Performant Unified GPU Kernels for Portable Singular Value Computation Across Hardware and Precision
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3754598.3754667.pdf
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Author(s)
Ringoot, Evelyne
Alomairy, Rabab
Churavy, Valentin
Edelman, Alan
Date Issued
December 20, 2025
Publisher
ACM|54th International Conference on Parallel Processing
Citation
This paper presents a portable, GPU-accelerated implementation of a QR-based singular value computation algorithm in Julia. The singular value decomposition (SVD) is a fundamental numerical tool in scientific computing and machine learning, providing optimal low-rank matrix approximations. Its importance has increased even more in large-scale machine learning pipelines, including large language models (LLMs), where it enables low-rank adaptation (LoRA). The implemented algorithm is based on the classic two-stage QR reduction, consisting of successive matrix reduction to band form and bidiagonal form. Our implementation leverages Julia’s multiple dispatch and metaprogramming capabilities, integrating with the GPUArrays and KernelAbstractions frameworks to provide a unified type and hardware-agnostic function. It supports diverse GPU architectures and data types, and is, to our knowledge, the first GPU-accelerated singular value implementation to support Apple Metal GPUs and half precision. Performance results on multiple GPU backends and data types demonstrate that portability does not require sacrificing performance: the unified function outperforms most linear algebra libraries (MAGMA, SLATE, rocSOLVER, oneMKL) for matrix sizes larger than 1024 × 1024, and achieves 80%-90% of the performance of cuSOLVER for large matrices.
Version
Final published version
Abstract
This paper presents a portable, GPU-accelerated implementation of a QR-based singular value computation algorithm in Julia. The singular value decomposition (SVD) is a fundamental numerical tool in scientific computing and machine learning, providing optimal low-rank matrix approximations. Its importance has increased even more in large-scale machine learning pipelines, including large language models (LLMs), where it enables low-rank adaptation (LoRA). The implemented algorithm is based on the classic two-stage QR reduction, consisting of successive matrix reduction to band form and bidiagonal form. Our implementation leverages Julia’s multiple dispatch and metaprogramming capabilities, integrating with the GPUArrays and KernelAbstractions frameworks to provide a unified type and hardware-agnostic function. It supports diverse GPU architectures and data types, and is, to our knowledge, the first GPU-accelerated singular value implementation to support Apple Metal GPUs and half precision. Performance results on multiple GPU backends and data types demonstrate that portability does not require sacrificing performance: the unified function outperforms most linear algebra libraries (MAGMA, SLATE, rocSOLVER, oneMKL) for matrix sizes larger than 1024 × 1024, and achieves 80%-90% of the performance of cuSOLVER for large matrices.
Description
ICPP ’25, San Diego, CA, USA
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1145/3754598.3754667
