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The expressive power of pooling in Graph Neural Networks

Permanent lenke
https://hdl.handle.net/10037/33043
DOI
https://doi.org/10.48550/arXiv.2304.01575
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article.pdf (592.9Kb)
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Dato
2023
Type
Journal article
Tidsskriftartikkel
Peer reviewed

Forfatter
Bianchi, Filippo Maria; Lachi, Veronica
Sammendrag
In Graph Neural Networks (GNNs), hierarchical pooling operators generate local summaries of the data by coarsening the graph structure and the vertex features. While considerable attention has been devoted to analyzing the expressive power of message-passing (MP) layers in GNNs, a study on how graph pooling affects the expressiveness of a GNN is still lacking. Additionally, despite the recent advances in the design of pooling operators, there is not a principled criterion to compare them. In this work, we derive sufficient conditions for a pooling operator to fully preserve the expressive power of the MP layers before it. These conditions serve as a universal and theoretically grounded criterion for choosing among existing pooling operators or designing new ones. Based on our theoretical findings, we analyze several existing pooling operators and identify those that fail to satisfy the expressiveness conditions. Finally, we introduce an experimental setup to verify empirically the expressive power of a GNN equipped with pooling layers, in terms of its capability to perform a graph isomorphism test.
Forlag
NeurIPS Proceedings
Sitering
Bianchi, Lachi. The expressive power of pooling in Graph Neural Networks. Advances in Neural Information Processing Systems. 2023
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  • Artikler, rapporter og annet (matematikk og statistikk) [354]
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