Linear Layouts: Robust Code Generation of Efficient Tensor Computation Using $\mathbb{F}_2$
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arXiv
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| Auteurs principaux: | , , , , , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911491077177344 |
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| author | Zhou, Keren Lezcano, Mario Goucher, Adam Rakhmati, Akhmed Niu, Jeff Lebar, Justin Szczerbuk, Pawel Bell, Peter Tillet, Phil Raoux, Thomas Moudallal, Zahi |
| author_facet | Zhou, Keren Lezcano, Mario Goucher, Adam Rakhmati, Akhmed Niu, Jeff Lebar, Justin Szczerbuk, Pawel Bell, Peter Tillet, Phil Raoux, Thomas Moudallal, Zahi |
| contents | Efficient tensor computation is a cornerstone of modern deep learning (DL) workloads, yet existing approaches struggle to achieve flexible and performant design and implementation of tensor layouts -- mappings between logical tensors and hardware resources. The increasing complexity of DL algorithms and hardware demands a generic and systematic approach to handling tensor layouts. In this work, we introduce Linear Layouts, a novel approach that models tensor layouts using linear algebra over $\mathbb{F}_2$. By representing tensor layouts as binary matrices acting on the bits of the hardware representation, our approach enables a generic layout definition -- as opposed to the classical case-by-case approach -- and allows for generic layout-to-layout conversions, eliminating the quadratic explosion that plagues existing solutions. We integrate linear layouts with Triton and demonstrate their effectiveness in optimizing individual Triton operators as well as kernels written in Triton. We also show that linear layouts reduce engineering effort in the compiler backend while fixing several bugs in Triton's legacy layout system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23819 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear Layouts: Robust Code Generation of Efficient Tensor Computation Using $\mathbb{F}_2$ Zhou, Keren Lezcano, Mario Goucher, Adam Rakhmati, Akhmed Niu, Jeff Lebar, Justin Szczerbuk, Pawel Bell, Peter Tillet, Phil Raoux, Thomas Moudallal, Zahi Programming Languages Hardware Architecture Distributed, Parallel, and Cluster Computing Performance Efficient tensor computation is a cornerstone of modern deep learning (DL) workloads, yet existing approaches struggle to achieve flexible and performant design and implementation of tensor layouts -- mappings between logical tensors and hardware resources. The increasing complexity of DL algorithms and hardware demands a generic and systematic approach to handling tensor layouts. In this work, we introduce Linear Layouts, a novel approach that models tensor layouts using linear algebra over $\mathbb{F}_2$. By representing tensor layouts as binary matrices acting on the bits of the hardware representation, our approach enables a generic layout definition -- as opposed to the classical case-by-case approach -- and allows for generic layout-to-layout conversions, eliminating the quadratic explosion that plagues existing solutions. We integrate linear layouts with Triton and demonstrate their effectiveness in optimizing individual Triton operators as well as kernels written in Triton. We also show that linear layouts reduce engineering effort in the compiler backend while fixing several bugs in Triton's legacy layout system. |
| title | Linear Layouts: Robust Code Generation of Efficient Tensor Computation Using $\mathbb{F}_2$ |
| topic | Programming Languages Hardware Architecture Distributed, Parallel, and Cluster Computing Performance |
| url | https://arxiv.org/abs/2505.23819 |