SLOG: An Inductive Spectral Graph Neural Network Beyond Polynomial Filter

Graph neural networks (GNNs) have exhibited superb power in many graph related tasks. Existing GNNs can be categorized into spatial GNNs and spectral GNNs. The spatial GNNs primarily capture the local information around each node, while the spectral GNNs are able to operate on the frequency signals of the entire graph. However, most, if not all, existing spectral GNNs are faced with two limitations: (1) the polynomial limitation that for most spectral GNNs, the expressive power in the spectral domain is limited to polynomial filters; and (2) the transductive limitation that for the node-level task, most spectral GNNs can only be applied on relatively smallscale graphs in transductive setting. In this paper, we propose a novel spectral graph neural network named SLOG to solve the above two limitations. For the polynomial limitation, SLOG proposes a novel filter with real-valued order with geometric interpretability, mathematical feasibility and adaptive filtering ability to go beyond polynomial. For the transductive limitation, SLOG combines the subgraph sampling technique in spatial GNNs and the signal processing technique in spectral GNNs together to make itself tailored to the inductive node-level tasks on large-scale graphs. Extensive experimental results on 16 datasets demonstrate the superiority of SLOG in inductive homophilic and heterophilic node classification task.