Graph Neural Networks with Convolutional ARMA Filters

TLDR

Graph neural networks commonly use polynomial spectral filters for graph convolutions. The paper proposes an ARMA‑based graph convolutional layer to achieve a more flexible frequency response, greater noise robustness, and improved global structure capture. The authors implement the ARMA filter as a recursive, distributed convolutional layer that is efficient, node‑localized, and transferable, and analyze its spectral properties. Experiments demonstrate that the ARMA layer significantly outperforms polynomial‑filter GNNs on node classification, graph signal classification, graph classification, and graph regression tasks.

Abstract

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.