Tensor ring decomposition employs a powerful framework for analyzing high-order data. This technique decomposes complex tensors into a sum of simpler matrices, often referred to as core matrices and factor matrices. Therefore, tensor ring decomposition enables efficient storage and computation with large datasets by exploiting the underlying patter

Tensors express multi-dimensional data, extending the concept of vectors and matrices to encompass higher dimensions. These structures find widespread application in fields such as machine learning, physics, and computer graphics. Rings, with their well-defined operations of addition and multiplication, provide a powerful framework for manipulating

Tensor ring decomposition provides a novel approach to data representation by decomposing high-order tensors into a sum of low-rank matrices. This factorization leverages the inherent structure within data, enabling efficient storage and processing. Applications range from recommender systems to natural language processing, where tensor decompositi