scholarly journals Hashing Based Answer Selection

2020 ◽  
Vol 34 (05) ◽  
pp. 9330-9337
Author(s):  
Dong Xu ◽  
Wu-Jun Li
Keyword(s):  
Question Answering ◽  
Matrix Representation ◽  
Matrix Representations ◽  
Binary Matrix ◽  
Large Memory ◽  
The Matrix ◽  
Novel Method ◽  
Online Prediction ◽  
Memory Cost ◽  
Vector Representations

Answer selection is an important subtask of question answering (QA), in which deep models usually achieve better performance than non-deep models. Most deep models adopt question-answer interaction mechanisms, such as attention, to get vector representations for answers. When these interaction based deep models are deployed for online prediction, the representations of all answers need to be recalculated for each question. This procedure is time-consuming for deep models with complex encoders like BERT which usually have better accuracy than simple encoders. One possible solution is to store the matrix representation (encoder output) of each answer in memory to avoid recalculation. But this will bring large memory cost. In this paper, we propose a novel method, called hashing based answer selection (HAS), to tackle this problem. HAS adopts a hashing strategy to learn a binary matrix representation for each answer, which can dramatically reduce the memory cost for storing the matrix representations of answers. Hence, HAS can adopt complex encoders like BERT in the model, but the online prediction of HAS is still fast with a low memory cost. Experimental results on three popular answer selection datasets show that HAS can outperform existing models to achieve state-of-the-art performance.

MRHS solver based on linear algebra and exhaustive search

2018 ◽  
Vol 12 (3) ◽  
pp. 143-157 ◽  
Author(s):  
Håvard Raddum ◽  
Pavol Zajac
Keyword(s):  
Linear Algebra ◽  
Matrix Representation ◽  
Equation System ◽  
Exhaustive Search ◽  
Binary Matrix ◽  
Algebraic Attacks ◽  
The Matrix ◽  
Speed Up ◽  
Symmetric Key

Abstract We show how to build a binary matrix from the MRHS representation of a symmetric-key cipher. The matrix contains the cipher represented as an equation system and can be used to assess a cipher’s resistance against algebraic attacks. We give an algorithm for solving the system and compute its complexity. The complexity is normally close to exhaustive search on the variables representing the user-selected key. Finally, we show that for some variants of LowMC, the joined MRHS matrix representation can be used to speed up regular encryption in addition to exhaustive key search.

Matrix representations of right ample semigroups

2015 ◽  
Vol 08 (03) ◽  
pp. 1550042 ◽  
Author(s):  
Junying Guo ◽  
Xiaojiang Guo ◽  
K. P. Shum
Keyword(s):  
Matrix Representation ◽  
Matrix Representations ◽  
Ample Semigroup ◽  
The Matrix

The properties of right ample semigroups have been extensively considered and studied by many authors. In this paper, we concentrate on the matrix representations of right ample semigroups. The (left; right) uniform matrix representation is initially defined. After some properties of left uniform matrix representations of a right ample semigroup are given, we prove that any irreducible left uniform representations of a right ample semigroup can be obtained by using an irreducible left uniform representation of some primitive right ample semigroup. In particular, a construction theorem of prime left uniform representation of right ample semigroups is established.

scholarly journals Eigenvalues of matrices related to the octonions

4open ◽  
2019 ◽  
Vol 2 ◽  
pp. 16
Author(s):  
Rogério Serôdio ◽  
Patricia Beites ◽  
José Vitória
Keyword(s):  
Matrix Representation ◽  
Real Matrix ◽  
Matrix Representations ◽  
Estimation Algorithms ◽  
The Matrix

A pseudo real matrix representation of an octonion, which is based on two real matrix representations of a quaternion, is considered. We study how some operations defined on the octonions change the set of eigenvalues of the matrix obtained if these operations are performed after or before the matrix representation. The established results could be of particular interest to researchers working on estimation algorithms involving such operations.

scholarly journals Isomorphism and matrix representation of point groups

2019 ◽  
Vol 15 (1) ◽  
pp. 88-92
Author(s):  
Wan Heng Fong ◽  
Aqilahfarhana Abdul Rahman ◽  
Nor Haniza Sarmin
Keyword(s):  
Group Theory ◽  
Matrix Representation ◽  
Point Group ◽  
Multiplication Table ◽  
Matrix Representations ◽  
The Matrix ◽  
Point Groups ◽  
Complete Set ◽  
Symmetry Of Molecules ◽  
Symmetry Operations

In chemistry, point group is a type of group used to describe the symmetry of molecules. It is a collection of symmetry elements controlled by a form or shape which all go through one point in space, which consists of all symmetry operations that are possible for every molecule. Next, a set of number or matrices which assigns to the elements of a group and represents the multiplication of the elements is said to constitute representation of a group. Here, each individual matrix is called a representative that corresponds to the symmetry operations of point groups, and the complete set of matrices is called a matrix representation of the group. This research was aimed to relate the symmetry in point groups with group theory in mathematics using the concept of isomorphism, where elements of point groups and groups were mapped such that the isomorphism properties were fulfilled. Then, matrix representations of point groups were found based on the multiplication table where symmetry operations were represented by matrices. From this research, point groups of order less than eight were shown to be isomorphic with groups in group theory. In addition, the matrix representation corresponding to the symmetry operations of these point groups wasis presented. This research would hence connect the field of mathematics and chemistry, where the relation between groups in group theory and point groups in chemistry were shown.

