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We propose a unified coded framework for distributed computing with straggling servers, by introducing a tradeoff between "latency of computation" and "load of communication" for some linear computation tasks. We show that the coded scheme…

Information Theory · Computer Science 2016-10-26 Songze Li , Mohammad Ali Maddah-Ali , A. Salman Avestimehr

A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…

Numerical Analysis · Mathematics 2012-12-27 Victor Y. Pan , Guoliang Qian

In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…

Information Theory · Computer Science 2014-08-12 Atri Rudra , Mary Wootters

We consider the problem of designing secure and private codes for distributed matrix-matrix multiplication. A master server owns two private matrices and hires worker nodes to help compute their product. The matrices should remain…

Information Theory · Computer Science 2022-02-15 Christoph Hofmeister , Rawad Bitar , Marvin Xhemrishi , Antonia Wachter-Zeh

Several efficient distributed algorithms have been developed for matrix-matrix multiplication: the 3D algorithm, the 2D SUMMA algorithm, and the 2.5D algorithm. Each of these algorithms was independently conceived and they trade-off memory…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-07-29 Rui Li , Yufan Xu , Aravind Sukumaran-Rajam , Atanas Rountev , P Sadayappan

We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…

Information Theory · Computer Science 2012-02-03 Venkatesan Guruswami , Srivatsan Narayanan , Carol Wang

We consider the problems of Private and Secure Matrix Multiplication (PSMM) and Fully Private Matrix Multiplication (FPMM), for which matrices privately selected by a master node are multiplied at distributed worker nodes without revealing…

Information Theory · Computer Science 2022-06-24 Jinbao Zhu , Songze Li

Generalized sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. Here we show that SpGEMM also yields efficient…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-03-19 Aydin Buluc , John Gilbert

Tensor accelerators have gained popularity because they provide a cheap and efficient solution for speeding up computational-expensive tasks in Deep Learning and, more recently, in other Scientific Computing applications. However, since…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-02-15 Paolo Sylos Labini , Massimo Bernaschi , Francesco Silvestri , Flavio Vella

Recently, coding has been a useful technique to mitigate the effect of stragglers in distributed computing. However, coding in this context has been mainly explored under the assumption of homogeneous workers, although the real-world…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-02-18 DaeJin Kim , Hyegyeong Park , Junkyun Choi

We consider distributed gradient descent in the presence of stragglers. Recent work on \em gradient coding \em and \em approximate gradient coding \em have shown how to add redundancy in distributed gradient descent to guarantee convergence…

Information Theory · Computer Science 2019-05-15 Rawad Bitar , Mary Wootters , Salim El Rouayheb

We study coded distributed matrix multiplication from an approximate recovery viewpoint. We consider a system of $P$ computation nodes where each node stores $1/m$ of each multiplicand via linear encoding. Our main result shows that the…

Information Theory · Computer Science 2021-05-06 Haewon Jeong , Ateet Devulapalli , Viveck R. Cadambe , Flavio Calmon

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

Signal Processing · Electrical Eng. & Systems 2023-07-19 Xiao Fu , Nico Vervliet , Lieven De Lathauwer , Kejun Huang , Nicolas Gillis

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…

Machine Learning · Statistics 2024-01-30 Alexandros E. Tzikas , Licio Romao , Mert Pilanci , Alessandro Abate , Mykel J. Kochenderfer

In this paper, we consider the iterative solution of linear algebraic equations under the condition that matrix-vector products with the coefficient matrix are computed only partially. At the same time, non-computed entries are set to…

Numerical Analysis · Mathematics 2024-10-15 Vassilis Kalantzis , Yuanzhe Xi , Lior Horesh , Yousef Saad

In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…

Numerical Analysis · Mathematics 2026-02-05 Mohamed Kamel Riahi

We present Modular Polynomial (MP) Codes for Secure Distributed Matrix Multiplication (SDMM). The construction is based on the observation that one can decode certain proper subsets of the coefficients of a polynomial with fewer evaluations…

Information Theory · Computer Science 2024-01-08 David Karpuk , Razane Tajeddine

We present a novel approach for accelerating convolutions during inference for CPU-based architectures. The most common method of computation involves packing the image into the columns of a matrix (im2col) and performing general matrix…

Computer Vision and Pattern Recognition · Computer Science 2024-11-26 Amir Ofir , Gil Ben-Artzi

We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…

Machine Learning · Statistics 2016-04-26 Krzysztof Choromanski , Francois Fagan

Matrix-vector multiplication is one of the most fundamental computing primitives. Given a matrix $A\in\mathbb{F}^{N\times N}$ and a vector $b$, it is known that in the worst case $\Theta(N^2)$ operations over $\mathbb{F}$ are needed to…

Data Structures and Algorithms · Computer Science 2017-11-21 Christopher De Sa , Albert Gu , Rohan Puttagunta , Christopher Ré , Atri Rudra