Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning

• URL: http://arxiv.org/abs/2507.21726v1
• Date: Tue, 29 Jul 2025 12:03:03 GMT
• Title: Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning
• Authors: Marius Willner, Marco Trenti, Dirk Lebiedz,
• Abstract summary: Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation.<n>In this work, we present a formal analysis of the differential geometry underlying TTNs.<n>We develop efficient first- and second-order optimization algorithms that exploit the intrinsic quotient structure of TTNs.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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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