Gated Graph Recurrent Neural Networks

Graph processes exhibit a temporal structure determined by the sequence index and and a spatial structure determined by the graph support. To learn from graph processes, an information processing architecture must then be able to exploit both underlying structures. We introduce Graph Recurrent Neural Networks (GRNNs), which achieve this goal by leveraging the hidden Markov model (HMM) together with graph signal processing (GSP). In the GRNN, the number of learnable parameters is independent of the length of the sequence and of the size of the graph, guaranteeing scalability. We also prove that GRNNs are permutation equivariant and that they are stable to perturbations of the underlying graph support. Following the observation that stability decreases with longer sequences, we propose a time-gated extension of GRNNs. We also put forward node- and edge-gated variants of the GRNN to address the problem of vanishing gradients arising from long range graph dependencies. The advantages of GRNNs over GNNs and RNNs are demonstrated in a synthetic regression experiment and in a classification problem where seismic wave readings from a network of seismographs are used to predict the region of an earthquake. Finally, the benefits of time, node and edge gating are experimentally validated in multiple time and spatial correlation scenarios.