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.

翻译：张量网络结构搜索（TN-SS）旨在自动发现最优的网络拓扑结构和秩配置，以实现高维数据表示中的高效张量分解。尽管近期取得进展，现有TN-SS方法在计算可处理性、结构自适应性以及针对不同张量特性的优化鲁棒性方面仍面临显著局限。它们主要存在三个关键挑战：单尺度优化难以捕捉多尺度结构，离散搜索空间阻碍了结构的平滑演化，以及结构与参数优化分离导致计算效率低下。我们提出RGTN（重整化群引导的张量网络搜索），一种受物理学启发的框架，通过多尺度重整化群流来革新TN-SS。与固定尺度的离散搜索方法不同，RGTN利用动态尺度变换实现跨分辨率的连续结构演化。其核心创新包括：可学习的边门控机制，用于在优化阶段修改拓扑结构；以及基于物理量的智能提议机制，例如衡量局部应力的节点张力和量化连接重要性的边信息流。RGTN从低复杂度的粗尺度开始，逐步细化至更精细的尺度，在寻找紧凑结构的同时，通过尺度诱导的扰动逃离局部极小值。在光场数据、高阶合成张量和视频补全任务上的大量实验表明，RGTN实现了最先进的压缩比，且运行速度比现有方法快4-600倍，验证了我们受物理学启发的方法的有效性。