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A step function based recursion method for 0/1 deep neural networks

APPLIED MATHEMATICS AND COMPUTATION 2025年 488卷

作者： Zhang, Hui Zhou, Shenglong Li, Geoffrey Ye Xiu, Naihua Wang, Yiju Qufu Normal Univ Sch Management Sci Rizhao 276800 Shandong Peoples R China Qufu Normal Univ Sch Management Sci Rizhao 276800 Shandong Peoples R China Imperial Coll London Dept EEE ITP Lab London England

The deep neural network with step function activation (0/1 DNNs) is a fundamental composite model in deep learning which has high efficiency and robustness to outliers. However, due to the discontinuity and lacking subgradient information of the 0/1 DNNs model, prior researches are largely focused on designing continuous functions to approximate the step activation and developing continuous optimization methods. In this paper, by introducing two sets of network node variables into the 0/1 DNNs and by exploring the composite structure of the resulted model, the 0/1 DNNs is decomposed into a unary optimization model associated with the step function and three derivational optimization subproblems associated with the other variables. For the unary optimization model and two derivational optimization subproblems, we present a closed form solution, and for the third derivational optimization subproblem, we propose an efficient proximal method. Based on this, a globally convergent step function based recursion method for the 0/1 DNNs is developed. The efficiency and performance of the proposed algorithm are validated via theoretical analysis as well as some illustrative numerical examples on classifying MNIST, FashionMNIST and Cifar10 datasets.

关键词： 0/1 DNNs Step function Separability recursion method

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recursion method for multiple-scattering XAFS Debye-Waller factors

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JOURNAL OF SYNCHROTRON RADIATION 1999年第3期6卷 313-314页

作者： Poiarkova, AV Rehr, JJ Univ Washington Dept Phys Seattle WA 98195 USA

An efficient, finite temperature, recursion method (RM) is introduced for calculations of the mean-square relative displacements sigma(2) in multiple scattering (MS) XAFS Debye-Waller factors. Instead of calculating total projected densities of modes, the calculations are based on a double delta-function representation. Results for the Debye-Waller factors are found to be in agreement with equation-of-motion (EM) method to within about 10% percent for all MS paths.

关键词： Debye-Waller factors XAFS recursion method

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recursion method FOR THE EXTENDED IMPURITY PROBLEM

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JOURNAL OF PHYSICS C-SOLID STATE PHYSICS 1980年第22期13卷 4157-4173页

作者： BYLANDER, DM REHR, JJ MAX PLANCK INST FESTKORPERFORSCH D-7000 STUTTGARTFED REP GER

The application of the recursion method of Haydock et al. (1975) to the problem of potential scattering on a lattice by an extended impurity is discussed. The approach is an alternative to the Koster-Slater method and yields bound state energies and lattice phaseshifts corresponding to the irreducible representations of the impurity point group symmetry, as well as the total density of states. The method avoids huge determinants by taking advantage of a fixed point in the recurrence relations and by using the asymptotic behaviour of the recurrence coefficients. The extrapolation of continued fraction coefficients and the construction of 'seed states' for the recursion method are discussed. Illustrative applications are made to the case of an extended impurity in a triangular lattice and to a shallow Coulomb impurity in an FCC lattice, the latter of which is compared with effective mass theory.

关键词： effective mass Particle scattering recursion method crystal lattices asymptotic behavior Impurities purity Recurrence relation Energy level

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THE BLOCK recursion LIBRARY - ACCURATE CALCULATION OF RESOLVENT SUBMATRICES USING THE BLOCK recursion method

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COMPUTER PHYSICS COMMUNICATIONS 1991年第1期64卷 123-130页

作者： GODIN, TJ HAYDOCK, R UNIV OREGON DEPT PHYSEUGENEOR 97403 UNIV OREGON INST MAT SCIEUGENEOR 97403

The Block recursion Library, a collection of FORTRAN subroutines, calculates submatrices of the resolvent of a linear operator. The resolvent, in matrix theory, is a powerful tool for extracting information about solutions of linear systems. The routines use the block recursion method and achieve high accuracy for very large systems of coupled equations. This technique is a generalization of the scalar recursion method, an accurate technique for finding the local density of states. A sample program uses these routines to find the quantum mechanical transmittance of a randomly disordered two-dimensional cluster of atoms.

关键词： recursion method RESOLVENT GREEN FUNCTIONS SCHRODINGER EQUATION TRANSMITTANCE

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The antiferromagnetic spin-3/2 Blume-Capel model on the Bethe lattice using the recursion method

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JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS 2004年第284期284卷 409-415页

作者： Ekiz, C Gaziosmanpasa Univ Dept Phys TR-60250 Tokat Turkey

The antiferromagnetic spin-3/2 Blume Capel model on the Bethe lattice in an external magnetic field is investigated and phase diagrams are obtained. Using the recursion method we obtain the plots of magnetization versus external field for different temperatures and construct the resulting phase diagrams. The model exhibits distinct critical regions, including the first-order, second-order and tricritical point. (C) 2004 Elsevier B.V. All rights reserved.

