Graph and graphon neural network stability

Abstract

Graph neural networks (GNNs) are learning architectures that rely on knowledge of the graph structure to generate meaningful representations of large-scale network data. GNN stability is thus important as in real-world scenarios there are typically uncertainties associated with the graph. We analyze GNN stability using kernel objects called graphons. Graphons are both limits of convergent graph sequences and generating models for deterministic and stochastic graphs. Building upon the theory of graphon signal processing, we define graphon neural networks and analyze their stability to graphon perturbations. We then extend this analysis by interpreting the graphon neural network as a generating model for GNNs on deterministic and stochastic graphs instantiated from the original and perturbed graphons. We observe that GNNs are stable to graphon perturbations with a stability bound that decreases asymptotically with the size of the graph. This asymptotic behavior is further demonstrated in an experiment of movie recommendation.

References in corpus (8)

• The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
• Discrete Signal Processing on Graphs
• Convolutional Neural Network Architectures for Signals Supported on Graphs
• Stability Properties of Graph Neural Networks
• MIMO Interference Alignment Over Correlated Channels with Imperfect CSI
• Graphon Signal Processing
• Graphon Neural Networks and the Transferability of Graph Neural Networks
• Stability of Graph Scattering Transforms

Cited by in corpus (3)

• Stability of Neural Networks on Riemannian Manifolds
• Stability of Graph Convolutional Neural Networks to Stochastic Perturbations
• Interferometric Graph Transform for Community Labeling