Increase and Conquer: Training Graph Neural Networks on Growing Graphs


Abstract in English

Graph neural networks (GNNs) use graph convolutions to exploit network invariances and learn meaningful features from network data. However, on large-scale graphs convolutions incur in high computational cost, leading to scalability limitations. Leveraging the graphon -- the limit object of a graph -- in this paper we consider the problem of learning a graphon neural network (WNN) -- the limit object of a GNN -- by training GNNs on graphs sampled Bernoulli from the graphon. Under smoothness conditions, we show that: (i) the expected distance between the learning steps on the GNN and on the WNN decreases asymptotically with the size of the graph, and (ii) when training on a sequence of growing graphs, gradient descent follows the learning direction of the WNN. Inspired by these results, we propose a novel algorithm to learn GNNs on large-scale graphs that, starting from a moderate number of nodes, successively increases the size of the graph during training. This algorithm is benchmarked on both a recommendation system and a decentralized control problem where it is shown to retain comparable performance, to its large-scale counterpart, at a reduced computational cost.

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