Singular value soft-thresholding via the polar decomposition

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.

Numerical Analysis (math.NA); Machine Learning (cs.LG); Optimization and Control (math.OC)

arXiv:2607.22484 [math.NA]

(or arXiv:2607.22484v1 [math.NA] for this version)

https://doi.org/10.48550/arXiv.2607.22484 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.