Recurrent GraphNeural NetworkswithSet-BasedAggregation

תקציר מקורי באנגליתarXiv:2609.15932v1 Announce Type: new 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, whic