Recurrent GraphNeural NetworkswithSet-BasedAggregation

Abstract:Recurrent GNNs iterate message passing to convergence, and their logical characterizations to date rely on multi-set aggregation, graded (counting) logics, and halting or acceptance conditions that cannot be verified from the network's parameters. We study recurrent GNNs with set-based aggregation and identify sufficient conditions checkable from the weights for networks to compile into formulas and formulas into networks. The main result is an effective, two-directional equivalence between a class of networks and the Boolean closure of reachability and safety properties, the fragment B$\Sigma^{\circ}_1$ of the modal $\mu$-calculus. The fragment is not an artifact: it is the exact expressive level of stabilization over finite vocabulary, which supports fixed points of a single polarity and Boolean combinations thereof, but not the composition of fixed points of opposite polarities. The correspondence needs no counting logic, no external halting signal, and no non-effective acceptance condition, yielding a verifiable path from weights to symbolic explanations for networks meeting the conditions.

Artificial Intelligence (cs.AI)

arXiv:2609.15932 [cs.AI]

(or arXiv:2609.15932v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2609.15932 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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