Stochastic Optimization of Tree Tensor Networks
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.
| Authors | Marius Willner, Maximilian Scharf, André Uschmajew et al. |
|---|---|
| Primary category | math.OC |
| Published | 1 September 2026 |
| Last updated at source | 2 October 2026 |
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