This paper aims at studying the sample complexity of graph convolutional networks (GCNs), by providing tight upper bounds of Rademacher complexity for GCN models with a single hidden layer. Under regularity conditions, theses derived complexity bounds explicitly depend on the largest eigenvalue of graph convolution filter and the degree distribution of the graph. Again, we provide a lower bound of Rademacher complexity for GCNs to show optimality of our derived upper bounds. Taking two commonly used examples as representatives, we discuss the implications of our results in designing graph convolution filters an graph distribution.

翻译：本文旨在研究图层变迁网络的样本复杂性,为GCN模型提供一个单一隐藏层的雷德马赫复杂度的紧上限。在常规条件下,这些衍生的复杂度明确取决于图层变迁过滤器的最大电子价值和图的分布度。我们为拉德马赫复杂度的较低部分提供了拉德马赫复杂度的下限,以显示我们衍生的上界的最佳性。我们以代表身份使用两个常用的例子,在设计图层变迁过滤器时,我们讨论了我们的结果对图表分布的影响。