Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspective

Graph neural networks (GNNs) have shown superiority in many prediction tasks over graphs due to their impressive capability of capturing nonlinear relations in graph-structured data. However, for node classification tasks, often, only marginal improvement of GNNs has been observed in practice over their linear counterparts. Previous works provide very few understandings of this phenomenon. In this work, we resort to Bayesian learning to give an in-depth investigation of the functions of non-linearity in GNNs for node classification tasks. Given a graph generated from the statistical model CSBM, we observe that the max-a-posterior estimation of a node label given its own and neighbors' attributes consists of two types of non-linearity, the transformation of node attributes and a ReLU-activated feature aggregation from neighbors.