Graph Neural Networks with convolutional ARMA filters

Popular graph neural networks implement convolution operations on graphs based on polynomial filters defined in the spectral domain. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filters that, compared to the polynomial ones, are more robust and provide a more flexible graph frequency response. We propose a 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 unseen during training. We report a spectral analysis of the proposed trainable filter, as well as experiments on four major downstream tasks: semi-supervised node classification, graph signal classification, graph classification, and graph regression. The results show that ARMA filters bring significant improvements over graph neural networks based on polynomial filters.