Block-Randomized Stochastic Methods for Tensor Ring Decomposition

TL;DR

This paper introduces a novel doubly randomized optimization framework for tensor ring decomposition, combining block coordinate descent and stochastic gradient methods to improve efficiency and convergence, especially for ill-conditioned problems.

Contribution

It proposes a new double-randomized optimization method for tensor ring decomposition, including an adaptive scaled version for better convergence and theoretical analysis.

Findings

Achieves lightweight updates with small memory footprint.

Improves convergence for ill-conditioned tensor problems.

Demonstrates strong numerical performance in experiments.

Abstract

Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be regarded as a sensible mix of randomized block coordinate descent and stochastic gradient descent, and hence functions in a double-random manner and can achieve lightweight updates and a small memory footprint. Further, to improve the convergence, especially for ill-conditioned problems, we propose a scaled version of the framework that can be viewed as an adaptive preconditioned or diagonally-scaled variant. Four different probability distributions for selecting the mini-batch and the adaptive strategy for determining the step size are also provided. Finally, we present the theoretical properties and numerical performance for our proposals.