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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/2505.24665 |
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| _version_ | 1866908958587879424 |
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| author | Yu, Hanlin Hauberg, Søren Hartmann, Marcelo Klami, Arto Arvanitidis, Georgios |
| author_facet | Yu, Hanlin Hauberg, Søren Hartmann, Marcelo Klami, Arto Arvanitidis, Georgios |
| contents | Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if the manifold has a non-trivial topology, it can never be correctly learned using a single flow. Instead multiple flows must be `glued together'. In this paper, we first propose the general training scheme for learning such a collection of flows, and secondly we develop the first numerical algorithms for computing geodesics on such manifolds. Empirically, we demonstrate that this leads to highly significant improvements in topology estimation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24665 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Geometry and Topology via Multi-Chart Flows Yu, Hanlin Hauberg, Søren Hartmann, Marcelo Klami, Arto Arvanitidis, Georgios Machine Learning Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if the manifold has a non-trivial topology, it can never be correctly learned using a single flow. Instead multiple flows must be `glued together'. In this paper, we first propose the general training scheme for learning such a collection of flows, and secondly we develop the first numerical algorithms for computing geodesics on such manifolds. Empirically, we demonstrate that this leads to highly significant improvements in topology estimation. |
| title | Learning Geometry and Topology via Multi-Chart Flows |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.24665 |