Recurrent GraphNeural NetworkswithSet-BasedAggregation
Paper proves two-directional equivalence between recurrent GNNs with set-based aggregation and Boolean closure of reachability/safety properties in modal mu-calculus, checkable from weights.
The authors study recurrent graph neural networks with set-based aggregation and identify sufficient conditions, checkable directly from network weights, for compiling networks into logical formulas and formulas into networks. They establish an effective two-directional equivalence with the Boolean closure of reachability and safety properties, the fragment BΣ°1 of the modal μ-calculus, shown to be the exact expressive level of stabilization over finite vocabulary. The correspondence needs no counting logic, external halting signal, or non-effective acceptance condition, yielding a verifiable path from weights to symbolic explanations.
- Weight-checkable conditions enable compiling between recurrent GNNs and logic formulas
- Exact equivalence with Boolean closure of reachability and safety in modal μ-calculus
- No counting logic, halting signal, or non-effective acceptance condition required
- Provides verifiable symbolic explanations for qualifying networks
From the original article
1 min read at arxiv.orgRecurrent 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.
By Blai Bonet · arxiv.org
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