An Anatomy of Graph Neural Networks Going Deep via the Lens of Mutual Information: Exponential Decay vs. Full Preservation

Graph Convolutional Network (GCN) has attracted intensive interests recently. One major limitation of GCN is that it often cannot benefit from using a deep architecture, while traditional CNN and an alternative Graph Neural Network architecture, namely GraphCNN, often achieve better quality with a deeper neural architecture. How can we explain this phenomenon? In this paper, we take the first step towards answering this question. We first conduct a systematic empirical study on the accuracy of GCN, GraphCNN, and ResNet-18 on 2D images and identified relative importance of different factors in architectural design. This inspired a novel theoretical analysis on the mutual information between the input and the output after $l$ GCN and GraphCNN layers. We identified regimes in which GCN suffers exponentially fast information lose and show that GraphCNN requires a much weaker condition for similar behavior to happen.