Multiresolution Reservoir Graph Neural Network

Graph neural networks are receiving increasing attention as state-of-the-art methods to process graph-structured data. However, similar to other neural networks, they tend to suffer from a high computational cost to perform training. Reservoir computing (RC) is an effective way to define neural networks that are very efficient to train, often obtaining comparable predictive performance with respect to the fully trained counterparts. Different proposals of reservoir graph neural networks have been proposed in the literature. However, their predictive performances are still slightly below the ones of fully trained graph neural networks on many benchmark datasets, arguably because of the oversmoothing problem that arises when iterating over the graph structure in the reservoir computation. In this work, we aim to reduce this gap defining a multiresolution reservoir graph neural network (MRGNN) inspired by graph spectral filtering. Instead of iterating on the nonlinearity in the reservoir and using a shallow readout function, we aim to generate an explicit $k$ -hop unsupervised graph representation amenable for further, possibly nonlinear, processing. Experiments on several datasets from various application areas show that our approach is extremely fast and it achieves in most of the cases comparable or even higher results with respect to state-of-the-art approaches.