Tensor Ring

Tensor ring (TR) decomposition is a powerful tensor network method used to efficiently represent and manipulate high-dimensional data, primarily focusing on low-rank approximations to reduce computational complexity. Current research emphasizes applications in diverse fields, including image and video inpainting, dynamic network analysis, and quantum machine learning, often employing TR-based models within autoencoders or variational quantum classifiers. The ability of TR decomposition to handle large-scale datasets and its adaptability to various problem formulations makes it a significant tool for advancing data analysis and machine learning across multiple scientific disciplines.