Sketching

…alongside randomized sampling and sketching. A local maximum-volume viewpoint gives sharp criteria for reliable rank revelation by pivoted Gaussian elimination and QR. The comparison with pivoted Cholesky on smooth-kernel matrices shows that greedy pivoting there cannot exhibit Kahan-like behavior. These results clarify the theoretical strengths and limitations of deterministic steps in matrix approximation.

…tensor-train representations using sketching, cross interpolation and a small sample of the relevant domain. For neural networks, this enables privacy-oriented obfuscation and interpretable estimates of topological phases. The method also supplies an efficient initialisation for tensor-train optimisation and improves the memory–computation trade-off in model compression.

…dynamic data structures and sketching interact, often transferring techniques between apparently different settings.