Renormalization Group Guided Tensor Network Structure Search

• URL: http://arxiv.org/abs/2512.24663v1
• Date: Wed, 31 Dec 2025 06:31:43 GMT
• Title: Renormalization Group Guided Tensor Network Structure Search
• Authors: Maolin Wang, Bowen Yu, Sheng Zhang, Linjie Mi, Wanyu Wang, Yiqi Wang, Pengyue Jia, Xuetao Wei, Zenglin Xu, Ruocheng Guo, Xiangyu Zhao,
• Abstract summary: Network structure search (TN-SS) aims to automatically discover optimal network topologies and rank robustness for efficient tensor decomposition in high-dimensional data representation.<n>We propose RGTN (Renormalization Group guided Network search), a physics-inspired framework transforming TN-SS via multi-scale renormalization group flows.
• Score: 58.0378300612202
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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