Analysing the Update step in Graph Neural Networks via Sparsification

In recent years, Message-Passing Neural Networks (MPNNs), the most prominent Graph Neural Network (GNN) framework, have celebrated much success in the analysis of graph-structured data. In MPNNs the computations are split into three steps, Aggregation, Update and Readout. In this paper, a series of models to successively sparsify the linear transform in the Update step is proposed. Specifically, the ExpanderGNN model with a tuneable sparsification rate and the Activation-Only GNN, which has no linear transform in the Update step, are proposed. In agreement with a growing trend in the relevant literature, the sparsification paradigm is changed by initialising sparse neural network architectures rather than expensively sparsifying already trained architectures. These novel benchmark models enable a better understanding of the influence of the Update step on model performance and outperform existing simplified benchmark models such as the Simple Graph Convolution (SGC). The ExpanderGNNs, and in some cases the Activation-Only models, achieve performance on par with their vanilla counterparts on several downstream graph prediction tasks, proving that often the update step has little impact on the performance and resulting in models with exponentially fewer trainable parameters than the state-of-the-art.