本文主要介绍最优传输的基本理论和Wasserstein重心问题及其在深度学习中的应用。研究的主要成果是提出了Sinkhorn重心网络，它是基于Wasserstein重心算法改造而来的多层卷积神经网络，主要思路是利用激活函数和卷积核替换掉Sinkhorn算法的Gibbs核，该网络可以用于多模态或者多通道特征的融合或者降维。文中以利用遥感数据进行尼日利亚社区尺度上的贫困预测问题为例，展示了Sinkhorn网络的应用。实验结果表明，相比于原有的线性层降维的方法，Sinkhorn网络能够以更小的参数量在测试集上取得更好的拟合效果。

This article mainly introduces the basic theory of optimal transportation and the Wasserstein barycenter problem, as well as their applications in deep learning. The main contribution of this research is the proposal of the Sinkhorn barycenter network, which is a multi-layer convolutional neural network based on the Wasserstein barycenter algorithm. The main idea is to replace the Gibbs kernel of the Sinkhorn algorithm with activation functions and convolution kernels. This network can be used for feature fusion or dimensionality reduction of multi-modal or multi-channel features. The application of the Sinkhorn network is demonstrated using remote sensing data for poverty prediction at the community scale in Nigeria. Experimental results show that compared to the original linear layer dimensionality reduction method, the Sinkhorn network achieves better fitting performance on the test set with fewer parameters.