Related papers: Double-Precision Matrix Multiplication Emulation v…
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…
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…
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 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…
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…
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…
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…
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…
We report cutting-edge performance results via mixed-precision spin adapted ab initio Density Matrix Renormalization Group (DMRG) electronic structure calculations utilizing the Ozaki scheme for emulating FP64 arithmetic through the use of…
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…
A lot of recent progress has been made in ultra low-bit quantization, promising significant improvements in latency, memory footprint and energy consumption on edge devices. Quantization methods such as Learned Step Size Quantization can…
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…
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…
Deep neural networks have achieved state-of-the-art results in a wide range of applications, from natural language processing and computer vision to speech recognition. However, as tasks become increasingly complex, model sizes continue to…
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…
The number of parameters in deep neural networks (DNNs) is rapidly increasing to support complicated tasks and to improve model accuracy. Correspondingly, the amount of computations and required memory footprint increase as well.…
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,…
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…
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.…
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…