Related papers: A matrix math facility for Power ISA(TM) processor…
We study superfast algorithms that computes low rank approximation of a matrix (hereafter referred to as LRA) that use much fewer memory cells and arithmetic operations than the input matrix has entries. We first specify a family of 2mn…
Matrix factorization (MF) is employed by many popular algorithms, e.g., collaborative filtering. The emerging GPU technology, with massively multicore and high intra-chip memory bandwidth but limited memory capacity, presents an opportunity…
Transformers are central to advances in artificial intelligence (AI), excelling in fields ranging from computer vision to natural language processing. Despite their success, their large parameter count and computational demands challenge…
After Strassen presented the first sub-cubic matrix multiplication algorithm, many Strassen-like algorithms are presented. Most of them with low asymptotic cost have large hidden leading coefficient which are thus impractical. To reduce the…
The Nvidia GPU architecture has introduced new computing elements such as the \textit{tensor cores}, which are special processing units dedicated to perform fast matrix-multiply-accumulate (MMA) operations and accelerate \textit{Deep…
Modern computing workloads commonly involve matrix-matrix multiplication (mmul) as a core computing pattern. Coarse-Grained Reconfigurable Arrays (CGRAs) can flexibly and efficiently support it, since they combine operation-level…
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…
Fast combinational multipliers with large bit widths can occupy significant silicon area, which also drives up power consumption. Area can be reduced through resource sharing (i.e., folding) at the expense of lower throughput, which is…
As nowadays Machine Learning (ML) techniques are generating huge data collections, the problem of how to efficiently engineer their storage and operations is becoming of paramount importance. In this article we propose a new lossless…
Efficient implementations of HPC applications for parallel architectures generally rely on external software packages (e.g., BLAS, LAPACK, CUDNN). While these libraries provide highly optimized routines for certain characteristics of inputs…
In-Memory Acceleration (IMA) promises major efficiency improvements in deep neural network (DNN) inference, but challenges remain in the integration of IMA within a digital system. We propose a heterogeneous architecture coupling 8 RISC-V…
The NVIDIA Volta GPU microarchitecture introduces a specialized unit, called "Tensor Core" that performs one matrix-multiply-and-accumulate on 4x4 matrices per clock cycle. The NVIDIA Tesla V100 accelerator, featuring the Volta…
This paper makes the case for a single-ISA heterogeneous computing platform, AISC, where each compute engine (be it a core or an accelerator) supports a different subset of the very same ISA. An ISA subset may not be functionally complete,…
The importance of general matrix multiplication (GEMM) is motivating new instruction set extensions for multiplying dense matrices in almost all contemporary ISAs, and these extensions are often implemented using high-performance systolic…
Tensor Core is a mixed-precision matrix-matrix multiplication unit on NVIDIA GPUs with a theoretical peak performance of more than 300 TFlop/s on Ampere architectures. Tensor Cores were developed in response to the high demand of dense…
Multiplication is a core operation in modern neural network (NN) computations, contributing significantly to energy consumption. The linear-complexity multiplication (L-Mul) algorithm is specifically proposed as an approximate…
Matrix-accelerated stencil computation is a hot research topic, yet its application to three-dimensional (3D) high-order stencils and HPC remains underexplored. With the emergence of matrix units on multicore CPUs, we analyze matrix-based…
Fast matrix multiplication is one of the most fundamental problems in algorithm research. The exponent of the optimal time complexity of matrix multiplication is usually denoted by $\omega$. This paper discusses new ideas for improving the…
Sparse-dense linear algebra is crucial in many domains, but challenging to handle efficiently on CPUs, GPUs, and accelerators alike; multiplications with sparse formats like CSR and CSF require indirect memory lookups. In this work, we…
We present an optimized single-precision implementation of the Sparse Approximate Matrix Multiply (\SpAMM{}) [M. Challacombe and N. Bock, arXiv {\bf 1011.3534} (2010)], a fast algorithm for matrix-matrix multiplication for matrices with…