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：我们研究了神经最优传输（NOT）算法，该算法采用通用最优传输公式并学习随机传输方案。研究表明，采用弱二次代价的NOT算法可能学习到非最优的伪方案。为解决该问题，我们引入了核弱二次代价，并证明其能提供更优的理论保障与实用性能。我们在非配对图像到图像翻译任务上测试了带核代价的NOT算法。