  Popular graph neural networks implement convolution operations on graphs
based on polynomial spectral filters. In this paper, we propose a novel graph
convolutional layer inspired by the auto-regressive moving average (ARMA)
filter that, compared to polynomial ones, provides a more flexible frequency
response, is more robust to noise, and better captures the global graph
structure. We propose a graph neural network implementation of the ARMA filter
with a recursive and distributed formulation, obtaining a convolutional layer
that is efficient to train, localized in the node space, and can be transferred
to new graphs at test time. We perform a spectral analysis to study the
filtering effect of the proposed ARMA layer and report experiments on four
downstream tasks: semi-supervised node classification, graph signal
classification, graph classification, and graph regression. Results show that
the proposed ARMA layer brings significant improvements over graph neural
networks based on polynomial filters.
