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Supporting multiple partial computations efficiently at each of the workers is a keystone in distributed coded computing in order to speed up computations and to fully exploit the resources of heterogeneous workers in terms of…

Information Theory · Computer Science 2024-11-25 Jesús Gómez-Vilardebó , Burak Hasırcıoğlu , Deniz Gündüz

Matrix multiplication over the real field constitutes a foundational operation in the training of deep learning models, serving as a computational cornerstone for both forward and backward propagation processes. However, the presence of…

Information Theory · Computer Science 2025-08-07 Hao Shi , Zhengyi Jiang , Zhongyi Huang , Bo Bai , Gong Zhang , Hanxu Hou

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

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-08-12 Anindya Bijoy Das , Aditya Ramamoorthy , David J. Love , Christopher G. Brinton

Linear regression is a fundamental and primitive problem in supervised machine learning, with applications ranging from epidemiology to finance. In this work, we propose methods for speeding up distributed linear regression. We do so by…

Information Theory · Computer Science 2024-04-02 Neophytos Charalambides , Hessam Mahdavifar , Mert Pilanci , Alfred O. Hero

Coded distributed matrix multiplication (CDMM) schemes, such as MatDot codes, seek efficient ways to distribute matrix multiplication task(s) to a set of $N$ distributed servers so that the answers returned from any $R$ servers are…

Information Theory · Computer Science 2021-05-18 Junge Wang , Zhuqing Jia , Syed A. Jafar

Approximate matrix multiplication with limited space has received ever-increasing attention due to the emergence of large-scale applications. Recently, based on a popular matrix sketching algorithm -- frequent directions, previous work has…

Machine Learning · Computer Science 2024-06-25 Yuanyu Wan , Lijun Zhang

Distributed matrix computations -- matrix-matrix or matrix-vector multiplications -- are well-recognized to suffer from the problem of stragglers (slow or failed worker nodes). Much of prior work in this area is (i) either sub-optimal in…

Information Theory · Computer Science 2020-06-03 Anindya B. Das , Aditya Ramamoorthy , Namrata Vaswani

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,…

Numerical Analysis · Mathematics 2018-05-24 Jürgen Dölz , Helmut Harbrecht , Michael D. Multerer

In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-07-28 Jiyan Yang , Xiangrui Meng , Michael W. Mahoney

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

Numerical Analysis · Mathematics 2016-06-07 Victor Y. Pan , Liang Zhao

We extend coded distributed computing over finite fields to allow the number of workers to be larger than the field size. We give codes that work for fully general matrix multiplication and show that in this case we serendipitously have…

Information Theory · Computer Science 2024-10-30 Gretchen L. Matthews , Pedro Soto

Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…

Numerical Analysis · Mathematics 2008-06-17 Per-Gunnar Martinsson

The current BigData era routinely requires the processing of large scale data on massive distributed computing clusters. Such large scale clusters often suffer from the problem of "stragglers", which are defined as slow or failed nodes. The…

Information Theory · Computer Science 2020-02-11 Aditya Ramamoorthy , Anindya Bijoy Das , Li Tang

Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…

Numerical Analysis · Mathematics 2017-05-23 Richard C. Barnard , Rick Archibald

Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…

Data Structures and Algorithms · Computer Science 2014-08-22 Michael B. Cohen , Yin Tat Lee , Cameron Musco , Christopher Musco , Richard Peng , Aaron Sidford

This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…

Numerical Analysis · Computer Science 2018-10-03 Shashanka Ubaru , Yousef Saad

We generalize the leverage score sampling sketch for $\ell_2$-subspace embeddings, to accommodate sampling subsets of the transformed data, so that the sketching approach is appropriate for distributed settings. This is then used to derive…

Information Theory · Computer Science 2024-06-27 Neophytos Charalambides , Mert Pilanci , Alfred Hero

A major hurdle in machine learning is scalability to massive datasets. Approaches to overcome this hurdle include compression of the data matrix and distributing the computations. \textit{Leverage score sampling} provides a compressed…

Information Theory · Computer Science 2020-09-16 Neophytos Charalambides , Mert Pilanci , Alfred O. Hero

Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-04-09 Huamin Li , Yuval Kluger , Mark Tygert