Quantization in Graph Convolutional Neural Networks

By replacing classical convolutions with graph filters, graph convolutional neural networks (GNNs) have emerged as powerful tools to learn a nonlinear mapping for data defined over graphs and address a variety of tasks encountered in many applications. GNNs inherit the distributed implementation of graph filters, where local exchanges among neighbor nodes are performed. In such distributed setting, the quantization can play a fundamental role to save communication and energy resources prior to data transmission, in scenarios where nodes are resource constrained. In this paper, we propose a quantized GNN architecture based on distributed graph filters for signals defined on graphs and analyze how the quantization noise can affect its performance. We show also that the expected error due to quantization at the GNN output is upper-bounded and the use of a decreasing quantization stepsize leads to more accuracy. The performance of the proposed schemes is evaluated by numerical experiments for the application of source localization.