Concepts de base
Message passing neural networks (MPNNs) can generalize effectively to unseen sparse, noisy graphs sampled from a mixture of graphons, as long as the graphs are sufficiently large.
Résumé
The paper studies the generalization capabilities of message passing neural networks (MPNNs) in a more realistic setting compared to previous work. The key modifications are:
Graphs are modeled as simple random graphs with Bernoulli-distributed edges, instead of weighted graphs.
Graphs and graph signals are sampled from perturbed graphons, instead of clean graphons.
Sparse graphs are analyzed, instead of dense graphs.
The authors propose a generative model for graph-signals based on a mixture of graphons, where each class is associated with a unique graphon. They derive non-asymptotic generalization bounds for supervised graph classification tasks using MPNNs in this more realistic setting. The bounds show that as the average number of nodes in the graphs increases, the generalization error decreases. This implies that MPNNs with higher complexity than the size of the training set can still generalize effectively, as long as the graphs are sufficiently large.
The theoretical results are supported by numerical experiments, which demonstrate that the proposed bounds are significantly tighter than existing bounds.
Stats
The average number of nodes in the graphs, N, is a key parameter that affects the generalization error. Specifically, the generalization error decreases as N increases.