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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.02842 |
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| _version_ | 1866912411493072896 |
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| author | Fiorini, Stefano Aktas, Hakan Duta, Iulia Coniglio, Stefano Morerio, Pietro Del Bue, Alessio Liò, Pietro |
| author_facet | Fiorini, Stefano Aktas, Hakan Duta, Iulia Coniglio, Stefano Morerio, Pietro Del Bue, Alessio Liò, Pietro |
| contents | Sheaf Neural Networks (SNNs) represent a powerful generalization of Graph Neural Networks (GNNs) that significantly improve our ability to model complex relational data. While directionality has been shown to substantially boost performance in graph learning tasks and is key to many real-world applications, existing SNNs fall short in representing it. To address this limitation, we introduce the Directed Cellular Sheaf, a special type of cellular sheaf designed to explicitly account for edge orientation. Building on this structure, we define a new sheaf Laplacian, the Directed Sheaf Laplacian, which captures both the graph's topology and its directional information. This operator serves as the backbone of the Directed Sheaf Neural Network (DSNN), the first SNN model to embed a directional bias into its architecture. Extensive experiments on nine real-world benchmarks show that DSNN consistently outperforms baseline methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02842 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sheaves Reloaded: A Directional Awakening Fiorini, Stefano Aktas, Hakan Duta, Iulia Coniglio, Stefano Morerio, Pietro Del Bue, Alessio Liò, Pietro Machine Learning Artificial Intelligence Sheaf Neural Networks (SNNs) represent a powerful generalization of Graph Neural Networks (GNNs) that significantly improve our ability to model complex relational data. While directionality has been shown to substantially boost performance in graph learning tasks and is key to many real-world applications, existing SNNs fall short in representing it. To address this limitation, we introduce the Directed Cellular Sheaf, a special type of cellular sheaf designed to explicitly account for edge orientation. Building on this structure, we define a new sheaf Laplacian, the Directed Sheaf Laplacian, which captures both the graph's topology and its directional information. This operator serves as the backbone of the Directed Sheaf Neural Network (DSNN), the first SNN model to embed a directional bias into its architecture. Extensive experiments on nine real-world benchmarks show that DSNN consistently outperforms baseline methods. |
| title | Sheaves Reloaded: A Directional Awakening |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2506.02842 |