AdS-GNN -- a Conformally Equivariant Graph Neural Network
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912381994532864 |
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| author | Zhdanov, Maksim Iqbal, Nabil Bekkers, Erik Forré, Patrick |
| author_facet | Zhdanov, Maksim Iqbal, Nabil Bekkers, Erik Forré, Patrick |
| contents | Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is equivariant under general conformal transformations. To achieve this, we lift data from flat Euclidean space to Anti de Sitter (AdS) space. This allows us to exploit a known correspondence between conformal transformations of flat space and isometric transformations on the AdS space. We then build upon the fact that such isometric transformations have been extensively studied on general geometries in the geometric deep learning literature. We employ message-passing layers conditioned on the proper distance, yielding a computationally efficient framework. We validate our model on tasks from computer vision and statistical physics, demonstrating strong performance, improved generalization capacities, and the ability to extract conformal data such as scaling dimensions from the trained network. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12880 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | AdS-GNN -- a Conformally Equivariant Graph Neural Network Zhdanov, Maksim Iqbal, Nabil Bekkers, Erik Forré, Patrick Machine Learning Artificial Intelligence High Energy Physics - Theory Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is equivariant under general conformal transformations. To achieve this, we lift data from flat Euclidean space to Anti de Sitter (AdS) space. This allows us to exploit a known correspondence between conformal transformations of flat space and isometric transformations on the AdS space. We then build upon the fact that such isometric transformations have been extensively studied on general geometries in the geometric deep learning literature. We employ message-passing layers conditioned on the proper distance, yielding a computationally efficient framework. We validate our model on tasks from computer vision and statistical physics, demonstrating strong performance, improved generalization capacities, and the ability to extract conformal data such as scaling dimensions from the trained network. |
| title | AdS-GNN -- a Conformally Equivariant Graph Neural Network |
| topic | Machine Learning Artificial Intelligence High Energy Physics - Theory |
| url | https://arxiv.org/abs/2505.12880 |