Related papers: Fast Approximate Matrix Multiplication by Solving …
Fast approximations to matrix multiplication have the potential to dramatically reduce the cost of neural network inference. Recent work on approximate matrix multiplication proposed to replace costly multiplications with table-lookups by…
We study the problem of approximating a matrix $\mathbf{A}$ with a matrix that has a fixed sparsity pattern (e.g., diagonal, banded, etc.), when $\mathbf{A}$ is accessed only by matrix-vector products. We describe a simple randomized…
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…
In this paper we study a worst case to average case reduction for the problem of matrix multiplication over finite fields. Suppose we have an efficient average case algorithm, that given two random matrices $A,B$ outputs a matrix that has a…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…
In this paper, we investigate the randomized algorithms for block matrix multiplication from random sampling perspective. Based on the A-optimal design criterion, the optimal sampling probabilities and sampling block sizes are obtained. To…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…
We present a method for randomizing formulas for bilinear computation of matrix products. We consider the implications of such randomization when there are two sources of error: One due to the formula itself only being approximately…
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
Matrix multiplication is a fundamental kernel in high performance computing. Many algorithms for fast matrix multiplication can only be applied to enormous matrices ($n>10^{100}$) and thus cannot be used in practice. Of all algorithms…
We consider the least-squares approximation of a matrix C in the set of doubly stochastic matrices with the same sparsity pattern as C. Our approach is based on applying the well-known Alternating Direction Method of Multipliers (ADMM) to a…
$\newcommand{\MatA}{\mathcal{M}}$ $\newcommand{\eps}{\varepsilon}$ $\newcommand{\NSize}{\mathsf{N}{}}$ $\newcommand{\MatB}{\mathcal{B}}$ $\newcommand{\Fnorm}[1]{\left\| {#1} \right\|_F}$ $\newcommand{\PrcOpt}[2]{\mu_{\mathrm{opt}}\pth{#1,…
Motivated by studying the power of randomness, certifying algorithms and barriers for fine-grained reductions, we investigate the question whether the multiplication of two $n\times n$ matrices can be performed in near-optimal…
There have been several algorithms designed to optimise matrix multiplication. From schoolbook method with complexity $O(n^3)$ to advanced tensor-based tools with time complexity $O(n^{2.3728639})$ (lowest possible bound achieved), a lot of…
We propose a strategy for the generation of fast and accurate versions of non-commutative recursive matrix multiplication algorithms. To generate these algorithms, we consider matrix and tensor norm bounds governing the stability and…