Graph and graphon neural network stability
This addresses stability issues in GNNs for applications like network data analysis, but it is incremental as it builds on existing graphon signal processing theory.
The paper tackled the problem of graph neural network (GNN) stability under graph uncertainties by analyzing stability using graphons as generating models, finding that GNNs are stable with a bound that decreases asymptotically with graph size, as demonstrated in a movie recommendation experiment.
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.