Tensor-Ring Decomposition with Index-Splitting

TL;DR

This paper introduces a novel approach to tensor-ring decomposition that addresses local minima trapping by identifying correlation structures, improving the robustness of tensor network representations in physics and other fields.

Contribution

The paper proposes an index-splitting strategy to effectively identify correlation structures, helping to avoid local minima in tensor-ring decomposition algorithms.

Findings

Enhanced decomposition accuracy in tensor networks

Reduced trapping in local minima during optimization

Improved applicability in physics and data analysis

Abstract

Tensor-ring decomposition of tensors plays a key role in various applications of tensor network representation in physics as well as in other fields. In most heuristic algorithms for the tensor-ring decomposition, one encounters the problem of local-minima trapping. Particularly, the minima related to the topological structure in the correlation are hard to escape. Therefore, identification of the correlation structure, somewhat analogous to finding matching ends of entangled strings, is the task of central importance. We show how this problem naturally arises in physical applications, and present a strategy for winning this string-pull game.