Cartan moving frames and the data manifolds
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912127510380544 |
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| author | Tron, Eliot Fioresi, Rita Couellan, Nicolas Puechmorel, Stéphane |
| author_facet | Tron, Eliot Fioresi, Rita Couellan, Nicolas Puechmorel, Stéphane |
| contents | The purpose of this paper is to employ the language of Cartan moving frames to study the geometry of the data manifolds and its Riemannian structure, via the data information metric and its curvature at data points. Using this framework and through experiments, explanations on the response of a neural network are given by pointing out the output classes that are easily reachable from a given input. This emphasizes how the proposed mathematical relationship between the output of the network and the geometry of its inputs can be exploited as an explainable artificial intelligence tool. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12057 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cartan moving frames and the data manifolds Tron, Eliot Fioresi, Rita Couellan, Nicolas Puechmorel, Stéphane Machine Learning Differential Geometry The purpose of this paper is to employ the language of Cartan moving frames to study the geometry of the data manifolds and its Riemannian structure, via the data information metric and its curvature at data points. Using this framework and through experiments, explanations on the response of a neural network are given by pointing out the output classes that are easily reachable from a given input. This emphasizes how the proposed mathematical relationship between the output of the network and the geometry of its inputs can be exploited as an explainable artificial intelligence tool. |
| title | Cartan moving frames and the data manifolds |
| topic | Machine Learning Differential Geometry |
| url | https://arxiv.org/abs/2409.12057 |