# Linear Layouts: Robust Code Generation of Efficient Tensor Computation Using mathbbF2

arXiv: https://arxiv.org/abs/2505.23819 · HTML: https://mlsanity.com/paper/2505.23819/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2025.

## Built on by (most cited first, 4 of 4)

- [Dato: A Task-Based Programming Model for Dataflow Accelerators](https://mlsanity.com/paper/2509.06794/) (2025)
- [CAKE: Compiler-Agent Co-Design for Frontier Kernel Evolution](https://mlsanity.com/paper/2608.12629/) (2026)
- [Axe: A Simple Unified Layout Abstraction for Machine Learning Compilers](https://mlsanity.com/paper/2601.19092/) (2026)
- [FBLayout: Optimizing Memory Layout for Efficient LLM Finetuning on Mobile GPUs](https://mlsanity.com/paper/2607.21624/) (2026)

## Abstract (arXiv)

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 mathbbF2. 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.