1 research outputs found
Counting Substructures with Higher-Order Graph Neural Networks: Possibility and Impossibility Results
While message passing Graph Neural Networks (GNNs) have become increasingly
popular architectures for learning with graphs, recent works have revealed
important shortcomings in their expressive power. In response, several
higher-order GNNs have been proposed that substantially increase the expressive
power, albeit at a large computational cost. Motivated by this gap, we explore
alternative strategies and lower bounds. In particular, we analyze a new
recursive pooling technique of local neighborhoods that allows different
tradeoffs of computational cost and expressive power. First, we prove that this
model can count subgraphs of size , and thereby overcomes a known limitation
of low-order GNNs. Second, we show how recursive pooling can exploit sparsity
to reduce the computational complexity compared to the existing higher-order
GNNs. More generally, we provide a (near) matching information-theoretic lower
bound for counting subgraphs with graph representations that pool over
representations of derived (sub-)graphs. We also discuss lower bounds on time
complexity.Comment: 26 pages, 4 figure