The paper presents a theoretical analysis of the expressive power of Graph Neural Networks (GNNs) for two important graph domains: dynamic graphs and static attributed undirected homogeneous graphs (SAUHGs) with node and edge attributes.
For static attributed graphs, the authors introduce the concept of attributed unfolding trees and the attributed 1-WL test. They prove that the attributed unfolding tree equivalence and the attributed 1-WL equivalence are equivalent, and that GNNs are universal approximators modulo this equivalence.
For dynamic graphs, the authors introduce the dynamic unfolding trees and the dynamic 1-WL test. They show that the dynamic unfolding tree equivalence and the dynamic 1-WL equivalence are equivalent, and that dynamic GNNs are universal approximators modulo this equivalence.
The proofs are mostly constructive, providing insights into the architecture of GNNs that can achieve the desired approximation. The authors also validate their theoretical results through experiments.
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Önemli Bilgiler Şuradan Elde Edildi
by Silvia Bedda... : arxiv.org 05-06-2024
https://arxiv.org/pdf/2210.03990.pdfDaha Derin Sorular