Sum aggregation plus readout in ACR-GNNs captures FO properties outside C2 on directed and undirected graphs, while bounded local aggregation or bounded degree restores exact match to graded modal logic with global counting.
Then,φmust be invari- ant under∼ L,c,∗ ∃ , whereLis the number of layers inN (Lemma 16)
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Towards Understanding the Expressive Power of GNNs with Global Readout
Sum aggregation plus readout in ACR-GNNs captures FO properties outside C2 on directed and undirected graphs, while bounded local aggregation or bounded degree restores exact match to graded modal logic with global counting.