Renormalization Group Guided Tensor Network Structure Search

TL;DR

This paper introduces RGTN, a physics-inspired, multi-scale tensor network search method that improves structure discovery efficiency and robustness, achieving state-of-the-art results in high-dimensional data compression.

Contribution

RGTN employs renormalization group flows and learnable edge gates for continuous, multi-scale tensor network structure search, overcoming limitations of existing discrete, single-scale methods.

Findings

Achieves state-of-the-art compression ratios.

Runs 4-600 times faster than existing methods.

Effective across diverse high-dimensional data types.

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.