Computer Science > Logic in Computer Science
[Submitted on 28 Apr 2024 (v1), last revised 30 Apr 2024 (this version, v2)]
Title:Decidability of Graph Neural Networks via Logical Characterizations
View PDFAbstract: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.
Submission history
From: Chia-Hsuan Lu [view email][v1] Sun, 28 Apr 2024 12:01:23 UTC (197 KB)
[v2] Tue, 30 Apr 2024 15:06:09 UTC (195 KB)
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