English
Related papers

Related papers: Output-Sparse Matrix Multiplication Using Compress…

200 papers

An "oblivious subspace embedding (OSE)" given some parameters eps,d is a distribution D over matrices B in R^{m x n} such that for any linear subspace W in R^n with dim(W) = d it holds that Pr_{B ~ D}(forall x in W ||B x||_2 in (1 +/-…

Data Structures and Algorithms · Computer Science 2012-11-07 Jelani Nelson , Huy L. Nguyen

We implement two novel algorithms for sparse-matrix dense-matrix multiplication (SpMM) on the GPU. Our algorithms expect the sparse input in the popular compressed-sparse-row (CSR) format and thus do not require expensive format conversion.…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-06-13 Carl Yang , Aydin Buluc , John D. Owens

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…

Data Structures and Algorithms · Computer Science 2024-04-15 Ashish Gola , Igor Shinkar , Harsimran Singh

We propose a non-commutative algorithm for multiplying 2x2 matrices using 7 coefficient products. This algorithm reaches simultaneously a better accuracy in practice compared to previously known such fast algorithms, and a time complexity…

Numerical Analysis · Mathematics 2024-07-01 Jean-Guillaume Dumas , Clément Pernet , Alexandre Sedoglavic

Motivated by the problems of computing sample covariance matrices, and of transforming a collection of vectors to a basis where they are sparse, we present a simple algorithm that computes an approximation of the product of two n-by-n real…

Data Structures and Algorithms · Computer Science 2015-03-19 Rasmus Pagh

In this paper, we develop a symmetric accelerated stochastic Alternating Direction Method of Multipliers (SAS-ADMM) for solving separable convex optimization problems with linear constraints. The objective function is the sum of a possibly…

Optimization and Control · Mathematics 2021-12-21 Jianchao Bai , Deren Han , Hao Sun , Hongchao Zhang

Most current sampling algorithms for high-dimensional distributions are based on MCMC techniques and are approximate in the sense that they are valid only asymptotically. Rejection sampling, on the other hand, produces valid samples, but is…

Artificial Intelligence · Computer Science 2012-07-04 Marc Dymetman , Guillaume Bouchard , Simon Carter

This article presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes…

Chemical Physics · Physics 2014-10-21 Jacob N. Sanders , Xavier Andrade , Alán Aspuru-Guzik

In the non-negative matrix factorization (NMF) problem, the input is an $m\times n$ matrix $M$ with non-negative entries and the goal is to factorize it as $M\approx AW$. The $m\times k$ matrix $A$ and the $k\times n$ matrix $W$ are both…

Data Structures and Algorithms · Computer Science 2021-03-09 Moses Charikar , Lunjia Hu

In this paper, we present novel deterministic algorithms for multiplying two $n \times n$ matrices approximately. Given two matrices $A,B$ we return a matrix $C'$ which is an \emph{approximation} to $C = AB$. We consider the notion of…

Data Structures and Algorithms · Computer Science 2014-08-21 Shiva Manne , Manjish Pal

This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Numerous renowned algorithms for tackling the compressed sensing problem…

Information Theory · Computer Science 2026-03-11 Xu Zhu , Yufei Ma , Xiaoguang Li , Tiejun Li

As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP for pursuing…

Information Theory · Computer Science 2014-04-01 Jian Wang , Seokbeop Kwon , Byonghyo Shim

Artificial intelligence workloads, especially transformer models, exhibit emergent sparsity in which computations perform selective sparse access to dense data. The workloads are inefficient on hardware designed for dense computations and…

Data Structures and Algorithms · Computer Science 2024-02-23 Brian Wheatman , Meghana Madhyastha , Randal Burns

In distribution compression, one aims to accurately summarize a probability distribution $\mathbb{P}$ using a small number of representative points. Near-optimal thinning procedures achieve this goal by sampling $n$ points from a Markov…

Machine Learning · Statistics 2022-10-19 Abhishek Shetty , Raaz Dwivedi , Lester Mackey

Computing the simulation preorder of a given Kripke structure (i.e., a directed graph with $n$ labeled vertices) has crucial applications in model checking of temporal logic. It amounts to solving a specific two-players reachability game,…

Computational Complexity · Computer Science 2016-08-31 Massimo Cairo , Romeo Rizzi

Multiplying two sparse matrices (SpGEMM) is a common computational primitive used in many areas including graph algorithms, bioinformatics, algebraic multigrid solvers, and randomized sketching. Distributed-memory parallel algorithms for…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-08-28 Yuxi Hong , Aydin Buluc

Computing the convolution $A\star B$ of two length-$n$ vectors $A,B$ is an ubiquitous computational primitive. Applications range from string problems to Knapsack-type problems, and from 3SUM to All-Pairs Shortest Paths. These applications…

Data Structures and Algorithms · Computer Science 2021-05-17 Karl Bringmann , Nick Fischer , Vasileios Nakos

Highly coherent sensing matrices arise in discretization of continuum problems such as radar and medical imaging when the grid spacing is below the Rayleigh threshold as well as in using highly coherent, redundant dictionaries as…

Information Theory · Computer Science 2015-05-30 Albert Fannjiang , Wenjing Liao

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…

Numerical Analysis · Mathematics 2021-10-12 Feng Wu , Kailing Zhang , Li Zhu , Jiayao Hu

Sparse matrix multiplication is traditionally performed in memory and scales to large matrices using the distributed memory of multiple nodes. In contrast, we scale sparse matrix multiplication beyond memory capacity by implementing sparse…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-11-15 Da Zheng , Disa Mhembere , Vince Lyzinski , Joshua Vogelstein , Carey E. Priebe , Randal Burns