Node-Variant Graph Filters in Graph Neural Networks
This work addresses a theoretical limitation in GNNs for graph signal processing, offering a method to control frequency creation, but it is incremental as it modifies existing GNN components without broad application results.
The paper tackled the problem of unknown and unlearnable frequency content created by nonlinear activation functions in graph neural networks (GNNs) by replacing them with node-variant graph filters (NVGFs), enabling design or learning of frequency creation mechanisms and separating it from nonlinearity, with simulations used to analyze its role.
Graph neural networks (GNNs) have been successfully employed in a myriad of applications involving graph signals. Theoretical findings establish that GNNs use nonlinear activation functions to create low-eigenvalue frequency content that can be processed in a stable manner by subsequent graph convolutional filters. However, the exact shape of the frequency content created by nonlinear functions is not known and cannot be learned. In this work, we use node-variant graph filters (NVGFs) -- which are linear filters capable of creating frequencies -- as a means of investigating the role that frequency creation plays in GNNs. We show that, by replacing nonlinear activation functions by NVGFs, frequency creation mechanisms can be designed or learned. By doing so, the role of frequency creation is separated from the nonlinear nature of traditional GNNs. Simulations on graph signal processing problems are carried out to pinpoint the role of frequency creation.