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Granformer: A granular transformer net with linear complexity

NEUROCOMPUTING 2024年 606卷

作者： Wang, Kaili Sun, Xinwei Shen, Tao Kunming Univ Sci & Technol Fac Informat Engn & Automat Kunming 650500 Peoples R China Kunming Univ Sci & Technol Yunnan Key Lab Comp Technol Applicat Kunming 650500 Peoples R China Kunming Univ Sci & Technol 727 South Jingming Rd Kunming 650500 Peoples R China

Recently, transformer models have demonstrated excellent performance across various intelligent applications owing to their ability to understand global context through self-attention mechanism. However, the extensively investigated multiplicative-based attention mechanism is inadequate for capturing relationship-based feature representations, as the dot product cannot depict the intricate semantic information between objects. Moreover, it has a great computational burden with a complexity of O(n2), ( n 2 ) , due to the global feature representation capability achieved by calculating the relationship between each token within the entire feature sequence. To solve the current problem, this paper proposes a granular transformer framework with linear complexity, wherein diverse granulation functions can be employed to supersede the prevailing multiplicative relationships, and an innovative linearization methodology in the form of matrix factorization is designed to reduce the computational burden. Relying on the intricate semantics information embedded within granular structures, the capacity for feature extraction is significantly more comprehensive. Then, a novel matrix factorization methodology is developed for the linearity of granulation-based attention, accomplished by implementing separate deformable convolution sampling and using an approximate iterative algorithm based on cubic equations to calculate the Moore-Penrose inverse. The mathematical proof that our method is approximate with the complete granulation-based attention matrix is investigated in detail. Finally, the performance of Granformer, an innovative reconfiguration of plug-and-play transformer block, is evaluated on representative intelligent applications, including 3D point cloud classification, emotion recognition and sentiment analysis, and object detection. The experimental results suggest that our methodologies outperform the state-of-the-art models.

关键词： Granular attention linear complexity Transformer Intelligent applications

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linear complexity of a Family of Binary pq²-Periodic Sequences From Euler Quotients

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IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第9期66卷 5774-5780页

作者： Zhang, Jingwei Gao, Shuhong Zhao, Chang-An Guangdong Univ Finance & Econ Sch Informat Sci Guangzhou 510320 Peoples R China Clemson Univ Sch Math & Stat Sci Clemson SC 29634 USA Sun Yat Sen Univ Sch Math Guangzhou 510275 Peoples R China Guangdong Key Lab Informat Secur Guangzhou 510006 Peoples R China

We first introduce a family of binary pq(2)-periodic sequences based on the Euler quotients modulo pq, where p and q are two distinct odd primes and p divides q - 1. The minimal polynomials and linear complexities are determined for the proposed sequences provided that 2(q-1) not equivalent to 1 mod q(2). The results show that the proposed sequences have high linear complexities.

关键词： Cryptography linear complexity binary sequences Euler quotients

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linear complexity of generalized sequences by comparison of PN-sequences

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REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 2020年第2期114卷 1-18页

作者： Fuster-Sabater, Amparo Cardell, Sara D. CSIC Inst Tecnol Fis & Informac Madrid Spain Univ Estadual Campinas Inst Matemat Estat & Comp Cient Campinas Brazil

linear complexity is a much used metric of the security of any binary sequence with application in communication systems and cryptography. In this work, we propose a method of computing the linear complexity of a popular family of cryptographic sequences, the so-called generalized sequences. Such a family is generated by means of the irregular decimation of a single Pseudo Noise sequence (PN-sequence). The computation method is based on the comparison of the PN-sequence with shifted versions of itself. The concept of linear recurrence relationship and the rows of the Sierpinski triangle play a leading part in this computation.

