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Matrix Multiplication with MMT4D

Introduction

Matrix multiplication (matmul) is an important operation in ML workloads that poses specific challenges to code generation. For example, matmul makes repeated accesses to the same data, which makes locality of reference a top concern.

Moreover, modern CPUs instruction set architectures (ISAs) offer specialized SIMD instructions that the matmul implementation needs to use to achieve optimal performance, and these instructions expect data to be in a particular layout.

This article is about an in-development MLIR operation, linalg.mmt4d, offering a compilation path for linalg.matmul that is designed from the ground up for these efficiency considerations.