Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning

Marius Willner; Marco Trenti; Dirk Lebiedz

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arXiv · 2507.21726

Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning

Marius Willner·Marco Trenti·Dirk Lebiedz

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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.

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math.OC cond-mat.other cs.LG

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BibTeX RIS

Marius Willner, Marco Trenti, Dirk Lebiedz. 2025-07-29. Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning. https://arxiv.org/abs/2507.21726

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