Fast and Effective GNN Training with Linearized Random Spanning Trees

We present a new effective and scalable framework for training GNNs in supervised node classification tasks, given graph-structured data. Our approach increasingly refines the weight update operations on a sequence of path graphs obtained by linearizing random spanning trees extracted from the input network. The path graphs are designed to retain essential topological and node information of the original graph. At the same time, the sparsity of path graphs enables a much lighter GNN training which, besides scalability, helps in mitigating classical training issues, like over-squashing and over-smoothing. We carry out an extensive experimental investigation on a number of real-world graph benchmarks, where we apply our framework to graph convolutional networks, showing simultaneous improvement of both training speed and test accuracy, as compared to well-known baselines.