  Network data can be conveniently modeled as a graph signal, where data values
are assigned to nodes of a graph that describes the underlying network
topology. Successful learning from network data is built upon methods that
effectively exploit this graph structure. In this work, we leverage graph
signal processing to characterize the representation space of graph neural
networks (GNNs). We discuss the role of graph convolutional filters in GNNs and
show that any architecture built with such filters has the fundamental
properties of permutation equivariance and stability to changes in the
topology. These two properties offer insight about the workings of GNNs and
help explain their scalability and transferability properties which, coupled
with their local and distributed nature, make GNNs powerful tools for learning
in physical networks. We also introduce GNN extensions using edge-varying and
autoregressive moving average graph filters and discuss their properties.
Finally, we study the use of GNNs in recommender systems and learning
decentralized controllers for robot swarms.

Machine Learning;Systems and Control;Systems and Control;Machine Learning