Convergence rates for pivoted QR and LU

What the math gives to ML

This paper gives a constructive way to build low-rank approximations by greedily selecting columns and repeatedly removing their contribution. Its transferable asset is not QR itself, which is standard numerical linear algebra, but the determinant-based explanation of why greedy pivots remain effective when singular values decay algebraically or geometrically. A promising neural-network use is adaptive landmark selection for compressing attention or kernel matrices: choose tokens by residual energy rather than uniformly or randomly, then represent all attention columns using the selected landmarks. The method provides an explicit residual-based stopping rule and a falsifiable accuracy-versus-rank tradeoff.