D-SLR matches or beats truncated SVD at three SVDs and cuts prediction changes on LLM embedding tables by about tenfold
The authors propose the Disjoint Row-Sparse plus Low-Rank (D-SLR) decomposition, in which each row is either stored verbatim or fitted by a shared low-rank basis but never both; under squared error this restriction is lossless, the algorithm scores every rank and stored-row count in closed form at about three SVDs, and it provides an assumption-free a-posteriori lower-bound certificate; on synthetic matrices and LLM embedding tables D-SLR is never worse than the truncated SVD at equal cost and, at half the table's parameters, changed about ten times fewer model predictions.