Related papers: Distributed Matrix Multiplication-Friendly Algebra…
In this paper, we propose a new secure distributed matrix multiplication (SDMM) scheme using the inner product partitioning. We construct a scheme with a minimal number of workers and no redundancy, and another scheme with redundancy…
We explore the problem of approximate matrix multiplication (AMM) within the sliding window model, where algorithms utilize limited space to perform large-scale matrix multiplication in a streaming manner. This model has garnered increasing…
Tensor operations, such as matrix multiplication, are central to large-scale machine learning applications. For user-driven tasks these operations can be carried out on a distributed computing platform with a master server at the user side…
This paper has two contributions. First, we propose a novel coded matrix multiplication technique called Generalized PolyDot codes that advances on existing methods for coded matrix multiplication under storage and communication…
We show that polynomial codes (and some related codes) used for distributed matrix multiplication are interleaved Reed-Solomon codes and, hence, can be collaboratively decoded. We consider a fault tolerant setup where $t$ worker nodes…
In distributed matrix multiplication, a common scenario is to assign each worker a fraction of the multiplication task, by partitioning the input matrices into smaller submatrices. In particular, by dividing two input matrices into…
We consider the problem of massive matrix multiplication, which underlies many data analytic applications, in a large-scale distributed system comprising a group of worker nodes. We target the stragglers' delay performance bottleneck, which…
A representation of finite fields that has proved useful when implementing finite field arithmetic in hardware is based on an isomorphism between subrings and fields. In this paper, we present an unified formulation for multiplication in…
Alternating direction methods of multipliers (ADMMs) are popular approaches to handle large scale semidefinite programs that gained attention during the past decade. In this paper, we focus on solving doubly nonnegative programs (DNN),…
This paper considers an optimization problem that components of the objective function are available at different nodes of a network and nodes are allowed to only exchange information with their neighbors. The decentralized alternating…
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…
We consider the problem of communication efficient secure distributed matrix multiplication. The previous literature has focused on reducing the number of servers as a proxy for minimizing communication costs. The intuition being, that the…
This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alternating direction methods of multipliers (ADMMs) for convex composite optimization problems. The…
We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance between two tuples of matrices is captured by a weight…
Deep Matrix Factorization (DMF) is an emerging approach to the problem of matrix completion. Recent works have established that gradient descent applied to a DMF model induces an implicit regularization on the rank of the recovered matrix.…
In this paper we are concentrating on the diversity-multiplexing gain trade-off (DMT) of some space-time lattice codes. First we give a DMT bound for lattice codes having restricted dimension. We then recover the well known results of the…
We propose a novel application of coded computing to the problem of the nearest neighbor estimation using MatDot Codes [Fahim. et.al. 2017], that are known to be optimal for matrix multiplication in terms of recovery threshold under storage…
In this paper, we present secure distributed matrix multiplication (SDMM) schemes over the complex numbers with good numerical stability and small mutual information leakage by utilizing polynomial interpolation with roots of unity.…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
Coded computation is an emerging research area that leverages concepts from erasure coding to mitigate the effect of stragglers (slow nodes) in distributed computation clusters, especially for matrix computation problems. In this work, we…