Covered Forest: Fine-grained generalization analysis of graph neural networks

arXiv (Cornell University)

Abstract

The expressive power of message-passing graph neural networks (MPNNs) is reasonably well understood, primarily through combinatorial techniques from graph isomorphism testing. However, MPNNs' generalization abilities -- making meaningful predictions beyond the training set -- remain less explored. Current generalization analyses often overlook graph structure, limit the focus to specific aggregation functions, and assume the impractical, hard-to-optimize $0$-$1$ loss function. Here, we extend recent advances in graph similarity theory to assess the influence of graph structure, aggregation, and loss functions on MPNNs' generalization abilities. Our empirical study supports our theoretical insights, improving our understanding of MPNNs' generalization properties.

Authors 3

1. Ben Finkelshtein

   University of Oxford

   Affiliation as printed

   University of Oxford

2. Floris Geerts

   University of Antwerp

   Affiliation as printed

   University of Antwerp

3. Ron Levie

   Technion – Israel Institute of Technology

   Affiliation as printed

   Technion -Israel Institute of Technology