Attending to Topological Spaces: The Cellular Transformer
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arXiv
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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910459795341312 |
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| author | Ballester, Rubén Hernández-García, Pablo Papillon, Mathilde Battiloro, Claudio Miolane, Nina Birdal, Tolga Casacuberta, Carles Escalera, Sergio Hajij, Mustafa |
| author_facet | Ballester, Rubén Hernández-García, Pablo Papillon, Mathilde Battiloro, Claudio Miolane, Nina Birdal, Tolga Casacuberta, Carles Escalera, Sergio Hajij, Mustafa |
| contents | Topological Deep Learning seeks to enhance the predictive performance of neural network models by harnessing topological structures in input data. Topological neural networks operate on spaces such as cell complexes and hypergraphs, that can be seen as generalizations of graphs. In this work, we introduce the Cellular Transformer (CT), a novel architecture that generalizes graph-based transformers to cell complexes. First, we propose a new formulation of the usual self- and cross-attention mechanisms, tailored to leverage incidence relations in cell complexes, e.g., edge-face and node-edge relations. Additionally, we propose a set of topological positional encodings specifically designed for cell complexes. By transforming three graph datasets into cell complex datasets, our experiments reveal that CT not only achieves state-of-the-art performance, but it does so without the need for more complex enhancements such as virtual nodes, in-domain structural encodings, or graph rewiring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14094 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Attending to Topological Spaces: The Cellular Transformer Ballester, Rubén Hernández-García, Pablo Papillon, Mathilde Battiloro, Claudio Miolane, Nina Birdal, Tolga Casacuberta, Carles Escalera, Sergio Hajij, Mustafa Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition Algebraic Topology Topological Deep Learning seeks to enhance the predictive performance of neural network models by harnessing topological structures in input data. Topological neural networks operate on spaces such as cell complexes and hypergraphs, that can be seen as generalizations of graphs. In this work, we introduce the Cellular Transformer (CT), a novel architecture that generalizes graph-based transformers to cell complexes. First, we propose a new formulation of the usual self- and cross-attention mechanisms, tailored to leverage incidence relations in cell complexes, e.g., edge-face and node-edge relations. Additionally, we propose a set of topological positional encodings specifically designed for cell complexes. By transforming three graph datasets into cell complex datasets, our experiments reveal that CT not only achieves state-of-the-art performance, but it does so without the need for more complex enhancements such as virtual nodes, in-domain structural encodings, or graph rewiring. |
| title | Attending to Topological Spaces: The Cellular Transformer |
| topic | Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition Algebraic Topology |
| url | https://arxiv.org/abs/2405.14094 |