Tensor Decomposition

Tensor decomposition studies how to represent multidimensional data using simpler factors, making patterns easier to analyze and large data or models cheaper to store and process. Common approaches include CP and Tucker factorization, tensor trains and matrix product states, and t-SVD, used for tasks such as missing-data recovery, anomaly detection, scientific modeling, and neural-network compression. Current work combines these methods with Bayesian rank selection, adaptive optimization, pretrained or neural priors, and theoretical analyses of recovery and identifiability. A central tension is choosing a factorization and rank that capture useful structure without imposing unrealistic shared-subspace or ordering assumptions, while balancing accuracy, robustness, and computational cost.