2023/03/29 by Yajie Yu, Hanyu Li, Yu, Yajie +3
Computer Science · Mathematics · Medicine · #Advanced Neural Network Applications #Advanced Neuroimaging Techniques and Applications #FOS: Mathematics #Numerical Analysis (math.NA) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2303.16492
openalex publication_date 2023/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.