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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.13749 |
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| _version_ | 1866913572954570752 |
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| author | Paolino, Raffaele Maskey, Sohir Welke, Pascal Kutyniok, Gitta |
| author_facet | Paolino, Raffaele Maskey, Sohir Welke, Pascal Kutyniok, Gitta |
| contents | We introduce $r$-loopy Weisfeiler-Leman ($r$-$\ell{}$WL), a novel hierarchy of graph isomorphism tests and a corresponding GNN framework, $r$-$\ell{}$MPNN, that can count cycles up to length $r + 2$. Most notably, we show that $r$-$\ell{}$WL can count homomorphisms of cactus graphs. This strictly extends classical 1-WL, which can only count homomorphisms of trees and, in fact, is incomparable to $k$-WL for any fixed $k$. We empirically validate the expressive and counting power of the proposed $r$-$\ell{}$MPNN on several synthetic datasets and present state-of-the-art predictive performance on various real-world datasets. The code is available at https://github.com/RPaolino/loopy |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13749 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning Paolino, Raffaele Maskey, Sohir Welke, Pascal Kutyniok, Gitta Machine Learning We introduce $r$-loopy Weisfeiler-Leman ($r$-$\ell{}$WL), a novel hierarchy of graph isomorphism tests and a corresponding GNN framework, $r$-$\ell{}$MPNN, that can count cycles up to length $r + 2$. Most notably, we show that $r$-$\ell{}$WL can count homomorphisms of cactus graphs. This strictly extends classical 1-WL, which can only count homomorphisms of trees and, in fact, is incomparable to $k$-WL for any fixed $k$. We empirically validate the expressive and counting power of the proposed $r$-$\ell{}$MPNN on several synthetic datasets and present state-of-the-art predictive performance on various real-world datasets. The code is available at https://github.com/RPaolino/loopy |
| title | Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2403.13749 |