Graph neural network using unrolled ARMA recursions
Fatemeh Ansarizadeh, D.B.H. Tay, Dhananjay Thiruvady · Journal of the Franklin Institute · 2025
• Generalizing graph ARMA filter using the principle of algorithm unrolling. • Achieving higher accuracy in classification and lower MSE in regression. • Lower training time despite more number of parameters due to less number of epochs. Graph neural networks (GNNs) are machine learning systems for data that benefit from graph models. The graph modelling exploits the correlations within the elements of the dataset. Analogous to convolutional neural networks (CNNs), where the conventional convolution exploits localised correlations for data on regular domains, graph convolution has been proposed for data on irregular domains. Graph convolution, also referred to as a graph filter, is a foundational technique in graph signal processing (GSP) and has significantly influenced the evolution of GNNs architectures. Most graph filters are based on polynomial functions, but more recently, filters based on rational functions have also been considered. The latter are also known as graph Auto-Regressive-Moving-Average (ARMA) filters. Graph ARMA filters are usually implemented using recursive algorithms, where the parameters are fixed for every recursion. In this work, inspired by the principle of algorithm unrolling, we develop graph ARMA filters, where the parameters change in every recursion. We analyse the convergence of these general recursions and derive conditions for convergence. Using this proposed filter in a GNN, we conduct extensive experiments on real-world datasets for semi-supervised node classification, graph signal classification, graph classification, and graph regression. Comparisons with other graph filters are also made, where the superiority of the proposed filter, in terms of higher accuracy and faster convergence, is demonstrated. As supported by the double descent risk curve, even though there is a substantial increase in the number of parameters, overfitting is not observed in the experiments.