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 might 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.

翻译：我们研究了使用一般最佳运输配方的神经优化运输算法(NOT),并学习了蒸汽运输计划。我们发现,由于微弱的二次成本,我们不会学到不理想的假计划。为了解决这个问题,我们引入了内核薄弱二次运输成本。我们显示,它们提供了更好的理论保障和实际性能。我们没有在未受重视的图像到图像翻译任务上进行内核成本测试。