Stochastic Optimization of Tree Tensor Networks

Marius Willner; Maximilian Scharf; André Uschmajew; Timo Felser; Marco Trenti

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arXiv · 2609.00870

Stochastic Optimization of Tree Tensor Networks

Marius Willner·Maximilian Scharf·André Uschmajew·Timo Felser·Marco Trenti

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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 RIS

Marius Willner, Maximilian Scharf, André Uschmajew, Timo Felser, Marco Trenti. 2026-09-01. Stochastic Optimization of Tree Tensor Networks. https://arxiv.org/abs/2609.00870

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