On the Explainability of Graph Convolutional Network With GCN Tangent Kernel

Graph convolutional network (GCN) is a powerful deep model in dealing with graph data. However, the explainability of GCN remains a difficult problem since the training behaviors for graph neural networks are hard to describe. In this work, we show that for GCN with wide hidden feature dimension, the output for semisupervised problem can be described by a simple differential equation. In addition, the dynamics of the behavior of output is decided by the graph convolutional neural tangent kernel (GCNTK), which is stable when the width of hidden feature tends to be infinite. And the solution of node classification can be explained directly by the differential equation for a semisupervised problem. The experiments on some toy models speak to the consistency of the GCNTK model and GCN.