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A Smoothed LASSO-Based DNN Sparsification Technique

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2021年第10期68卷 4287-4298页

作者： Koneru, Basava Naga Girish Chandrachoodan, Nitin Vasudevan, Vinita IIT Madras Dept Elect Engn Chennai 600036 Tamil Nadu India

Deep Neural Networks (DNNs) are increasingly being used in a variety of applications. However, DNNs have huge computational and memory requirements. One way to reduce these requirements is to sparsify DNNs by using smoothed LASSO (Least Absolute Shrinkage and Selection Operator) functions. In this paper, we show that irrespective of error profile, the sparsity values obtained using various smoothed LASSO functions are similar, provided the maximum error of these functions with respect to the LASSO function is the same. We also propose a layer-wise DNN pruning algorithm, where the layers are pruned based on their individual allocated accuracy loss budget, determined by estimates of the reduction in number of multiply-accumulate operations (in convolutional layers) and weights (in fully connected layers). Further, the structured LASSO variants in both convolutional and fully connected layers are explored within the smoothed LASSO framework and the tradeoffs involved are discussed. The efficacy of proposed algorithm in enhancing the sparsity within the allowed degradation in DNN accuracy and results obtained on structured LASSO variants are shown on MNIST, SVHN, CIFAR-10, and Imagenette datasets and on larger networks such as ResNet-50 and Mobilenet.

关键词： Smoothing methods Neurons Training approximation algorithms Sensitivity Convergence Cost function Deep neural networks LASSO smoothing functions sparsity structured LASSO

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A note for approximating the submodular cover problem over integer lattice with low adaptive and query complexities

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INFORMATION PROCESSING LETTERS 2023年 182卷

作者： Pham, Canh, V Ha, Dung T. K. Phenikaa Univ ORLab Hanoi 12116 Vietnam Vietnam Natl Univ Univ Engn & Technol Fac Informat Technol Hanoi 10000 Vietnam

This paper studies the Diminishing Return Submodular Cover (DRSC) problem as follows: given a diminishing return submodular function f :Z(+)(E)-> R+ over the ground set E of size n, a positive integer B as the maximum value of a coordinate of a vector in Z(+)(E) and a threshold alpha > 0, the problem asks to find the vector with the smallest size x so that f(x) >= alpha. This problem has been attracted by much research recently due to its importance in machine learning and combinatorial optimization. However, because of high query and adaptive complexities, the existing algorithms might still not be efficient enough when working with large input data. This paper proposes a randomized and bicriteria approximation algorithm that has O (log n) adaptive complexity and O ((n + log n log B) log(nB)) query complexity. Our algorithm significantly reduces both adaptive and query complexities compared to some state-of-the-art algorithms by factors of Omega(log(m) log(2)(mn log B)(1 + log(log B)/ log(n))), Omega(min{n/ log(n),log(B)}) respectively, where m = f (B center dot 1). (c) 2023 Elsevier B.V. All rights reserved.

关键词： submodular Cover integer lattice adaptive complexity approximation algorithms

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A WATER-FILLING PRIMAL-DUAL ALGORITHM FOR APPROXIMATING NONLINEAR COVERING PROBLEMS

A WATER-FILLING PRIMAL-DUAL ALGORITHM FOR APPROXIMATING NONL...

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作者： Fielbaum, Andrés Morales, Ignacio Verschae, José TU Delft Delft Netherlands Pontificia Universidad Católica Santiago Chile

Obtaining strong linear relaxations for capacitated covering problems constitutes a significant technical challenge. For one of the most basic cases, the relaxation based on knapsack-cover inequalities has an integrality gap of 2. We generalize the setting considering items that can be taken fractionally to cover a given demand, with a cost given by an arbitrary nondecreasing function (not necessarily convex) of the chosen fraction. We generalize the knapsack-cover inequalities and use them to obtain a polynomial (2 + \varepsilon )-approximation algorithm. Our primal-dual procedure has a natural interpretation as a water-filling algorithm, which overcomes the difficulties implied by having different growth rates in the cost functions: when the cost of an item increases slowly at some superior segment, it carefully increases the priority of all preceding segments. We generalize our algorithm to the Unsplittable Flow-Cover problem on a line, also for fractional items with nonlinear costs. We obtain a 4-approximation in pseudopolynomial time (4 + \varepsilon in polynomial time), matching the approximation ratio of the classical setting. We also present a rounding algorithm with an approximation guarantee of 2. This result is coupled with a polynomial time separation algorithm that allows solving our linear relaxation up to a loss of a (1 + \varepsilon ) factor. © 2022 Society for Industrial and Applied Mathematics.

