Related papers: More Asymmetry Yields Faster Matrix Multiplication
Modern Neural Network (NN) architectures heavily rely on vast numbers of multiply-accumulate arithmetic operations, constituting the predominant computational cost. Therefore, this paper proposes a high-throughput, scalable and energy…
Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…
In this paper we introduce a generic model for multiplicative algorithms which is suitable for the MapReduce parallel programming paradigm. We implement three typical machine learning algorithms to demonstrate how similarity comparison,…
We develop a new, group-theoretic approach to bounding the exponent of matrix multiplication. There are two components to this approach: (1) identifying groups G that admit a certain type of embedding of matrix multiplication into the group…
We present an approximate algorithm for matrix multiplication based on matrix sketching techniques. First one of the matrix is chosen and sparsified using the online matrix sketching algorithm, and then the matrix product is calculated…
The distance matrix of a dataset $X$ of $n$ points with respect to a distance function $f$ represents all pairwise distances between points in $X$ induced by $f$. Due to their wide applicability, distance matrices and related families of…
Quaternion symmetry is ubiquitous in the physical sciences. As such, much work has been afforded over the years to the development of efficient schemes to exploit this symmetry using real and complex linear algebra. Recent years have also…
Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…
We give new positive and negative results (some conditional) on speeding up computational algebraic geometry over the reals: (1) A new and sharper upper bound on the number of connected components of a semialgebraic set. Our bound is novel…
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework…
In this paper, we demonstrate how a class of advanced matrix concentration inequalities, introduced in \cite{brailovskaya2024universality}, can be used to eliminate the dimensional factor in the convergence rate of matrix completion. This…
We introduce a modification of the linear sieve whose weights satisfy strong factorization properties, and consequently equidistribute primes up to size $x$ in arithmetic progressions to moduli up to $x^{10/17}$. This surpasses the level of…
Distributed network optimization has been studied for well over a decade. However, we still do not have a good idea of how to design schemes that can simultaneously provide good performance across the dimensions of utility optimality,…
Initiated by Mulmuley, Vazirani, and Vazirani (1987), many algebraic algorithms have been developed for matching and related problems. In this paper, we review basic facts and discuss possible improvements with the aid of fast computation…
In this paper, we study a nonconvex, nonsmooth, and non-Lipschitz generalized symmetric matrix factorization model that unifies a broad class of matrix factorization formulations arising in machine learning, image science, engineering, and…
Despite their tremendous success and versatility, Deep Neural Networks (DNNs) such as Large Language Models (LLMs) suffer from inference inefficiency and rely on advanced computational infrastructure. To address these challenges and make…
In this paper we develop algorithms for approximating matrix multiplication with respect to the spectral norm. Let A\in{\RR^{n\times m}} and B\in\RR^{n \times p} be two matrices and \eps>0. We approximate the product A^\top B using two…
In this study, we propose a simple method for fault-tolerant Strassen-like matrix multiplications. The proposed method is based on using two distinct Strassen-like algorithms instead of replicating a given one. We have realized that using…
For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…
The alternating direction method of multipliers (ADMM) were extensively investigated in the past decades for solving separable convex optimization problems. Fewer researchers focused on exploring its convergence properties for the nonconvex…