PreprintCC BY-NC-SA 4.0arXiv
Stochastic Optimization of Tree Tensor Networks
Abstract
Tensor networks, originally developed for quantum many-body physics, are promising models for machine learning. We derive stochastic Riemannian optimizers for tree tensor networks (TTNs) on both their parameter and quotient manifolds, including adaptive and learning-rate-free schemes suitable for minibatch training. Using a hybrid CNN-TTN architecture, we evaluate the methods on Fashion-MNIST, CIFAR10, and Imagenette. The proposed optimizers achieve predictive performance comparable to unconstrained optimization while enabling numerically stable downstream compression.
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BibTeX
@misc{willner2026stochastic,
title = {{Stochastic Optimization of Tree Tensor Networks}},
author = {Marius Willner and Maximilian Scharf and André Uschmajew and Timo Felser and Marco Trenti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.00870},
eprint = {2609.00870},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00870},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Stochastic Optimization of Tree Tensor Networks
AU - Marius Willner
AU - Maximilian Scharf
AU - André Uschmajew
AU - Timo Felser
AU - Marco Trenti
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.00870
UR - https://arxiv.org/abs/2609.00870
AB - Tensor networks, originally developed for quantum many-body physics, are promising models for machine learning. We derive stochastic Riemannian optimizers for tree tensor networks (TTNs) on both their parameter and quotient manifolds, including adaptive and learning-rate-free schemes suitable for minibatch training. Using a hybrid CNN-TTN architecture, we evaluate the methods on Fashion-MNIST, CIFAR10, and Imagenette. The proposed optimizers achieve predictive performance comparable to unconstrained optimization while enabling numerically stable downstream compression.
ER -