关键词： approximation algorithms

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Mathematical Model To Calculate The Trajectories Of Electromagnetic Mill Operating Elements

Technical Electrodynamics

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Technical Electrodynamics 2021年第2期2021卷 26-34页

作者： Makarchuk, O. Calus, D. Moroz, V. Lviv Polytechnic National University 12 S. Bandera str. Lviv79013 Ukraine Czestochowa University of Technology Avenue 17 p.o. box 42-200 Czestochowa Poland

The purpose of the research under consideration is to develop a mathematical model to calculate the trajectories of the ferromagnetic operating elements (millstones) of an electromagnetic mill, moving in a rotating magnetic field under electrodynamic and hydrodynamic resistance forces being limited by the space of the mill’s working chamber. The millstone motion is described through the equations of plane motion of arbitrary-shaped two-dimensional body. The driving forces of this motion are determined on the basis of the approximation of the tabulated functions connecting the module and the orientation of the equivalent force applied to the millstone, with its position in the working chamber and composite MMF phase of mill inductor winding. These tabulated functions are derived from the estimation of the magnetic field inside a working chamber with millstones, in two-dimensional quasi-stationary approximation, using FEM analysis. The publication contains the approximation algorithm for these tabulated vector functions of a vector argument, mathematical statement of millstones trajectories calculating, and analysis of mathematical experiments results that make it possible to evaluate the adequacy of the model. The developed tool enables conducting quantitative analysis of grinding/mixing process and will help to establish relationships between the electromagnetic mill design parameters and its performance. References 21, figures 6. © 2021, Technical Electrodynamics. All Rights Reserved.

关键词： approximation algorithms

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Modular arithmetic and subset sum problem: A state-of-art technique in information security issues towards smart vehicular system

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International Journal of Vehicle Information and Communication Systems 2021年第3-4期6卷 274-294页

作者： Bhowmik, Anirban Department of Computer Application Cyber Research and Training Institute West Bengal Burdwan India

Now-a-days vehicles have been used at a large scale in the modern society. But in many countries the current traffic-safety statistics are very terrifying. This article focuses on the communication security issues in smart vehicular applications. Transmitting messages efficiently and honestly among vehicles is the key issue in this system. At present, the communication in smart transportation systems is vulnerable to various types of security attacks. The different types of attacks in the dense environment mean that the vehicle may receive multiple messages at the same time and it causes authentication problems. To address these problems, we have introduced some technique based on approximation algorithm and linear congruence. A new encryption technique is introduced named as reflected encryption. The different types of experiments on our technique show that our scheme is very secure, robust and efficient for data transmission in smart vehicular system or IoV. Copyright © 2021 Inderscience Enterprises Ltd.

关键词： approximation algorithms

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Gradient Methods With Dynamic Inexact Oracles

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IEEE CONTROL SYSTEMS LETTERS 2021年第4期5卷 1163-1168页

作者： Han, Shuo Univ Illinois Dept Elect & Comp Engn Chicago IL 60607 USA

We present a framework for generalizing the primal-dual gradient method, also known as the gradient descent ascent method, for solving convex-concave minimax problems. The framework is based on the observation that the primal-dual gradient method can be viewed as an inexact gradient method applied to the primal problem. Unlike the setting of traditional inexact gradient methods, the inexact gradient is computed by a dynamic inexact oracle, which is a discrete-time dynamical system whose output asymptotically approaches the exact gradient. For minimax problems, dynamic inexact oracles are capable of modeling a range of first-order methods for computing the gradient of the primal objective, which relies on solving the inner maximization problem. We provide a unified convergence analysis of gradient methods with dynamic inexact oracles and demonstrate its use in creating new accelerated primal-dual algorithms.

关键词： Gradient methods Heuristic algorithms Radio frequency Convergence approximation algorithms Acceleration Handheld computers Optimization algorithms stability of nonlinear systems

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Parallel and Scalable Heat Methods for Geodesic Distance Computation

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2021年第2期43卷 579-594页

作者： Tao, Jiong Zhang, Juyong Deng, Bailin Fang, Zheng Peng, Yue He, Ying Univ Sci & Technol China Sch Math Sci Hefei 230026 Anhui Peoples R China Cardiff Univ Sch Comp Sci & Informat Cardiff CF10 3AT Wales Nanyang Technol Univ Sch Comp Sci & Engn Singapore 639798 Singapore

In this paper, we propose a parallel and scalable approach for geodesic distance computation on triangle meshes. Our key observation is that the recovery of geodesic distance with the heat method [1] can be reformulated as optimization of its gradients subject to integrability, which can be solved using an efficient first-order method that requires no linear system solving and converges quickly. Afterward, the geodesic distance is efficiently recovered by parallel integration of the optimized gradients in breadth-first order. Moreover, we employ a similar breadth-first strategy to derive a parallel Gauss-Seidel solver for the diffusion step in the heat method. To further lower the memory consumption from gradient optimization on faces, we also propose a formulation that optimizes the projected gradients on edges, which reduces the memory footprint by about 50 percent. Our approach is trivially parallelizable, with a low memory footprint that grows linearly with respect to the model size. This makes it particularly suitable for handling large models. Experimental results show that it can efficiently compute geodesic distance on meshes with more than 200 million vertices on a desktop PC with 128 GB RAM, outperforming the original heat method and other state-of-the-art geodesic distance solvers.

