  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.

Machine Learning;Machine Learning