关键词： Decimated sequence linear complexity Generalized generator Sierpinski triangle Recurrence relationship

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linear complexity of Binary Threshold Sequences Derived from Generalized Polynomial Quotient with Prime-Power Modulus

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INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE 2020年第5期31卷 569-581页

作者： Wang, Lianhua Du, Xiaoni Northwest Normal Univ Coll Math & Stat Lanzhou 730070 Gansu Peoples R China Guilin Univ Elect Technol Guangxi Key Lab Cryptog & Informat Secur Guilin 541004 Guangxi Peoples R China

In this paper, firstly we extend the polynomial quotient modulo an odd prime p to its general case with modulo p(r) and r >= 1. From the new quotient proposed, we define a class of p(r+1)-periodic binary threshold sequences. Then combining the Legendre symbol and Euler quotient modulo pr together, with the condition of 2(p-1) not equivalent to 1 (mod p(2)), we present exact values of the linear complexity for p equivalent to +/- 3 (mod 8), and all the possible values of the linear complexity for p equivalent to +/- 1 (mod 8). The linear complexity is very close to the period and is of desired value for cryptographic purpose. Our results extend the linear complexity results of the corresponding p(2)-periodic binary sequences in earlier work.

关键词： Euler quotient Legendre function pseudorandom binary sequences linear complexity cryptography

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Post-quantum protocol for computing set intersection cardinality with linear complexity

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IET INFORMATION SECURITY 2020年第6期14卷 661-669页

作者： Debnath, Sumit Kumar Stanica, Pantelimon Choudhury, Tanmay Kundu, Nibedita Natl Inst Technol Jamshedpur Dept Math Jamshedpur 831014 Bihar India Naval Postgrad Sch Dept Appl Math Monterey CA 93943 USA LNM Inst Informat Technol Dept Math Jaipur 302031 Rajasthan India

Nowadays, the necessity of electronic information increases rapidly. As a consequence, often, that information needs to be shared among mutually distrustful parties. In this area, private set intersection (PSI) and its variants play an important role when the participants wish to do secret operations on their input sets. Unlike the most modern public key cryptosystems relying on number theoretic problems, lattice-based cryptographic constructions provide security in the presence of a quantum computer. Consequently, developing PSI and its variants using lattice based cryptosystem becomes an interesting direction for research. This study presents thefirst size-hiding post quantumPSI cardinality (PSI-CA) protocol whose complexity islinearin the size of the sets of the participants. The authors use space-efficient probabilistic data structure (Bloom filter) as its building block. Further, they extend the authors' PSI-CA to its authorised version, i.e. authorised PSI-CA. Security for both of them is achieved in the standard model based on the hardness of the decisional learning with errors problem.

关键词： data structures public key cryptography cryptography cryptographic protocols quantum computing data privacy post-quantum protocol intersection cardinality linear complexity electronic information increases mutually distrustful parties private set intersection secret operations input sets modern public key cryptosystems number theoretic problems lattice-based cryptographic constructions quantum computer lattice based cryptosystem size-hiding post quantum PSI cardinality protocol whose complexity authors authorised PSI-CA

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Robust principal component analysis: A factorization-based approach with linear complexity

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INFORMATION SCIENCES 2020年 513卷 581-599页

作者： Peng, Chong Chen, Yongyong Kang, Zhao Chen, Chenglizhao Cheng, Qiang Qingdao Univ Coll Comp Sci & Technol Qingdao Peoples R China Univ Macau Dept Comp & Informat Sci Taipa Macao Peoples R China Univ Elect Sci & Technol China Sch Comp Sci & Engn Chengdu Peoples R China Univ Kentucky Dept Comp Sci Lexington KY 40506 USA Univ Kentucky Inst Biomed Informat Lexington KY 40506 USA

Low-rankness has been widely observed in real world data and there is often a need to recover low-rank matrices in many machine learning and data mining problems. Robust principal component analysis (RPCA) has been used for such problems by separating the data into a low-rank and a sparse part. The convex approach to RPCA has been well studied due to its elegant properties in theory and many extensions have been developed. However, the state-of-the-art algorithms for the convex approach and their extensions are usually expensive in complexity due to the need for solving singular value decomposition (SVD) of large matrices. In this paper, we propose a novel RPCA model based on matrix tri-factorization, which only needs the computation of SVDs for very small matrices. Thus, this approach reduces the complexity of RPCA to be linear and makes it fully scalable. It also overcomes the drawback of the state-of-the-art scalable approach such as AltProj, which requires the precise knowledge of the true rank of the low-rank component. As a result, our method is about 4 times faster than AltProj. Our method can be used as a light-weight, scalable tool for RPCA in the absence of the precise value of the true rank. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Robust principal component analysis Factorization linear complexity

