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Stochastic Optimization of Tree Tensor Networks

arXiv 2609.00870 ↗First posted 1 Sep 2026math.OC cs.CV physics.comp-phcited by 0

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Abstract (arXiv)

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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References · 20

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8 more
  1. 2026Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifoldscited by 6
  2. 2024Ultra-low latency quantum-inspired machine learning predictors implemented on FPGAcited by 4
  3. 2025Riemannian Optimization on Tree Tensor Networks with Application in Machine Learningcited by 3
  4. 2026An Embarrassingly Simple Way to Optimize Orthogonal Matrices at Scalecited by 3
  5. 2024Bounds on the geodesic distances on the Stiefel manifold for a family of Riemannian metricscited by 2
  6. 2024Learning-Rate-Free Stochastic Optimization over Riemannian Manifoldscited by 1
  7. 2026Natural Riemannian gradient for learning functional tensor networkscited by 1
  8. 2026Quantum-Inspired Robust and Scalable SAR Object Classificationcited by 1

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