Title: Generalizing Graph Convolutional Networks via Heat Kernel. Abstract: Graph convolutional networks (GCNs) have emerged as a powerful framework for mining and learning with graphs. A recent study shows that GCNs can be simplified as a linear model by removing nonlinearities and weight matrices across all consecutive layers, resulting the simple graph convolution (SGC) model. In this paper, we aim to understand GCNs and generalize SGC as a linear model via heat kernel (HKGCN), which acts as a low-pass filter on graphs and enables the aggregation of information from extremely large receptive fields. We theoretically show that HKGCN is in nature a continuous propagation model and GCNs without nonlinearities (i.e., SGC) are the discrete versions of it. Its low-pass filter and continuity properties facilitate the fast and smooth convergence of feature propagation. Experiments on million-scale networks show that the linear HKGCN model not only achieves consistently better results than SGC but also can match or even beat advanced GCN models, while maintaining SGC’s superiority in efficiency.