Riemannian Geometry

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2 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

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Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning
Jul 29, 2025Marius Willner, Marco Trenti, Dirk LebiedzTensor Networks Riemannian Optimization
Chair of Mathematical Data Science, University of Augsburg, Augsburg, Germany · Tensor AI Solutions GmbH, Pfaffenhofen a.d. Roth, Germany · Institute for Numerical Mathematics, University of Ulm, Ulm, Germany
Riemannian Denoising Diffusion Probabilistic Models
May 7, 2025Zichen Liu, Wei Zhang, Christof Schütte +1Generative Modeling Score-Based Generative Modeling
Center for Data Science, Peking University, Beijing 100871, P.R. China · Zuse Institute Berlin, Takustrasse 7, Berlin 14195, Germany · Institute of Mathematics, Freie Universität Berlin and Zuse Institute Berlin, Takustrasse 7, Berlin 14195, Germany +1

Jul 29, 2025, math.OCJ/K move · Enter open · S save

Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning

Marius Willner, Marco Trenti, Dirk Lebiedz

Chair of Mathematical Data Science, University of Augsburg, Augsburg, Germany · Tensor AI Solutions GmbH, Pfaffenhofen a.d. Roth, Germany · Institute for Numerical Mathematics, University of Ulm, Ulm, Germany

Tensor Networks Riemannian Optimization Riemannian Geometry

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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 quotient geometry underlying the TTN parameter space. Our framework allows for arbitrary horizontal distributions, and we develop efficient first- and second-order optimization algorithms that exploit this geometry. Additionally, we devise a backpropagation algorithm for training TTNs in a kernel learning setting. We validate our methods through numerical experiments on a representative digit classification task and reveal an important tradeoff between two different horizontal distributions that are available for TTNs: while one offers cleaner geometric statements, the other ultimately leads to more efficient algorithms.

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Latest papers 32

Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning

Riemannian Denoising Diffusion Probabilistic Models