90C08 (Secondary) I.2.6; G.3; G.4 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. |
| title | Universal Neural Optimal Transport |
| topic | Machine Learning Optimization and Control 68T07 (Primary) 90C08 (Secondary) I.2.6; G.3; G.4 |
| url | https://arxiv.org/abs/2212.00133 |