  Graph neural networks (GNNs) are a powerful architecture for tackling graph
learning tasks, yet have been shown to be oblivious to eminent substructures,
such as cycles. We present TOGL, a novel layer that incorporates global
topological information of a graph using persistent homology. TOGL can be
easily integrated into any type of GNN and is strictly more expressive in terms
of the Weisfeiler--Lehman test of isomorphism. Augmenting GNNs with our layer
leads to beneficial predictive performance, both on synthetic data sets, which
can be trivially classified by humans but not by ordinary GNNs, and on
real-world data.
