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Graph neural networks (GNNs) use graph convolutions to exploit networkinvariances and learn meaningful feature representations from network data.However, on large-scale graphs convolutions incur in high computational cost,leading to scalability limitations. Leveraging the graphon -- the limit objectof a graph -- in this paper we consider the problem of learning a graphonneural network (WNN) -- the limit object of a GNN -- by training GNNs on graphssampled from the graphon. Under smoothness conditions, we show that: (i) theexpected distance between the learning steps on the GNN and on the WNNdecreases asymptotically with the size of the graph, and (ii) when training ona sequence of growing graphs, gradient descent follows the learning directionof the WNN. Inspired by these results, we propose a novel algorithm to learnGNNs on large-scale graphs that, starting from a moderate number of nodes,successively increases the size of the graph during training. This algorithm isfurther benchmarked on a decentralized control problem, where it retainscomparable performance to its large-scale counterpart at a reducedcomputational cost.

Learning by Transference: Training Graph Neural Networks on Growing Graphs