On the Stability of Graph Convolutional Neural Networks: A Probabilistic Perspective

TL;DR

This paper introduces a probabilistic framework to analyze the stability of graph convolutional neural networks (GCNNs) against graph perturbations, emphasizing the role of data distribution for more robust model understanding.

Contribution

It presents a novel distribution-aware stability analysis for GCNNs, moving beyond worst-case scenarios to incorporate data distribution effects.

Findings

Probabilistic stability bounds for GCNNs under graph perturbations

Enhanced robustness against adversarial attacks demonstrated

Validation through extensive experiments on real datasets

Abstract

Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these models, i.e., their sensitivity to small changes in the graph structure, remains in rather limited settings, hampering the development and deployment of robust and trustworthy models in practice. To fill this gap, we study how perturbations in the graph topology affect GCNN outputs and propose a novel formulation for analyzing model stability. Unlike prior studies that focus only on worst-case perturbations, our distribution-aware formulation characterizes output perturbations across a broad range of input data. This way, our framework enables, for the first time, a probabilistic perspective on the interplay between the statistical properties of the node data and perturbations in the graph topology. We conduct extensive experiments to validate our theoretical findings and demonstrate their benefits over existing baselines, in terms of both representation stability and adversarial attacks on downstream tasks. Our results demonstrate the practical significance of the proposed formulation and highlight the importance of incorporating data distribution into stability analysis.