Related papers: Ozaki Scheme II: A GEMM-oriented emulation of floa…
As the demand for AI computation rapidly increases, more hardware is being developed to efficiently perform the low-precision matrix multiplications required by such workloads. However, these operations are generally not directly applicable…
In this paper, we propose a method for emulating double-precision general matrix--matrix multiplication (DGEMM), a fundamental and performance-critical kernel in many high-performance computing applications. Ozaki-I and Ozaki-II are…
Modern computing architectures feature low-precision matrix multiplication units that achieve substantially higher throughput than their high-precision counterparts. Motivated by this architectural trend, the emulation of high-precision…
The Ozaki-II scheme is an emulation method that leverages the Chinese Remainder Theorem to compute high-precision matrix multiplication via a sequence of low-precision matrix multiplications. In this scheme, the attainable numerical…
Deep learning hardware achieves high throughput and low power consumption by reducing computing precision and specializing in matrix multiplication. For machine learning inference, fixed-point value computation is commonplace, where the…
This study was aimed at simultaneously achieving sufficient accuracy and high performance for general matrix multiplications. Recent architectures, such as NVIDIA GPUs, feature high-performance units designed for low-precision matrix…
Large matrix multiplication is a cornerstone of modern machine learning workloads, yet traditional approaches suffer from cubic computational complexity (e.g., $\mathcal{O}(n^3)$ for a matrix of size $n\times n$). We present Low-Rank GEMM,…
The rapid growth of artificial intelligence (AI) has made low-precision formats such as FP16, FP8, and, most recently, block-scaled FP4 the primary focus of modern GPUs, where Tensor Cores now deliver orders-of-magnitude higher throughput…
General Matrix Multiplication (GEMM) is a critical operation underpinning a wide range of applications in high-performance computing (HPC) and artificial intelligence (AI). The emergence of hardware optimized for low-precision arithmetic…
This paper lays out insights and opportunities for implementing higher-precision matrix-matrix multiplication (GEMM) from (in terms of) lower-precision high-performance GEMM. The driving case study approximates double-double precision…
Efficient multiple precision linear numerical computation libraries such as MPLAPACK are critical in dealing with ill-conditioned problems. Specifically, there are optimization methods for matrix multiplication, such as the Strassen…
Optimized multiple precision basic linear computation, especially matrix multiplication, is crucial for solving ill-conditioned problems. The recently proposed Ozaki scheme, which implements accurate matrix multiplication using existing…
General Matrix Multiplication (GEMM) is a fundamental operation widely used in scientific computations. Its performance and accuracy significantly impact the performance and accuracy of applications that depend on it. One such application…
Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due…
General Matrix Multiplication (GEMM) is a crucial algorithm for various applications such as machine learning and scientific computing, and an efficient GEMM implementation is essential for the performance of these systems. While…
We present an interface and an implementation of the General Matrix Multiply (GEMM) routine for multiple small matrices processed simultaneously on NVIDIA graphics processing units (GPUs). We focus on matrix sizes under 16. The…
Recent architectures integrate high-performance and power-efficient matrix engines. These engines demonstrate remarkable performance in low-precision matrix multiplication, which is crucial in deep learning. Several techniques have been…
The GEneral Matrix Multiplication (GEMM) is one of the essential algorithms in scientific computing. Single-thread GEMM implementations are well-optimised with techniques like blocking and autotuning. However, due to the complexity of…
An important linear algebra routine, GEneral Matrix Multiplication (GEMM), is a fundamental operator in deep learning. Compilers need to translate these routines into low-level code optimized for specific hardware. Compiler-level…
In this paper, we discuss numerical methods for the eigenvalue decomposition of real symmetric matrices. While many existing methods can compute approximate eigenpairs with sufficiently small backward errors, the magnitude of the resulting…