Grothendieck constant is norm of Strassen matrix multiplication tensor
Sign Up to like & getrecommendations! Published in 2019 at "Numerische Mathematik"
DOI: 10.1007/s00211-019-01070-6
Abstract: We show that two important quantities from two disparate areas of complexity theory --- Strassen's exponent of matrix multiplication $\omega$ and Grothendieck's constant $K_G$ --- are intimately related. They are different measures of size for… read more here.
Keywords: grothendieck constant; tensor; grothendieck; matrix multiplication ... See more keywords
A New Fast Recursive Matrix Multiplication Algorithm
Sign Up to like & getrecommendations! Published in 2019 at "Cybernetics and Systems Analysis"
DOI: 10.1007/s10559-019-00163-2
Abstract: A new recursive algorithm is proposed for multiplying matrices of order n = 2q (q > 1). This algorithm is based on a fast hybrid algorithm for multiplying matrices of order n = 4μ with… read more here.
Keywords: fast recursive; recursive matrix; new fast; matrix multiplication ... See more keywords
An Efficient Method of Matrix Multiplication for Heaps of Pieces
Sign Up to like & getrecommendations! Published in 2018 at "IFAC-PapersOnLine"
DOI: 10.1016/j.ifacol.2018.06.302
Abstract: Abstract In this paper, we outline a method for carrying out efficient (max, +) matrix multiplication when using the heaps of pieces framework. We present an algorithm for multiplying an arbitrary m by r matrix… read more here.
Keywords: heaps pieces; efficient method; matrix multiplication;
Visualizing Matrix Multiplication
Sign Up to like & getrecommendations! Published in 2018 at "PRIMUS"
DOI: 10.1080/10511970.2017.1313344
Abstract: Abstract Efficient visualizations of computational algorithms are important tools for students, educators, and researchers. In this article, we point out an innovative visualization technique for matrix multiplication. This method differs from the standard, formal approach… read more here.
Keywords: visualizing matrix; matrix multiplication; multiplication;
On the Geometry of Border Rank Algorithms for n × 2 by 2 × 2 Matrix Multiplication
Sign Up to like & getrecommendations! Published in 2017 at "Experimental Mathematics"
DOI: 10.1080/10586458.2016.1162230
Abstract: ABSTRACT We make an in-depth study of the known border rank (i.e., approximate) algorithms for the matrix multiplication tensor encoding the multiplication of an n × 2 matrix by a 2 × 2 matrix. read more here.
Keywords: multiplication; geometry; border rank; algorithms matrix ... See more keywords
The Geometry of Rank Decompositions of Matrix Multiplication I: 2 × 2 Matrices
Sign Up to like & getrecommendations! Published in 2019 at "Experimental Mathematics"
DOI: 10.1080/10586458.2017.1403981
Abstract: ABSTRACT This is the first in a series of papers on rank decompositions of the matrix multiplication tensor. In this paper, we establish general facts about rank decompositions of tensors, describe potential ways to search… read more here.
Keywords: rank decompositions; geometry; decompositions matrix; geometry rank ... See more keywords
A Rank 18 Waring Decomposition of sM 〈3〉 with 432 Symmetries
Sign Up to like & getrecommendations! Published in 2021 at "Experimental Mathematics"
DOI: 10.1080/10586458.2018.1547231
Abstract: Abstract The recent discovery that the exponent of matrix multiplication is determined by the rank of the symmetrized matrix multiplication tensor has invigorated interest in better understanding symmetrized matrix multiplication. Author present an explicit rank… read more here.
Keywords: 432 symmetries; rank waring; waring decomposition; decomposition 432 ... See more keywords
Eidetic: An In-Memory Matrix Multiplication Accelerator for Neural Networks
Sign Up to like & getrecommendations! Published in 2023 at "IEEE Transactions on Computers"
DOI: 10.1109/tc.2022.3214151
Abstract: This paper presents the Eidetic architecture, which is an SRAM-based ASIC neural network accelerator that eliminates the need to continuously load weights from off-chip, while also minimizing the need to go off chip for intermediate… read more here.
Keywords: eidetic memory; memory matrix; accelerator; matrix multiplication ... See more keywords
Straggler-Exploiting Fully Private Distributed Matrix Multiplication With Chebyshev Polynomials
Sign Up to like & getrecommendations! Published in 2023 at "IEEE Transactions on Communications"
DOI: 10.1109/tcomm.2023.3236385
Abstract: In this paper, we consider coded computation for matrix multiplication tasks in distributed computing to mitigate straggler effects. We assume that the stragglers’ computation results can be leveraged at the master by assigning multiple sub-tasks… read more here.
Keywords: fully private; chebyshev polynomials; master; matrix multiplication ... See more keywords
Optimizing Hardware Accelerated General Matrix-Matrix Multiplication for CNNs on FPGAs
Sign Up to like & getrecommendations! Published in 2020 at "IEEE Transactions on Circuits and Systems II: Express Briefs"
DOI: 10.1109/tcsii.2020.2965154
Abstract: Convolution is inarguably the most complex operation utilized in Convolutional Neural Networks (convnets). Owing to the billions of independent multiply-adds involved, convolution is being massively parallelized by the simultaneous utilization of many cores of Graphical… read more here.
Keywords: matrix; general matrix; optimizing hardware; matrix multiplication ... See more keywords
More Efficient Secure Matrix Multiplication for Unbalanced Recommender Systems
Sign Up to like & getrecommendations! Published in 2023 at "IEEE Transactions on Dependable and Secure Computing"
DOI: 10.1109/tdsc.2021.3139318
Abstract: With recent advances in homomorphic encryption (HE), it becomes feasible to run non-interactive machine learning (ML) algorithms on encrypted data without decryption. In this work, we propose novel encoding methods to pack matrix in a… read more here.
Keywords: mml mml; mml; matrix multiplication; secure matrix ... See more keywords