# Stochastic Optimization of Tree Tensor Networks

arXiv: https://arxiv.org/abs/2609.00870 · HTML: https://mlsanity.com/paper/2609.00870/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 43 references that are in the map.
- First posted on arXiv 1 Sep 2026.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [How to Escape Saddle Points Efficiently](https://mlsanity.com/paper/1703.00887/) (2017)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [DoG is SGD's Best Friend: A Parameter-Free Dynamic Step Size Schedule](https://mlsanity.com/paper/2302.12022/) (2023)
- [Learning Relevant Features of Data with Multi-scale Tensor Networks](https://mlsanity.com/paper/1801.00315/) (2017)
- [Quantum-inspired Machine Learning on high-energy physics data](https://mlsanity.com/paper/2004.13747/) (2020)
- [Machine learning with tree tensor networks, CP rank constraints, and tensor dropout](https://mlsanity.com/paper/2305.19440/) (2023)
- [Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds](https://mlsanity.com/paper/2605.09238/) (2026)
- [Ultra-low latency quantum-inspired machine learning predictors implemented on FPGA](https://mlsanity.com/paper/2409.16075/) (2024)
- [Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning](https://mlsanity.com/paper/2507.21726/) (2025)
- [An Embarrassingly Simple Way to Optimize Orthogonal Matrices at Scale](https://mlsanity.com/paper/2602.14656/) (2026)
- [Bounds on the geodesic distances on the Stiefel manifold for a family of Riemannian metrics](https://mlsanity.com/paper/2408.07072/) (2024)
- [Learning-Rate-Free Stochastic Optimization over Riemannian Manifolds](https://mlsanity.com/paper/2406.02296/) (2024)
- [Natural Riemannian gradient for learning functional tensor networks](https://mlsanity.com/paper/2604.09263/) (2026)
- [Quantum-Inspired Robust and Scalable SAR Object Classification](https://mlsanity.com/paper/2604.25755/) (2026)

## 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.