Decidability of graph neural networks via logical characterizations

Conference item

We present results concerning the expressiveness and decidability of a popular graph learning formalism, graph neural networks (GNNs), exploiting connections with logic. We use a family of recently-discovered decidable logics involving ``Presburger quantifiers''. We show how to use these logics to measure the expressiveness of classes of GNNs, in some cases getting exact correspondences between the expressiveness of logics and GNNs. We also employ the logics, and the techniques used to analyze them, to obtain decision procedures for verification problems over GNNs. We complement this with undecidability results for static analysis problems involving the logics, as well as for GNN verification problems.

Authors: Benedikt, M; Lu, C-H; Motik, B; Tan, T

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Lipics
• Host title: Proceedings of the 51st International Colloquium on Automata Languages and Programming (ICALP 2024)
• Volume: 297
• Pages: 127:1-127:20
• Publication date: 2024-07-08
• Acceptance date: 2024-04-19
• Event title: 51st International Colloquium on Automata Languages and Programming (ICALP 2024)
• Event location: Talinn, Estonia
• Event website: https://compose.ioc.ee/icalp2024/
• Event start date: 2024-04-08
• Event end date: 2024-04-12
• DOI: 10.4230/LIPIcs.ICALP.2024.127
• Language: English
• Keywords: graph neural networks; logic