Gated Graph Recurrent Neural Networks

Abstract

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.

Graph Neural Networks for Decentralized Controllers

“…A GNN is an information processing architecture built upon the notion of graph filters and the use of nonlinearities [11,27]. In particular, GCNNs [15] and GRNNs [16] exploit the operation of graph convolution [17] and use pointwise nonlinearities, resulting in local architectures that only involve communication with nearby agents, thus respecting the partial information structure. Additionally, they have a naturally distributed implementation, and are also stable and equivariant, helping in transfer learning and scalability [16,19].…”

“…To further increase the descriptive power of the parametrized mapping between the agent states X(t) and the actions taken U(t), we consider GRNNs [16]. GRNNs learn a hidden state Z(t) from the sequence {X(t)} as follows…”

“…which we adopt nonlinear maps between the local state and the control action given by two different types of graph neural networks (GNNs) [11], either graph convolutional neural networks (GCNNs) [12][13][14][15] or graph recurrent neural networks (GRNNs) [16]. While these learning models naturally respect the decentralized requirement of network systems, we further adapt them to handle delays.…”

“…GRNNs, on the other hand, model the dynamical evolution of the network by learning a hidden state that keeps track of this dynamic, and is then leveraged to compute the action. In this way, the hidden state learns to keep track of the relevant past information as it pertains to the actions taken [16].…”

“…Both GCNNs and GRNNs process only local information (relied by neighboring agents) and can be computed in a distributed manner (each agent computes its corresponding output). Furthermore, they both exhibit the properties of permutation equivariance and stability to perturbations [16,19]. The former means that these architectures exploit the topological symmetries in the underlying network, while the latter implies the output is not significantly affected by small changes in the network structure.…”