Universal Transferability for GNNs Via Graphons

Graph neural networks (GNNs) provide state-of-the-art results in a wide variety of tasks which typically involve predicting features at the nodes of a graph. A particularly useful feature of GNNs is their ability to extrapolate learning from smaller to larger graphs, a phenomenon known as transferability. In this short article we use the theory of graphon neural networks to prove a Universal Transferability Theorem which guarantees that all graph neural networks are transferable on sequences of graphs converging to a given graphon in appropriate norms. These results summarize and extend work to appear in [18].