Related papers: Karatsuba Matrix Multiplication and its Efficient …
This paper presents the derivation of a new algorithm for multiplying of two Kaluza numbers. Performing this operation directly requires 1024 real multiplications and 992 real additions. The proposed algorithm can compute the same result…
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…
Accelerators for sparse matrix multiplication are important components in emerging systems. In this paper, we study the main challenges of accelerating Sparse Matrix Multiplication (SpMM). For the situations that data is not stored in the…
The advent of memristive devices offers a promising avenue for efficient and scalable analog computing, particularly for linear algebra operations essential in various scientific and engineering applications. This paper investigates the…
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…
Dense Matrix Multiplication (MatMul) is arguably one of the most ubiquitous compute-intensive kernels, spanning linear algebra, DSP, graphics, and machine learning applications. Thus, MatMul optimization is crucial not only in…
Matrix multiplications between asymmetric bit-width operands, especially between 8- and 4-bit operands are likely to become a fundamental kernel of many important workloads including neural networks and machine learning. While existing SIMD…
Matrix multiplication is a fundamental kernel in large-scale artificial intelligence and scientific computing, but its performance on conventional electronic accelerators is increasingly constrained by memory bandwidth and energy…
This paper explores practical aspects of using a high-level functional language for GPU-based arithmetic on ``midsize'' integers. By this we mean integers of up to about a quarter million bits, which is sufficient for most practical…
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…
Coded matrix multiplication is a technique to enable straggler-resistant multiplication of large matrices in distributed computing systems. In this paper, we first present a conceptual framework to represent the division of work amongst…
This is the second of two papers to describe a matrix sparsification algorithm that takes a general real or complex matrix as input and produces a sparse output matrix of the same size. The first paper presented the original algorithm, its…
Matrix-matrix multiplication is a basic operation in linear algebra and an essential building block for a wide range of algorithms in various scientific fields. Theory and implementation for the dense, square matrix case are well-developed.…
Sparse matrix-vector multiplication (SpMV) is a crucial computing kernel with widespread applications in iterative algorithms. Over the past decades, research on SpMV optimization has made remarkable strides, giving rise to various…
A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…
The exponentially growing model size drives the continued success of deep learning, but it brings prohibitive computation and memory cost. From the algorithm perspective, model sparsification and quantization have been studied to alleviate…
Matrix multiplication (MatMul) is the computational backbone of modern machine learning, yet its classical complexity remains a bottleneck for large-scale data processing. We propose a hybrid quantum-classical algorithm for matrix…
In-memory computing hardware accelerators allow more than 10x improvements in peak efficiency and performance for matrix-vector multiplications (MVM) compared to conventional digital designs. For this, they have gained great interest for…
The widespread adoption of machine learning algorithms necessitates hardware acceleration to ensure efficient performance. This acceleration relies on custom matrix engines that operate on full or reduced-precision floating-point…
In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…