Graphon and Graph Neural Network Stability

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...

Full description

Saved in:
Bibliographic Details
Main Authors: Ruiz, Luana, Wang, Zhiyang, Ribeiro, Alejandro
Format: Conference Proceeding
Language:English
Subjects:
Analytical models
Asymptotic stability
graph neural networks
graph signal processing
graphons
Motion pictures
Perturbation methods
Signal processing
stability
Stochastic processes
Uncertainty
Online Access:Request full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2379-190X
DOI:10.1109/ICASSP39728.2021.9414838