Transferability of Graph Neural Networks: an Extended Graphon Approach

TL;DR

This paper investigates the transferability of spectral graph convolutional neural networks (GCNNs) across different graphs using graphon analysis, providing theoretical guarantees for transferability under various graph models.

Contribution

It introduces a graphon-based framework to prove transferability of GCNNs with continuous filters, including unbounded graphon cases, and establishes non-asymptotic stability results.

Findings

GCNNs with continuous filters are transferable across graphs approximating the same graphon.

Transferability extends to graphs approximating unbounded graphon shift operators.

Non-asymptotic linear stability of GCNNs is established.

Abstract

We study spectral graph convolutional neural networks (GCNNs), where filters are defined as continuous functions of the graph shift operator (GSO) through functional calculus. A spectral GCNN is not tailored to one specific graph and can be transferred between different graphs. It is hence important to study the GCNN transferability: the capacity of the network to have approximately the same repercussion on different graphs that represent the same phenomenon. Transferability ensures that GCNNs trained on certain graphs generalize if the graphs in the test set represent the same phenomena as the graphs in the training set. In this paper, we consider a model of transferability based on graphon analysis. Graphons are limit objects of graphs, and, in the graph paradigm, two graphs represent the same phenomenon if both approximate the same graphon. Our main contributions can be summarized as follows: 1) we prove that any fixed GCNN with continuous filters is transferable under graphs that approximate the same graphon, 2) we prove transferability for graphs that approximate unbounded graphon shift operators, which are defined in this paper, and, 3) we obtain non-asymptotic approximation results, proving linear stability of GCNNs. This extends current state-of-the-art results which show asymptotic transferability for polynomial filters under graphs that approximate bounded graphons.