Geodesics in the Deep Linear Network
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918466943975424 |
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| author | Chen, Alan |
| author_facet | Chen, Alan |
| contents | We derive a general system of ODEs and associated explicit solutions in a special case for geodesics between full rank matrices in the deep linear network geometry. In the process, we find horizontal straight lines in the invariant balanced manifold that remain geodesics under Riemannian submersion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07324 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geodesics in the Deep Linear Network Chen, Alan Differential Geometry Machine Learning Dynamical Systems We derive a general system of ODEs and associated explicit solutions in a special case for geodesics between full rank matrices in the deep linear network geometry. In the process, we find horizontal straight lines in the invariant balanced manifold that remain geodesics under Riemannian submersion. |
| title | Geodesics in the Deep Linear Network |
| topic | Differential Geometry Machine Learning Dynamical Systems |
| url | https://arxiv.org/abs/2510.07324 |