Deeper Insights into Deep Graph Convolutional Networks: Stability and Generalization

TL;DR

This paper provides a theoretical analysis of the stability and generalization of deep graph convolutional networks, highlighting key factors influencing their performance and offering insights for designing more reliable models.

Contribution

It offers the first comprehensive theoretical exploration of stability and generalization in deep GCNs, extending beyond single-layer analysis.

Findings

Stability and generalization depend on the maximum eigenvalue of graph filters.

Deeper GCNs are more sensitive to spectral properties.

Theoretical bounds inform better GCN design.

Abstract

Graph convolutional networks (GCNs) have emerged as powerful models for graph learning tasks, exhibiting promising performance in various domains. While their empirical success is evident, there is a growing need to understand their essential ability from a theoretical perspective. Existing theoretical research has primarily focused on the analysis of single-layer GCNs, while a comprehensive theoretical exploration of the stability and generalization of deep GCNs remains limited. In this paper, we bridge this gap by delving into the stability and generalization properties of deep GCNs, aiming to provide valuable insights by characterizing rigorously the associated upper bounds. Our theoretical results reveal that the stability and generalization of deep GCNs are influenced by certain key factors, such as the maximum absolute eigenvalue of the graph filter operators and the depth of the network. Our theoretical studies contribute to a deeper understanding of the stability and generalization properties of deep GCNs, potentially paving the way for developing more reliable and well-performing models.