Singular value soft-thresholding via the polar decomposition
2026-07-24 • Machine Learning
Machine Learning
AI summaryⓘ
The authors explain a way to do singular value soft-thresholding, which is used in data processing, by turning it into a problem of finding the matrix polar decomposition. This method can run much faster on GPUs compared to the usual way of using the singular value decomposition (SVD). However, because of mathematical challenges with the sign function involved, the authors suggest this approach might only work well when you don't need very precise results. They have not yet tested how reliable this method is in different situations.
singular value soft-thresholdingmatrix polar decompositionsingular value decompositionGPU computingsign functionnumerical accuracymatrix computationslow-rank approximationalgorithm speed-up
Authors
Stephen Becker
Abstract
Singular value soft-thresholding can be computed via a reduction to the matrix polar decomposition, which allows one to exploit GPU-friendly algorithms for computing the polar decomposition. Empirically, there is a significant speed-up on GPUs compared to the standard approach using the SVD. We leave the investigation of robustness to future work, but note that due to the discontinuous nature of the sign function, the reduction to the polar decomposition is likely only suitable for low-accuracy applications.