关键词： Blume-Capel model Bethe lattice recursion method phase diagrams

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A GENERAL TERMINATOR FOR THE recursion method

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JOURNAL OF PHYSICS C-SOLID STATE PHYSICS 1985年第11期18卷 2235-2248页

作者： HAYDOCK, R NEX, CMM Inst. of Theor. Sci. Oregon Univ. Eugene OR USA

A general method is presented for approximating continuous densities of states, and wavefunctions over infinite regions, within the recursion method by means of a terminator which is an infinite set of approximate basis states and their Hamiltonian matrix elements. This is an analytical and computational solution to the problem of approximating the projected density of states for a Hamiltonian having an arbitrary number of bands with van Hove singularities. It also enables calculation of charge densities and other quantities related to the wavefunctions. The method is applied to many-band problems. Criteria are developed for the convergence of densities of states, and the asymptotic convergence of the terminator is related to singularities in the spectrum.

关键词： Singularity Converge Density of states Terminator Device Component recursion method Hamiltonian Countries (nations) WAVE FUNCTIONS Charge density infinite set

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Energy gap dependence on anion concentration for Ga_xIn_1-xAs_yP_1-y quaternary alloy by recursion method

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MODERN PHYSICS LETTERS B 2004年第18期18卷 955-962页

作者： El-Hasan, M Estatieh, R An Najah N Univ Dept Phys Nablus Palestine Israel Palestine Coll Technol Tulkarem Palestine Israel

Three terminators have been tested, square root terminator, quadreture terminator and linear terminator, it was found that the linear terminator is the best, so it was used in calculating local density of states (LDOS) and it's orbital decomposition, alloy average density of states, and energy gap for different anion concentrations for InP lattice matched alloy. The results were compared with our previous calculations of (LDOS), and results from other methods. Energy gap was compared with experimental measurements. A five orbital sp(3)s* per atom model was used in the tight-binding representation of the Hamiltonian.

关键词： electronic density of state semiconductor alloys recursion method

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ANALYTIC SOLUTION BY THE recursion method OF THE ANDERSON MODEL FOR STRONG DISORDER

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JOURNAL OF PHYSICS C-SOLID STATE PHYSICS 1981年第3期14卷 229-234页

作者： HAYDOCK, R Cavendish Lab. Univ. of Cambridge Cambridge UK

The recursion method is applied analytically to the Anderson model in the strong disorder limit. The chain basis and chain parameters are determined exactly to lowest order in the hopping energy. It is shown that for all dimensionalities there is a dense spectrum of exponentially localised states with a characteristic length independent of energy and proportional to the ratio of hopping to disorder. This calculation extends the application of the recursion method to all degrees of disorder and answers some questions about denseness of the spectrum, correlation of parameters, and completeness of the chain basis.

关键词： recursion method Anderson model maladjustment

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Electronic structure of Ga_xIn_1-xAs_yP_1-y quaternary alloy by recursion method

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INTERNATIONAL JOURNAL OF MODERN PHYSICS B 1999年第1期13卷 97-106页

作者： El-Hasan, M An Najah Natl Univ Dept Phys Nablus W Bank Israel

The electronic structure of GaxIn1-xAsyP1-y quaternary alloy, calculated by recursion method is reported. A five orbitals sp(3)s* per atom model was used in the tight-binding representation of the Hamiltonian. The local density of states and its orbital decomposition (LDOS), integrated density of states (IDOS) and structural energy (STE) were calculated for Ga, In, As and P sites in Ga0.5In0.5As0.5P0.5, GaInAsP lattice matched to InP and lattice matched to GaAs as well. There are 216 atoms arranged in a zinc-blend structure. The calculated quantities are as expected for such systems.

关键词： Density of states recursion method gallium arsenides Electronic structure Gallium crystal lattices Indium phosphide quaternary alloys

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APPLICATION OF THE recursion method TO SPIN-WAVE ANALYSIS OF FERROMAGNETIC-RESONANCE IN DEFECTED FERROMAGNETS

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JOURNAL OF PHYSICS C-SOLID STATE PHYSICS 1988年第19期21卷 3533-3544页

作者： SCHMIDT, W Inst. of Molecular Phys. Polish Acad. of Sci. Poznan Poland

A general theory of ferromagnetic resonance (FMR) is developed from the assumptions of inhomogeneous local crystalline anisotropy and static magnetic field. The Hamiltonian is given in the harmonic approximation. The high-frequency magnetisation is calculated from the very general thermodynamic formula m+or-=Tr( rho M+or-), with density matrix rho in the Kubo approximation. The Green function is expressed by a continued fraction, with coefficients given by the moments of the spectral density of magnons. The theory is applied to ferromagnetic metals with dislocations. FMR gives information on the spectrum of spin waves localised at dislocation lines. Numerical calculations are given for the spectral density width of magnon excitations. The paper contains novel general considerations on the application of the recursion method to the description of the resonance line in defected ferromagnets. In the literature, the higher moments are generally too great and bear no information about magnon excitations in FMR. The author removes this difficulty by limiting the calculations of the moments to a region of the magnon band that is quasi-degenerate with the signal frequency for different static fields in the FMR experiment. The latter is realised by cut-off wavevectors. The moments are calculated from the spectral density for the low-frequency region of the magnon band. Effects of elliptical terms due to defects as well as high-lying excitations are included in the second-order perturbation theory. The paper is aimed at calculating the shape of the resonance line in ferromagnets with dislocations.

关键词： dislocation line recursion method Magnon RESONANCE LINES Spectral density Wave analysis Moment of force Ferromagnetic resonance Ferromagnetic materials Continued fraction Ferromagnetism

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