G-Signatures: Global Graph Propagation With Randomized Signatures

Abstract: Graph neural networks (GNNs) have evolved into one of the most popular deep learning architectures. However, GNNs suffer from over-smoothing node information and, therefore, struggle to solve tasks where global graph properties are relevant. We introduce G-Signatures, a novel graph learning method that enables global graph propagation via randomized signatures. G-Signatures use a new graph lifting concept to embed graph structured information, which can be interpreted as path in latent space. We further introduce the idea of latent space path mapping, which allows us to repetitively traverse latent space paths, and, thus globally process information. G-Signatures excel at extracting and processing global graph properties, and effectively scale to large graph problems. Empirically, we confirm the advantages of our G-Signatures at several classification and regression tasks.