Closing the Theory-Practice Gap in Oblivious Subspace Embeddings

Michal Dereziński discusses oblivious subspace embeddings, random dimension-reduction maps that approximately preserve all vector norms in a low-dimensional subspace. Such maps support least-squares regression and low-rank approximation, yet efficient optimal embedding dimensions have left a gap between theory and practice. Analyzing universality in sparse random matrices leads to a resolution of the Nelson–Nguyen conjecture up to sub-polylogarithmic factors in SODA 2026. Joint work with Shabarish Chenakkod, Xiaoyu Dong, and Mark Rudelson.