关键词： Optimization Linear systems Memory management Computational modeling Heat recovery approximation algorithms Heat method heat diffusion poisson equation scalability parallel algorithm

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Smallest k-Enclosing Rectangle Revisited

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DISCRETE & COMPUTATIONAL GEOMETRY 2021年第2期66卷 769-791页

作者： Chan, Timothy M. Har-Peled, Sariel Univ Illinois Dept Comp Sci 201 N Goodwin Ave Urbana IL 61801 USA

Given a set of n points in the plane, and a parameter k, we consider the problem of computing the minimum (perimeter or area) axis-aligned rectangle enclosing k points. We present the first near quadratic time algorithm for this problem, improving over the previous near- O(n(5/2))-time algorithm by Kaplan et al. (25th European Symposium on algorithms. Leibniz Int Proc Inform, vol. 87, # 52. Leibniz-Zent Inform, Wadern, 2017). We provide an almost matching conditional lower bound, under the assumption that (min,+)-convolution cannot be solved in truly subquadratic time. Furthermore, we present a new reduction (for both perimeter and area) that can make the time bound sensitive to k, giving near O(nk) time. We also present a near linear time (1 + epsilon)-approximation algorithm to the minimum area of the optimal rectangle containing k points. In addition, we study related problems including the 3-sided, arbitrarily oriented, weighted, and subset sum versions of the problem.

关键词： Geometric optimization Outliers approximation algorithms Conditional lower bounds

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Weak NP-Hardness for the 2-D L⁰-Norm InSAR Phase Unwrapping

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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS 2023年 20卷 1-1页

作者： Zhu, Bao Yu, Hanwen Lan, Yang Wang, Yong Univ Elect Sci & Technol China Sch Resources & Environm Chengdu 611731 Sichuan Peoples R China Xidian Univ Acad Adv Interdisciplinary Res Xian 710126 Shannxi Peoples R China

Two-dimensional phase unwrapping (PU) is an essential step in interferometric synthetic aperture radar (InSAR) analysis. Although the L-0-norm PU method is desired, it is nondeterministic polynomial (NP)-hard. Thus, many PU meth-ods have been proposed to find near-optimal solutions of the L-0-norm. As PU is an ill-posed problem, it is difficult to choose the method with the most accurate solution unless reference data are available. In this letter, we prove that the NP-hardness of the L-0-norm is weak, suggesting that the alpha-approximation algorithm of the L-0-norm can be devised, that is, the obtained near-optimal solutions can be within a factor of alpha of the L-0-norm optimal value. The primary contribution of the proof is that the alpha value of each obtained PU solution can be considered as a new index to assess the PU performance without using reference data. The validity and effectiveness of the alpha-based index have been verified using simulated and acquired interferometric datasets and three PU methods.

关键词： approximation algorithms Indexes Synthetic aperture radar Phase measurement Surfaces Root mean square Remote sensing Interferometric synthetic aperture radar (InSAR) L-0-norm phase unwrapping (PU) weak nondeterministic polynomial (NP)-hardness

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A Bayesian Framework of Non-Synchronous Measurements at Coprime Positions for Sound Source Localization With High Resolution

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2023年 72卷

作者： Liu, Qin Chu, Ning Yu, Liang Shao, Zhunyuan Qin, Huixian Wu, Peng Zhejiang Univ Coll Energy Engn Hangzhou 310027 Peoples R China Zhejiang Shangfeng Special Blower Co Ltd Shaoxing 312352 Peoples R China Shanghai Jiao Tong Univ State Key Lab Mech Syst & Vibrat Shanghai 200240 Peoples R China

The noise distribution in the mechanical system is tightly connected to the structure design and particular operating conditions. The noise source localization can effectively assist with the operating condition monitoring and noise reduction design of the mechanical device. The performance limitation of the array aperture for lower frequency acoustic localization is broken up by the non-synchronous measurement at coprime positions (CP-NSM), while this method has high uncertainty and requires an efficient adaptive regularization method to solve its corresponding acoustic inverse problem. The algorithms under the Bayesian framework with Student-t priors (variational Bayesian approximation and subspace variational Bayesian) are derived and deployed to solve the acoustic inverse problem in the CP-NSM method, and the results are compared with those obtained by the interior-point method and the alternating direction method of the multipliers algorithm. The proposed Bayesian methods have the advantages of adaptive regularization parameter estimation, which can reduce the influence of various interferences in CP-NSM. At the same time, in addition to using simulations and experiments in the anechoic chambers, the proposed Bayesian algorithms are validated further in real industrial applications. The proposed method is applied to improve the noise reduction design of the centrifugal fan, a mechanical device containing more information from noise sources.

关键词： Acoustics Bayes methods Inverse problems Acoustic measurements Acoustic arrays Position measurement approximation algorithms Coprime position non-synchronous measurement (NSM) sound source localization variational Bayesian virtual array

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