用任意最优运输成本训练生成网络（CS LG）---刘持诚

我们提出了一种新的算法，利用辅助神经网络来表达两个数据分布之间的最优传输图的潜力。在后文中，我们使用上述图谱来训练生成网络。与间接使用欧几里得距离的 WGANs 不同，这种新方法允许直接使用任何可以选择的运输成本函数来匹配手头的问题。例如，它允许使用平方距离作为运输成本函数，产生了概率分布为 Wasserstein-2 metric，从而实现了快速稳定的梯度下降。它还允许使用以图像为中心的距离，如结构相似性指标，其结果有明显的差异。

原文题目：Training Generative Networks with general Optimal Transport distances

原文：We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs, where the Euclidean distance is implicitly used, this new method allows to explicitly use any transportation cost function that can be chosen to match the problem at hand. For example, it allows to use the squared distance as a transportation cost function, giving rise to the Wasserstein-2 metric for probability distributions, which results in fast and stable gradient descends. It also allows to use image centered distances, like the structure similarity index, with notable differences in the results.

原文作者：Vaios Laschos, Jan Tinapp, Klaus Obermayer

原文地址：https://arxiv.org/abs/1910.00535