{"ID":2889160,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.21726","arxiv_id":"2507.21726","title":"Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning","abstract":"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.","short_abstract":"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 qu...","url_abs":"https://arxiv.org/abs/2507.21726","url_pdf":"https://arxiv.org/pdf/2507.21726v2","authors":"[\"Marius Willner\",\"Marco Trenti\",\"Dirk Lebiedz\"]","published":"2025-07-29T12:03:03Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cond-mat.other\",\"cs.LG\"]","methods":"[]","has_code":false}