Homomorphism Counts for Graph Neural Networks: All About That Basis
arxiv(2024)
摘要
A large body of work has investigated the properties of graph neural networks
and identified several limitations, particularly pertaining to their expressive
power. Their inability to count certain patterns (e.g., cycles) in a graph lies
at the heart of such limitations, since many functions to be learned rely on
the ability of counting such patterns. Two prominent paradigms aim to address
this limitation by enriching the graph features with subgraph or homomorphism
pattern counts. In this work, we show that both of these approaches are
sub-optimal in a certain sense and argue for a more fine-grained approach,
which incorporates the homomorphism counts of all structures in the “basis”
of the target pattern. This yields strictly more expressive architectures
without incurring any additional overhead in terms of computational complexity
compared to existing approaches. We prove a series of theoretical results on
node-level and graph-level motif parameters and empirically validate them on
standard benchmark datasets.
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