OT-net: a reusable neural optimal transport solver

With the widespread application of optimal transport (OT), its calculation becomes essential, and various algorithms have emerged. However, the existing methods either have low efficiency or cannot represent discontinuous maps. A novel reusable neural OT solver OT-Net is thus presented, which first learns Brenier’s height representation via the neural network to get its potential, and then obtains the OT map by the gradient of the potential. The algorithm has two merits: (1) When new target samples are added, the OT map can be calculated straightly, which greatly improves the efficiency and reusability of the map. (2) It can easily represent discontinuous maps, which allows it to match any target distribution with discontinuous supports and achieve sharp boundaries, and thus eliminate mode collapse. Moreover, we conducted error analyses on the proposed algorithm and demonstrated the empirical success of our approach in image generation, color transfer, and domain adaptation.