Renormalization Group Guided Tensor Network Structure Search

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Wang, Maolin, Yu, Bowen, Zhang, Sheng, Mi, Linjie, Wang, Wanyu, Wang, Yiqi, Jia, Pengyue, Wei, Xuetao, Xu, Zenglin, Guo, Ruocheng, Zhao, Xiangyu
Format:	Preprint
Published:	2025
Subjects:	Computer Vision and Pattern Recognition Artificial Intelligence
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

_version_	1866915701120303104
author	Wang, Maolin Yu, Bowen Zhang, Sheng Mi, Linjie Wang, Wanyu Wang, Yiqi Jia, Pengyue Wei, Xuetao Xu, Zenglin Guo, Ruocheng Zhao, Xiangyu
author_facet	Wang, Maolin Yu, Bowen Zhang, Sheng Mi, Linjie Wang, Wanyu Wang, Yiqi Jia, Pengyue Wei, Xuetao Xu, Zenglin Guo, Ruocheng Zhao, Xiangyu
contents	Tensor network structure search (TN-SS) aims to automatically discover optimal network topologies and rank configurations for efficient tensor decomposition in high-dimensional data representation. Despite recent advances, existing TN-SS methods face significant limitations in computational tractability, structure adaptivity, and optimization robustness across diverse tensor characteristics. They struggle with three key challenges: single-scale optimization missing multi-scale structures, discrete search spaces hindering smooth structure evolution, and separated structure-parameter optimization causing computational inefficiency. We propose RGTN (Renormalization Group guided Tensor Network search), a physics-inspired framework transforming TN-SS via multi-scale renormalization group flows. Unlike fixed-scale discrete search methods, RGTN uses dynamic scale-transformation for continuous structure evolution across resolutions. Its core innovation includes learnable edge gates for optimization-stage topology modification and intelligent proposals based on physical quantities like node tension measuring local stress and edge information flow quantifying connectivity importance. Starting from low-complexity coarse scales and refining to finer ones, RGTN finds compact structures while escaping local minima via scale-induced perturbations. Extensive experiments on light field data, high-order synthetic tensors, and video completion tasks show RGTN achieves state-of-the-art compression ratios and runs 4-600$\times$ faster than existing methods, validating the effectiveness of our physics-inspired approach.
format	Preprint
id	arxiv_https___arxiv_org_abs_2512_24663
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Renormalization Group Guided Tensor Network Structure Search Wang, Maolin Yu, Bowen Zhang, Sheng Mi, Linjie Wang, Wanyu Wang, Yiqi Jia, Pengyue Wei, Xuetao Xu, Zenglin Guo, Ruocheng Zhao, Xiangyu Computer Vision and Pattern Recognition Artificial Intelligence Tensor network structure search (TN-SS) aims to automatically discover optimal network topologies and rank configurations for efficient tensor decomposition in high-dimensional data representation. Despite recent advances, existing TN-SS methods face significant limitations in computational tractability, structure adaptivity, and optimization robustness across diverse tensor characteristics. They struggle with three key challenges: single-scale optimization missing multi-scale structures, discrete search spaces hindering smooth structure evolution, and separated structure-parameter optimization causing computational inefficiency. We propose RGTN (Renormalization Group guided Tensor Network search), a physics-inspired framework transforming TN-SS via multi-scale renormalization group flows. Unlike fixed-scale discrete search methods, RGTN uses dynamic scale-transformation for continuous structure evolution across resolutions. Its core innovation includes learnable edge gates for optimization-stage topology modification and intelligent proposals based on physical quantities like node tension measuring local stress and edge information flow quantifying connectivity importance. Starting from low-complexity coarse scales and refining to finer ones, RGTN finds compact structures while escaping local minima via scale-induced perturbations. Extensive experiments on light field data, high-order synthetic tensors, and video completion tasks show RGTN achieves state-of-the-art compression ratios and runs 4-600$\times$ faster than existing methods, validating the effectiveness of our physics-inspired approach.
title	Renormalization Group Guided Tensor Network Structure Search
topic	Computer Vision and Pattern Recognition Artificial Intelligence
url	https://arxiv.org/abs/2512.24663