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Kernel Neural Optimal Transport

Alexander Korotin · Daniil Selikhanovych · Evgeny Burnaev

MH1-2-3-4 #133

Keywords: [ Generative models ] [ optimal transport ] [ kernels ] [ neural networks ]


We study the Neural Optimal Transport (NOT) algorithm which uses the general optimal transport formulation and learns stochastic transport plans. We show that NOT with the weak quadratic cost may learn fake plans which are not optimal. To resolve this issue, we introduce kernel weak quadratic costs. We show that they provide improved theoretical guarantees and practical performance. We test NOT with kernel costs on the unpaired image-to-image translation task.

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