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linear complexity of d-Ary Sequence Derived from Euler Quotients over GF(q)

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Chinese Journal of Electronics 2019年第3期28卷 529-534页

作者： YE Zhifan KE Pinhui CHEN Zhixiong Fujian Provincial Key Laboratory of Network Security and Cryptology Fujian Normal University Department of Mathematics and Physics Fujian Jiangxia University School of Mathematics Putian University

For an odd prime p and positive integers r,d such that 0r,a generic construction of dary sequence based on Euler quotients is presented in this *** with the known construction,in which the support set of the sequence is fixed and d is usually required to be a prime,the support set of the proposed sequence is flexible and d could be any positive integer less then prin our ***,the linear complexity of the proposed sequence over prime field GF（q）with the assumption of qp-1■ mod p2is *** algorithm of computing the linear complexity of the sequence is also *** results indicate that,with some constrains on the support set,the new sequences possess large linear complexities.

关键词： linear complexity Euler quotient d-ary sequence

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About the linear complexity of quaternary sequences with even length

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CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 2020年第4期12卷 725-741页

作者： Zhao, Lu Tiangong Univ Sch Math Sci Tianjin 300387 Peoples R China

Several classes of quaternary sequences of even period with optimal autocorrelation have been constructed by Su et al. based on interleaving certain kinds of binary sequences of odd period, i.e. Legendre sequence, twin-prime sequence and generalized GMW sequence. In this correspondence, the exact values of linear complexity over finite fieldF4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {F}_{4}$\end{document}and Galois ringDOUBLE-STRUCK CAPITAL Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {Z}_{4}$\end{document}of the quaternary sequences are derived, respectively.

关键词： Quaternary sequence Interleaved structure linear complexity Finite field Galois ring

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Multidimensional linear complexity analysis of periodic arrays

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APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 2020年第1期31卷 43-63页

作者： Arce-Nazario, Rafael Castro, Francis Gomez-Perez, Domingo Moreno, Oscar Ortiz-Ubarri, Jose Rubio, Ivelisse Tirkel, Andrew Univ Puerto Rico Dept Comp Sci 17 Ave Univ Ste 1701 San Juan PR 00925 USA Univ Cantabria Fac Sci Santander 39071 Spain Gauss Res Fdn POB 21613 San Juan PR 00931 USA Sci Technol 8 Cecil St East Brighton Vic 3187 Australia

The linear complexity of a sequence is an important parameter for many applications, especially those related to information security, and hardware implementation. It is desirable to develop a corresponding measure and theory for multidimensional arrays that are consistent with those of sequences. In this paper we use Grobner bases to develop a theory for analyzing the multidimensional linear complexity of general periodic arrays. We also analyze arrays constructed using the method of composition and establish tight bounds for their multidimensional linear complexity.

关键词： linear complexity Multidimensional linear complexity Periodic arrays Multidimensional arrays Multisequences Grobner bases

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ON THE k-ERROR linear complexity OF SEQUENCES FROM FUNCTION FIELDS

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BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY 2020年第2期102卷 342-352页

作者： Zhou, Yuhui Han, Yuhui Ding, Yang Shanghai Univ Dept Math Shanghai Peoples R China

The linear complexity and the error linear complexity are two important security measures for stream ciphers. We construct periodic sequences from function fields and show that the error linear complexity of these periodic sequences is large. We also give a lower bound for the error linear complexity of a class of nonperiodic sequences.

关键词： sequence linear complexity error linear complexity algebraic function fields local expansion

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