Sparse Factorization

Sparse factorization techniques aim to represent data or matrices using a product of smaller, sparser matrices, thereby reducing computational cost and storage requirements while preserving essential information. Current research focuses on developing efficient algorithms for various factorization types, including low-rank and dense-sparse approaches, often incorporating neural networks or Bayesian methods for improved accuracy and hyperparameter tuning. These advancements are impacting diverse fields, from accelerating linear equation solvers and compressing large language models to enhancing interpretability in clinical data analysis and improving optimal transport computations.