Related papers: DGEMM without FP64 Arithmetic - Using FP64 Emulati…
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…
This paper addresses emulation algorithms for matrix multiplication. General Matrix-Matrix Multiplication (GEMM), a fundamental operation in the Basic Linear Algebra Subprograms (BLAS), is typically optimized for specific hardware…
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…
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…
Largely due to their increased native capacity for numerical intensity and power efficiency, reduced-precision floating-point computing resources, primarily used in artificial intelligence (AI) applications, have expanded at a greater rate…
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…
AI models are increasing in size and recent advancement in the community has shown that unlike HPC applications where double precision datatype are required, lower-precision datatypes such as fp8 or int4 are sufficient to bring the same…
Finite element simulations play a critical role in a wide range of applications, from automotive design to tsunami modeling and computational electromagnetics. Performing these simulations efficiently at the high resolutions needed for…
Mixing precisions for performance has been an ongoing trend as the modern hardware accelerators started including new, and mostly lower-precision, data formats. The advantage of using them is a great potential of performance gain and energy…
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…
Deep learning models typically use single-precision (FP32) floating point data types for representing activations and weights, but a slew of recent research work has shown that computations with reduced-precision data types (FP16, 16-bit…
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…
Modern processors deliver higher throughput for lower-precision arithmetic than for higher-precision arithmetic. For matrix multiplication, the Ozaki scheme exploits this performance gap by splitting the inputs into lower-precision…
FPGAs are a promising platform for accelerating Deep Learning (DL) applications, due to their high performance, low power consumption, and reconfigurability. Recently, the leading FPGA vendors have enhanced their architectures to more…
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…
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…
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…
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…
Modern AI accelerators provide high-throughput low-precision matrix engines, but their support for FP32 GEMM is often limited or inefficient. This work presents SGEMM-cube, a precision-recovery FP32 GEMM approximation on Ascend NPUs using…
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,…