Graphon Neural Networks and the Transferability of Graph Neural Networks

TL;DR

This paper introduces graphon neural networks as a theoretical framework to analyze the transferability of GNNs across different graphs, establishing bounds that depend on spectral properties and highlighting a tradeoff between discriminability and transferability.

Contribution

It defines graphon NNs as limits of GNNs and proves bounds on their difference, linking spectral properties to transferability.

Findings

Bound on GNN and graphon-NN output difference diminishes with more nodes.

Transferability improves when graph convolutional filters are bandlimited.

Tradeoff identified between GNN discriminability and transferability.

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.