Homomorphism Counts for Graph Neural Networks: All About That Basis

Graph neural networks are architectures for learning invariant functions over graphs. 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 …

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