Learning by Transference: Training Graph Neural Networks on Growing Graphs

TL;DR

This paper introduces a method for training graph neural networks on growing graphs by leveraging graphon theory, enabling scalable learning on large networks with reduced computational costs.

Contribution

It proposes a novel algorithm that trains GNNs on increasing graph sizes, guided by the graphon limit, to improve scalability and efficiency.

Findings

Expected distance between GNN and WNN decreases with graph size

Gradient descent on growing graphs follows WNN learning direction

Algorithm achieves comparable performance with lower computational cost

Abstract

Graph neural networks (GNNs) use graph convolutions to exploit network invariances 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 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 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 further benchmarked on a decentralized control problem, where it retains comparable performance to its large-scale counterpart at a reduced computational cost.