The Cambrian Explosion of Mixed-Precision Matrix Multiplication for Quantized Deep Learning Inference

Recent advances in deep learning (DL) have led to a shift from traditional 64-bit floating point (FP64) computations toward reduced-precision formats, such as FP16, BF16, and 8- or 16-bit integers, combined with mixed-precision arithmetic. This transition enhances computational throughput, reduces memory and bandwidth usage, and improves energy efficiency, offering significant advantages for resource-constrained edge devices. To support this shift, hardware architectures have evolved accordingly, now including adapted ISAs (Instruction Set Architectures) that expose mixed-precision vector units and matrix engines tailored for DL workloads. At the heart of many DL and scientific computing tasks is the general matrix-matrix multiplication gemm, a fundamental kernel historically optimized using axpy vector instructions on SIMD (single instruction, multiple data) units. However, as hardware moves toward mixed-precision dot-product-centric operations optimized for quantized inference, these legacy approaches are being phased out. In response to this, our paper revisits traditional high-performance gemm and describes strategies for adapting it to mixed-precision integer (MIP) arithmetic across modern ISAs, including x86_64, ARM, and RISC-V. Concretely, we illustrate novel micro-kernel designs and data layouts that better exploit today's specialized hardware and demonstrate significant performance gains from MIP arithmetic over floating-point implementations across three representative CPU architectures. These contributions highlight a new era of gemm optimization-driven by the demands of DL inference on heterogeneous architectures, marking what we term as the "Cambrian period" for matrix multiplication.

Automatic Generators for a Family of Matrix Multiplication Routines with Apache TVM

We explore the utilization of the Apache TVM open source framework to automatically generate a family of algorithms that follow the approach taken by popular linear algebra libraries, such as GotoBLAS2, BLIS and OpenBLAS, in order to obtain high-performance blocked formulations of the general matrix multiplication (GEMM). % In addition, we fully automatize the generation process, by also leveraging the Apache TVM framework to derive a complete variety of the processor-specific micro-kernels for GEMM. This is in contrast with the convention in high performance libraries, which hand-encode a single micro-kernel per architecture using Assembly code. % In global, the combination of our TVM-generated blocked algorithms and micro-kernels for GEMM 1)~improves portability, maintainability and, globally, streamlines the software life cycle; 2)~provides high flexibility to easily tailor and optimize the solution to different data types, processor architectures, and matrix operand shapes, yielding performance on a par (or even superior for specific matrix shapes) with that of hand-tuned libraries; and 3)~features a small memory footprint.