Graphon Neural Networks and the Transferability of Graph Neural Networks
This work addresses the challenge of applying GNNs to varying graph structures, which is incremental as it builds on existing GNN theory to analyze transferability.
The paper tackles the problem of analyzing the transferability of graph neural networks (GNNs) across different graphs by introducing graphon neural networks as limit objects and proving a bound on the output difference, which vanishes under bandlimited filters, establishing a tradeoff between discriminability and transferability.
Graph neural networks (GNNs) rely on graph convolutions to extract local features from network data. These graph convolutions combine information from adjacent nodes using coefficients that are shared across all nodes. Since these coefficients are shared and do not depend on the graph, one can envision using the same coefficients to define a GNN on another graph. This motivates analyzing the transferability of GNNs across graphs. In this paper we introduce graphon NNs as limit objects of GNNs and prove a bound on the difference between the output of a GNN and its limit graphon-NN. This bound vanishes with growing number of nodes if the graph convolutional filters are bandlimited in the graph spectral domain. This result establishes a tradeoff between discriminability and transferability of GNNs.