Rank $K$ Approximation

Rank-$k$ approximation aims to represent a high-dimensional data matrix (e.g., a large language model's weight matrix) using a significantly lower-rank approximation, thereby reducing storage and computational costs while preserving essential information. Current research focuses on improving the efficiency and accuracy of algorithms like alternating minimization and sketching techniques, including the development of sparse sketching matrices for faster computation and the exploration of stable rank for guiding dimensionality reduction. These advancements are crucial for handling massive datasets in various fields, enabling efficient processing of large language models, improved dimensionality reduction methods, and fairer data analysis techniques across different subgroups.