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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/2505.13539 |
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| _version_ | 1866918036195246080 |
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| author | Fritz, Rodrigo Suárez-Serrato, Pablo Mijangos, Victor Martinez-Hernandez, Anayanzi D. Richards, Eduardo Ivan Velazquez |
| author_facet | Fritz, Rodrigo Suárez-Serrato, Pablo Mijangos, Victor Martinez-Hernandez, Anayanzi D. Richards, Eduardo Ivan Velazquez |
| contents | We present EuLearn, the first surface datasets equitably representing a diversity of topological types. We designed our embedded surfaces of uniformly varying genera relying on random knots, thus allowing our surfaces to knot with themselves. EuLearn contributes new topological datasets of meshes, point clouds, and scalar fields in 3D. We aim to facilitate the training of machine learning systems that can discern topological features. We experimented with specific emblematic 3D neural network architectures, finding that their vanilla implementations perform poorly on genus classification. To enhance performance, we developed a novel, non-Euclidean, statistical sampling method adapted to graph and manifold data. We also introduce adjacency-informed adaptations of PointNet and Transformer architectures that rely on our non-Euclidean sampling strategy. Our results demonstrate that incorporating topological information into deep learning workflows significantly improves performance on these otherwise challenging EuLearn datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13539 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | EuLearn: A 3D database for learning Euler characteristics Fritz, Rodrigo Suárez-Serrato, Pablo Mijangos, Victor Martinez-Hernandez, Anayanzi D. Richards, Eduardo Ivan Velazquez Computational Geometry Computer Vision and Pattern Recognition Machine Learning Differential Geometry Geometric Topology We present EuLearn, the first surface datasets equitably representing a diversity of topological types. We designed our embedded surfaces of uniformly varying genera relying on random knots, thus allowing our surfaces to knot with themselves. EuLearn contributes new topological datasets of meshes, point clouds, and scalar fields in 3D. We aim to facilitate the training of machine learning systems that can discern topological features. We experimented with specific emblematic 3D neural network architectures, finding that their vanilla implementations perform poorly on genus classification. To enhance performance, we developed a novel, non-Euclidean, statistical sampling method adapted to graph and manifold data. We also introduce adjacency-informed adaptations of PointNet and Transformer architectures that rely on our non-Euclidean sampling strategy. Our results demonstrate that incorporating topological information into deep learning workflows significantly improves performance on these otherwise challenging EuLearn datasets. |
| title | EuLearn: A 3D database for learning Euler characteristics |
| topic | Computational Geometry Computer Vision and Pattern Recognition Machine Learning Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2505.13539 |