Related papers: Fast and Practical Strassen's Matrix Multiplicatio…
An open-source C++ framework for discovering fast matrix multiplication schemes using the flip graph approach is presented. The framework supports multiple coefficient rings -- binary ($\mathbb{Z}_2$), modular ternary ($\mathbb{Z}_3$) and…
Power ISA(TM) Version 3.1 has introduced a new family of matrix math instructions, collectively known as the Matrix-Multiply Assist (MMA) facility. The instructions in this facility implement numerical linear algebra operations on small…
The Sch\"onhage-Strassen algorithm (SSA) is the de-facto standard for multiplication of large integers. For $N$-bit numbers it has a time bound of $O(N \cdot \log N \cdot \log \log N)$. De, Kurur, Saha and Saptharishi (DKSS) presented an…
Matrix multiplication is a fundamental classical computing operation whose efficiency becomes a major challenge at scale, especially for machine learning applications. Quantum computing, with its inherent parallelism and exponential storage…
Generalised matrix-matrix multiplication forms the kernel of many mathematical algorithms. A faster matrix-matrix multiply immediately benefits these algorithms. In this paper we implement efficient matrix multiplication for large matrices…
The devices designed for the Internet-of-Things encompass a large variety of distinct processor architectures, forming a highly heterogeneous zoo. In order to tackle this, we employ a simulator to estimate the performance of the…
Recently, tensor algebra have witnessed significant applications across various domains. Each operator in tensor algebra features different computational workload and precision. However, current general accelerators, such as VPU, GPGPU, and…
Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an…
The inference and training stages of Graph Neural Networks (GNNs) are often dominated by the time required to compute a long sequence of matrix multiplications between the sparse graph adjacency matrix and its embedding. To accelerate these…
Kernel matrix-vector multiplication (KMVM) is a foundational operation in machine learning and scientific computing. However, as KMVM tends to scale quadratically in both memory and time, applications are often limited by these…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
Sparse general matrix-matrix multiplication (SpGEMM) is a critical operation in many applications. Current multithreaded implementations are based on Gustavson's algorithm and often perform poorly on large matrices due to limited cache…
A fast algorithm for the approximate multiplication of matrices with decay is introduced; the Sparse Approximate Matrix Multiply (SpAMM) reduces complexity in the product space, a different approach from current methods that economize…
Can linear systems be solved faster than matrix multiplication? While there has been remarkable progress for the special cases of graph structured linear systems, in the general setting, the bit complexity of solving an $n \times n$ linear…
Randomized algorithms are overwhelming methods for low-rank approximation that can alleviate the computational expenditure with great reliability compared to deterministic algorithms. A crucial thought is generating a standard Gaussian…
We propose a more accurate variant of an algorithm for multiplying 4x4 matrices using 48 multiplications over any ring containing an inverse of 2. This algorithm has an error bound exponent of only log 4 $\gamma$$\infty$,2 $\approx$ 2.386.…
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 two fast algorithms for matrix-vector multiplication $y=Ax$, where $A$ is a Hankel matrix. The current asymptotically fastest method is based on the Fast Fourier Transform (FFT), however in multiprecision arithmetics with very…
We present a simple randomized algorithm for approximate matrix multiplication (AMM) whose error scales with the *output* norm $\|AB\|_F$. Given any $n\times n$ matrices $A,B$ and a runtime parameter $r\leq n$, the algorithm produces in…
General Matrix Multiplication (GEMM) is a critical kernel in high-performance computing and deep learning. While modern architectures like ARM's Scalable Matrix Extension (SME) introduce dedicated hardware for matrix operations, existing…