Unified GCNs: Towards Connecting GCNs with CNNs

Graph Convolutional Networks (GCNs) have been widely demonstrated their powerful ability in graph data representation and learning. Existing graph convolution layers are mainly designed based on graph signal processing and transform aspect which usually suffer from some limitations, such as over-smoothing, over-squashing and non-robustness, etc. As we all know that Convolution Neural Networks (CNNs) have received great success in many computer vision and machine learning. One main aspect is that CNNs leverage many learnable convolution filters (kernels) to obtain rich feature descriptors and thus can have high capacity to encode complex patterns in visual data analysis. Also, CNNs are flexible in designing their network architecture, such as MobileNet, ResNet, Xception, etc. Therefore, it is natural to arise a question: can we design graph convolutional layer as flexibly as that in CNNs? Innovatively, in this paper, we consider connecting GCNs with CNNs deeply from a general perspective of depthwise separable convolution operation. Specifically, we show that GCN and GAT indeed perform some specific depthwise separable convolution operations. This novel interpretation enables us to better understand the connections between GCNs (GCN, GAT) and CNNs and further inspires us to design more Unified GCNs (UGCNs). As two showcases, we implement two UGCNs, i.e., Separable UGCN (S-UGCN) and General UGCN (G-UGCN) for graph data representation and learning. Promising experiments on several graph representation benchmarks demonstrate the effectiveness and advantages of the proposed UGCNs.