Tensors express multi-dimensional data, extending the concept of vectors and matrices to more info 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 ma

Tensor ring decomposition offers 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 decomposition