Stochastic Optimization of Tree Tensor Networks

2026-09-01

AI Summary

研究通过为树张量网络开发随机黎曼优化器，解决了其在参数和商流形上的优化问题，并在多个图像数据集上验证了方法的有效性。

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.

Problem

• Stochastic Optimization
• Tree Tensor Networks
• Parameter Manifolds
• Quotient Manifolds

Innovation

• Stochastic Riemannian Optimizers
• Tree Tensor Networks (TTNs)
• Adaptive Schemes
• Learning-rate-free
• Downstream Compression