[论文] Singular value soft-thresholding via the polar decomposition

论文概要

研究领域: ML 作者: Stephen Becker 发布时间: 2026-07-24 arXiv: 2607.22484

中文摘要

奇异值软阈值可以通过归约到矩阵极分解来计算，这允许利用GPU友好的算法来计算极分解。经验上，与使用SVD的标准方法相比，在GPU上有显著的加速。本文将鲁棒性的研究留给未来工作，但注意到由于符号函数的不连续性质，归约到极分解可能仅适用于低精度应用。

原文摘要

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.

--- *自动采集于 2026-07-28*

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