שמור ב:
| Main Authors: | , , |
|---|---|
| פורמט: | Preprint |
| יצא לאור: |
2020
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| נושאים: | |
| גישה מקוונת: | https://arxiv.org/abs/2012.03174 |
| תגים: |
הוספת תג
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תוכן הענינים:
- 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 $k$, 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.