scholarly journals Crystal structures and continued fractions

2021 ◽  
Vol 2099 (1) ◽  
pp. 012012
Author(s):  
L V Pekhtereva ◽  
V A Seleznev
Keyword(s):  
Crystal Structure ◽  
Crystal Structures ◽  
Continued Fractions ◽  
Matrix Representation ◽  
Integer Lattice ◽  
Natural Numbers ◽  
Matrix Representations ◽  
The Matrix

Abstract In this paper, we consider the properties of a flat crystal structure associated with the matrix representation of finite continued fractions generating unimodular morphisms of a flat integer lattice. The used matrix representations of the continued fractions and their properties are obtained in [1]. The constructed model allows us to explain the existing limitations of the sets of Weiss parameters (the rational ratio of the lengths of the edges of the forming cell) of crystals by the Gauss-Kuzmin distribution of natural numbers in the representation of continued fractions.

scholarly journals Two Types of Single Valued Neutrosophic Covering Rough Sets and an Application to Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 710 ◽  
Author(s):  
Jingqian Wang ◽  
Xiaohong Zhang
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Rough Sets ◽  
Approximation Space ◽  
Matrix Representations ◽  
Neutrosophic Sets ◽  
Approximation Spaces ◽  
The Matrix ◽  
Novel Method ◽  
Covering Rough Set

In this paper, to combine single valued neutrosophic sets (SVNSs) with covering-based rough sets, we propose two types of single valued neutrosophic (SVN) covering rough set models. Furthermore, a corresponding application to the problem of decision making is presented. Firstly, the notion of SVN β -covering approximation space is proposed, and some concepts and properties in it are investigated. Secondly, based on SVN β -covering approximation spaces, two types of SVN covering rough set models are proposed. Then, some properties and the matrix representations of the newly defined SVN covering approximation operators are investigated. Finally, we propose a novel method to decision making (DM) problems based on one of the SVN covering rough set models. Moreover, the proposed DM method is compared with other methods in an example.

scholarly journals Image-based textile decoding

2020 ◽  
pp. 1-14
Author(s):  
Siqiang Chen ◽  
Masahiro Toyoura ◽  
Takamasa Terada ◽  
Xiaoyang Mao ◽  
Gang Xu
Keyword(s):  
Deep Learning ◽  
Grid Point ◽  
Intermediate Representation ◽  
Training Set ◽  
Binary Matrix ◽  
The Matrix ◽  
Correct Pattern ◽  
Grid Points ◽  
Textile Fabric ◽  
Direct Correspondence

A textile fabric consists of countless parallel vertical yarns (warps) and horizontal yarns (wefts). While common looms can weave repetitive patterns, Jacquard looms can weave the patterns without repetition restrictions. A pattern in which the warps and wefts cross on a grid is defined in a binary matrix. The binary matrix can define which warp and weft is on top at each grid point of the Jacquard fabric. The process can be regarded as encoding from pattern to textile. In this work, we propose a decoding method that generates a binary pattern from a textile fabric that has been already woven. We could not use a deep neural network to learn the process based solely on the training set of patterns and observed fabric images. The crossing points in the observed image were not completely located on the grid points, so it was difficult to take a direct correspondence between the fabric images and the pattern represented by the matrix in the framework of deep learning. Therefore, we propose a method that can apply the framework of deep learning viau the intermediate representation of patterns and images. We show how to convert a pattern into an intermediate representation and how to reconvert the output into a pattern and confirm its effectiveness. In this experiment, we confirmed that 93% of correct pattern was obtained by decoding the pattern from the actual fabric images and weaving them again.

scholarly journals EXTENSION OF THE POINCARÉ GROUP AND NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (31) ◽  
pp. 5765-5785 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Group ◽  
Gauge Transformation ◽  
Space Time ◽  
Gauge Fields ◽  
Poincaré Group ◽  
Matrix Representations ◽  
Poincare Group ◽  
Yang Mills ◽  
The Matrix ◽  
Transversal Plane

In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices. The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.

A content spectral-based text representation

2021 ◽  
pp. 1-12
Author(s):  
Melesio Crespo-Sanchez ◽  
Ivan Lopez-Arevalo ◽  
Edwin Aldana-Bobadilla ◽  
Alejandro Molina-Villegas
Keyword(s):  
Machine Learning ◽  
Text Analysis ◽  
Question Answering ◽  
Learning Algorithms ◽  
Machine Learning Algorithms ◽  
Text Representation ◽  
Feature Vectors ◽  
Learning Tasks ◽  
Semantic Component ◽  
Vector Representations

In the last few years, text analysis has grown as a keystone in several domains for solving many real-world problems, such as machine translation, spam detection, and question answering, to mention a few. Many of these tasks can be approached by means of machine learning algorithms. Most of these algorithms take as input a transformation of the text in the form of feature vectors containing an abstraction of the content. Most of recent vector representations focus on the semantic component of text, however, we consider that also taking into account the lexical and syntactic components the abstraction of content could be beneficial for learning tasks. In this work, we propose a content spectral-based text representation applicable to machine learning algorithms for text analysis. This representation integrates the spectra from the lexical, syntactic, and semantic components of text producing an abstract image, which can also be treated by both, text and image learning algorithms. These components came from feature vectors of text. For demonstrating the goodness of our proposal, this was tested on text classification and complexity reading score prediction tasks obtaining promising results.

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