Graph Convolutional Networks (GCNs) are known to suffer from performance degradation as the number of layers increases, which is usually attributed to over-smoothing. Despite the apparent consensus, we observe that there exists a discrepancy between the theoretical understanding of over-smoothing and the practical capabilities of GCNs. Specifically, we argue that over-smoothing does not necessarily happen in practice, a deeper model is provably expressive, can converge to global optimum with linear convergence rate, and achieve very high training accuracy as long as properly trained. Despite being capable of achieving high training accuracy, empirical results show that the deeper models generalize poorly on the testing stage and existing theoretical understanding of such behavior remains elusive. To achieve better understanding, we carefully analyze the generalization capability of GCNs, and show that the training strategies to achieve high training accuracy significantly deteriorate the generalization capability of GCNs. Motivated by these findings, we propose a decoupled structure for GCNs that detaches weight matrices from feature propagation to preserve the expressive power and ensure good generalization performance. We conduct empirical evaluations on various synthetic and real-world datasets to validate the correctness of our theory.

本文针对图卷积网络（GCNs）在层数增多时表现下降的问题进行了研究，发现合理训练后更深的模型具有极高的训练准确性，但泛化能力较差。通过分析GCNs的泛化能力，本文提出了一种解耦结构，使得GCNs既能保留表达能力，又能保证较好的泛化性能。各种合成和真实数据集的实证评估证实了这一理论。

关于训练图卷积网络深度的可证明优势