SVDinsTN: A Tensor Network Paradigm for Efficient Structure Search from Regularized Modeling Perspective
Authors: Yu-Bang Zheng, Xi-Le Zhao, Junhua Zeng, Chao Li, Qibin Zhao, Heng-Chao Li, Ting-Zhu Huang

Tensor network (TN) representation is a powerful technique for computer vision and machine learning. TN structure search (TN-SS) aims to search for a customized structure to achieve a compact representation which is a challenging NP-hard problem. Recent "sampling-evaluation"-based methods require sampling an extensive collection of structures and evaluating them one by one resulting in prohibitively high computational costs. To address this issue we propose a novel TN paradigm named SVD-inspired TN decomposition (SVDinsTN) which allows us to efficiently solve the TN-SS problem from a regularized modeling perspective eliminating the repeated structure evaluations. To be specific by inserting a diagonal factor for each edge of the fully-connected TN SVDinsTN allows us to calculate TN cores and diagonal factors simultaneously with the factor sparsity revealing a compact TN structure. In theory we prove a convergence guarantee for the proposed method. Experimental results demonstrate that the proposed method achieves approximately 100 1000 times acceleration compared to the state-of-the-art TN-SS methods while maintaining a comparable level of representation ability.