Faster Arbitrary-Precision Dot Product and Matrix Multiplication

Accelerating Neural Network Training using Arbitrary Precision Approximating Matrix Multiplication Algorithms

10.1145/3458744.3474050 ◽

2021 ◽

Author(s):

Grey Ballard ◽

Jack Weissenberger ◽

Luoping Zhang

Keyword(s):

Neural Network ◽

Matrix Multiplication ◽

Neural Network Training ◽

Network Training ◽

Arbitrary Precision

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Precision-extension technique for accurate vector–matrix multiplication with a CNT transistor crossbar array

Nanoscale ◽

10.1039/c9nr06715a ◽

2019 ◽

Vol 11 (44) ◽

pp. 21449-21457 ◽

Cited By ~ 2

Author(s):

Sungho Kim ◽

Yongwoo Lee ◽

Hee-Dong Kim ◽

Sung-Jin Choi

Keyword(s):

Matrix Multiplication ◽

Crossbar Array ◽

Dot Product ◽

Vector Matrix

A precision-extension technique for a dot-product engine can perform vector–matrix multiplication experimentally without any error.

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Black-white contrast of dislocation loops

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100108787 ◽

1978 ◽

Vol 36 (1) ◽

pp. 328-329

Author(s):

J. J. Hren ◽

W. D. Cooper ◽

L. J. Sykes

Keyword(s):

Electron Microscopy ◽

Transmission Electron Microscopy ◽

Dislocation Loops ◽

Major Premise ◽

Burgers Vector ◽

Transmission Electron ◽

Primary Means ◽

Contrast Analysis ◽

Dot Product ◽

Imaging Conditions

Small dislocation loops observed by transmission electron microscopy exhibit a characteristic black-white strain contrast when observed under dynamical imaging conditions. In many cases, the topography and orientation of the image may be used to determine the nature of the loop crystallography. Two distinct but somewhat overlapping procedures have been developed for the contrast analysis and identification of small dislocation loops. One group of investigators has emphasized the use of the topography of the image as the principle tool for analysis. The major premise of this method is that the characteristic details of the image topography are dependent only on the magnitude of the dot product between the loop Burgers vector and the diffracting vector. This technique is commonly referred to as the (g•b) analysis. A second group of investigators has emphasized the use of the orientation of the direction of black-white contrast as the primary means of analysis.

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Stable and Supported Semantics in Continuous Vector Spaces

Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning ◽

10.24963/kr.2020/7 ◽

2020 ◽

Author(s):

Yaniv Aspis ◽

Krysia Broda ◽

Alessandra Russo ◽

Jorge Lobo

Keyword(s):

Logic Program ◽

Matrix Multiplication ◽

Vector Spaces ◽

Continuous Space ◽

Continuous Vector ◽

Novel Approach ◽

Gradient Based ◽

Normal Logic ◽

Parameter Values ◽

Normal Logic Program

We introduce a novel approach for the computation of stable and supported models of normal logic programs in continuous vector spaces by a gradient-based search method. Specifically, the application of the immediate consequence operator of a program reduct can be computed in a vector space. To do this, Herbrand interpretations of a propositional program are embedded as 0-1 vectors in $\mathbb{R}^N$ and program reducts are represented as matrices in $\mathbb{R}^{N \times N}$. Using these representations we prove that the underlying semantics of a normal logic program is captured through matrix multiplication and a differentiable operation. As supported and stable models of a normal logic program can now be seen as fixed points in a continuous space, non-monotonic deduction can be performed using an optimisation process such as Newton's method. We report the results of several experiments using synthetically generated programs that demonstrate the feasibility of the approach and highlight how different parameter values can affect the behaviour of the system.

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