# Efficient GPU implementation of randomized SVD and its applications

arXiv: https://arxiv.org/abs/2110.03423 · HTML: https://mlsanity.com/paper/2110.03423/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 36 references that are in the map.
- First posted on arXiv 5 Oct 2021.

## Builds on (most cited first, 2 of 2)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Faster Matrix Completion Using Randomized SVD](https://mlsanity.com/paper/1810.06860/) (2018)

## Built on by (most cited first, 5 of 5)

- [Working memory inspired hierarchical video decomposition with transformative representations](https://mlsanity.com/paper/2204.10105/) (2022)
- [Alternating minimization for square root principal component pursuit](https://mlsanity.com/paper/2501.00471/) (2024)
- [k-SVD with Gradient Descent](https://mlsanity.com/paper/2502.00320/) (2025)
- [Quasi-SVD: Learning a Lie-constrained matrix factorisation for real-time imaging](https://mlsanity.com/paper/2607.25967/) (2026)
- [Fast Differentiable SVD on GPU via Polar Decomposition](https://mlsanity.com/paper/2609.32505/) (2026)

## Abstract (arXiv)

Matrix decompositions are ubiquitous in machine learning, including applications in dimensionality reduction, data compression and deep learning algorithms. Typical solutions for matrix decompositions have polynomial complexity which significantly increases their computational cost and time. In this work, we leverage efficient processing operations that can be run in parallel on modern Graphical Processing Units (GPUs), predominant computing architecture used e.g. in deep learning, to reduce the computational burden of computing matrix decompositions. More specifically, we reformulate the randomized decomposition problem to incorporate fast matrix multiplication operations (BLAS-3) as building blocks. We show that this formulation, combined with fast random number generators, allows to fully exploit the potential of parallel processing implemented in GPUs. Our extensive evaluation confirms the superiority of this approach over the competing methods and we release the results of this research as a part of the official CUDA implementation (https://docs.nvidia.com/cuda/cusolver/index.html).