Deeper Insights into Deep Graph Convolutional Networks: Stability and Generalization

Several pioneering works [3, 4] introduced the initial concept of graph neural networks (GNNs), incorporating recurrent mechanisms and necessitating neural network parameters to define contraction mappings. Concurrently, Micheli [5] introduced the neural network for graphs, commonly referred to as NN4G, over a comparable timeframe. It is worth noting that the NN4G diverges from recurrent mechanisms and instead employs a feed-forward architecture, exhibiting similarities to contemporary GNNs. In recent years, (contemporary) GNNs have gained significant attention as an effective methodology for modeling graph data [6-11]. To obtain a comprehensive understanding of GNNs and deep learning for graphs, we refer the readers to relevant survey papers for an extensive overview [12-15]. Among the various GNN variants, one of the most powerful and frequently used GNNs is graph convolutional networks (GCNs). A widely accepted perspective posits that GCNs can be regarded as an extension or generalization of traditional spatial filters, which are commonly employed in Euclidean data analysis, to the realm of non-Euclidean data. Due to its success on non-Euclidean data, GCN has attracted widespread attention on its theoretical exploration.