相关论文: Low-Bandwidth Matrix Multiplication: Faster Algori…

We study matrix multiplication in the low-bandwidth model: There are $n$ computers, and we need to compute the product of two $n \times n$ matrices. Initially computer $i$ knows row $i$ of each input matrix. In one communication round each…

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…

We consider the problem of multiplying sparse matrices (over a semiring) where the number of non-zero entries is larger than main memory. In the classical paper of Hong and Kung (STOC '81) it was shown that to compute a product of dense $U…

We give two algorithms for output-sparse matrix multiplication (OSMM), the problem of multiplying two $n \times n$ matrices $A, B$ when their product $AB$ is promised to have at most $O(n^{\delta})$ many non-zero entries for a given value…

Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…

What is the time complexity of matrix multiplication of sparse integer matrices with $m_{in}$ nonzeros in the input and $m_{out}$ nonzeros in the output? This paper provides improved upper bounds for this question for almost any choice of…

Matrix multiplication is a fundamental task in almost all computational fields, including machine learning and optimization, computer graphics, signal processing, and graph algorithms (static and dynamic). Twin-width is a natural complexity…

We consider the problem of sparse matrix multiplication by the column row method in a distributed setting where the matrix product is not necessarily sparse. We present a surprisingly simple method for "consistent" parallel processing of…

Multiplication of a sparse matrix with another (dense or sparse) matrix is a fundamental operation that captures the computational patterns of many data science applications, including but not limited to graph algorithms, sparsely connected…

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…

In many problems in Computational Physics and Chemistry, one finds a special kind of sparse matrices, termed "banded matrices". These matrices, which are defined as having non-zero entries only within a given distance from the main…

We multiply two $n \times n$ matrices $S,T$ over semirings in the Congested Clique model, where $n$ fully connected nodes communicate synchronously using $O(\log n)$-bit messages, within $O(nz(S)^{1/3} nz(T)^{1/3}/n + 1)$ rounds of…

We propose a novel approach to iterated sparse matrix dense matrix multiplication, a fundamental computational kernel in scientific computing and graph neural network training. In cases where matrix sizes exceed the memory of a single…

In a large-scale and distributed matrix multiplication problem $C=A^{\intercal}B$, where $C\in\mathbb{R}^{r\times t}$, the coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may…

Matrix-matrix multiplication is a basic operation in linear algebra and an essential building block for a wide range of algorithms in various scientific fields. Theory and implementation for the dense, square matrix case are well-developed.…

This is the first of two papers to describe a matrix sparsification algorithm that takes a general real or complex matrix as input and produces a sparse output matrix of the same size. The non-zero entries in the output are chosen to…

Matrix computations are a fundamental building-block of edge computing systems, with a major recent uptick in demand due to their use in AI/ML training and inference procedures. Existing approaches for distributing matrix computations…

Sparse matrix multiplication is an important component of linear algebra computations. Implementing sparse matrix multiplication on an associative processor (AP) enables high level of parallelism, where a row of one matrix is multiplied in…

We consider the problem of designing a coding scheme that allows both sparsity and privacy for distributed matrix-vector multiplication. Perfect information-theoretic privacy requires encoding the input sparse matrices into matrices…

We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where…