Graph Neural Networks: Architectures, Stability and Transferability
This work provides foundational theoretical insights for researchers and practitioners using GNNs in domains like recommendation systems and wireless networks, though it is incremental in extending known CNN concepts to graphs.
The paper tackles the theoretical understanding of Graph Neural Networks (GNNs) by showing they generalize convolutional neural networks and exhibit properties like equivariance to permutation and stability to graph deformations, which explain their empirical performance, and it demonstrates transferability across networks with different node numbers through convergence to graphon neural networks.
Graph Neural Networks (GNNs) are information processing architectures for signals supported on graphs. They are presented here as generalizations of convolutional neural networks (CNNs) in which individual layers contain banks of graph convolutional filters instead of banks of classical convolutional filters. Otherwise, GNNs operate as CNNs. Filters are composed with pointwise nonlinearities and stacked in layers. It is shown that GNN architectures exhibit equivariance to permutation and stability to graph deformations. These properties help explain the good performance of GNNs that can be observed empirically. It is also shown that if graphs converge to a limit object, a graphon, GNNs converge to a corresponding limit object, a graphon neural network. This convergence justifies the transferability of GNNs across networks with different number of nodes. Concepts are illustrated by the application of GNNs to recommendation systems, decentralized collaborative control, and wireless communication networks.