Graph Neural Networks: Architectures, Stability, and Transferability

Graph neural networks (GNNs) are information processing architectures for signals supported on graphs. They presented here as generalizations of convolutional (CNNs) in which individual layers contain banks graph filters instead classical filters. Otherwise, GNNs operate CNNs. Filters composed pointwise nonlinearities and stacked layers. It is shown that GNN exhibit equivariance to permutation stability deformations. These properties help explain the good performance can be observed empirically. also if graphs converge a limit object, graphon, corresponding graphon network. This convergence justifies transferability across with different numbers nodes. Concepts illustrated by application recommendation systems, decentralized collaborative control, wireless communication networks.