Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912628782137344 |
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| author | Willner, Marius Trenti, Marco Lebiedz, Dirk |
| author_facet | Willner, Marius Trenti, Marco Lebiedz, Dirk |
| contents | Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the differential geometry underlying TTNs. Building on this foundation, we develop efficient first- and second-order optimization algorithms that exploit the intrinsic quotient structure of TTNs. Additionally, we devise a backpropagation algorithm for training TTNs in a kernel learning setting. We validate our methods through numerical experiments on a representative machine learning task. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21726 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning Willner, Marius Trenti, Marco Lebiedz, Dirk Optimization and Control Other Condensed Matter Machine Learning 15A69, 53C20, 65K10 Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the differential geometry underlying TTNs. Building on this foundation, we develop efficient first- and second-order optimization algorithms that exploit the intrinsic quotient structure of TTNs. Additionally, we devise a backpropagation algorithm for training TTNs in a kernel learning setting. We validate our methods through numerical experiments on a representative machine learning task. |
| title | Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning |
| topic | Optimization and Control Other Condensed Matter Machine Learning 15A69, 53C20, 65K10 |
| url | https://arxiv.org/abs/2507.21726 |