Graphon Neural Networks and the Transferability of Graph Neural Networks

Abstract

Graph neural networks (GNNs) rely on graph convolutions to extract local features from network data. These graph convolutions combine information from adjacent nodes using coefficients that are shared across all nodes. Since these coefficients are shared and do not depend on the graph, one can envision using the same coefficients to define a GNN on another graph. This motivates analyzing the transferability of GNNs across graphs. In this paper we introduce graphon NNs as limit objects of GNNs and prove a bound on the difference between the output of a GNN and its limit graphon-NN. This bound vanishes with growing number of nodes if the graph convolutional filters are bandlimited in the graph spectral domain. This result establishes a tradeoff between discriminability and transferability of GNNs.

References in corpus (10)

• The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
• Geometric deep learning: going beyond Euclidean data
• Neural Tangent Kernel: Convergence and Generalization in Neural Networks
• Convolutional Neural Network Architectures for Signals Supported on Graphs
• Stability Properties of Graph Neural Networks
• Rate-optimal graphon estimation
• Nonparametric graphon estimation
• Invariance-Preserving Localized Activation Functions for Graph Neural Networks
• Graphon Signal Processing
• Stability of Graph Scattering Transforms

Cited by in corpus (5)

• Graphon Signal Processing
• Graph Deep Learning for Time Series Forecasting
• Graph and graphon neural network stability
• Stability of Neural Networks on Riemannian Manifolds
• Graph Neural Networks for Distributed Linear-Quadratic Control