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Distributed generalized Nash equilibrium seeking:event-triggered coding-decoding-based secure communication

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Science China(Information Sciences) 2024年第7期67卷 271-284页

作者： Shaofu YANG Wenying XU Wangli HE Jinde CAO School of Computer Science and Engineering Southeast University School of Mathematics Southeast University Key Laboratory of Advanced Control and Optimization for Chemical Processes East China University of Science and Technology

In this paper, we consider the distributed generalized Nash equilibrium(GNE) seeking problem in strongly monotone games. The transmission among players is implemented through a digital communication network with limited bandwidth. For improving communication efficiency or/and security, an event-triggered coding-decoding-based communication is first proposed, where the data(decision variable) are first mapped to a series of finite-level codewords and, only when an event condition is satisfied, then sent to the neighboring agents. Moreover, a distributed communication-efficient GNE seeking algorithm is constructed accordingly,and the overrelaxation scheme is further taken into consideration. Through primal-dual analysis, the proposed algorithm is proven to converge to a variational GNE with fixed step-sizes by recasting it as an inexact forward-backward iteration. Finally, numerical simulations illustrate the benefit of the proposed algorithms in terms of saving communication resources.

关键词： noncooperative games event-triggered communication coding-decoding quantization

quantization of a Class of Super W-Agebras

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Algebra Colloquium 2022年第4期29卷 633-642页

作者： Yu Zhang Xiaomin Tang School of Mathematical Science Heilongjiang University Harbin 150080China

We study a class of super W-algebras whose even part is the Virasoro type Lie algebra W(2,2).We quantize the Lie superbialgebra of the super W-algebra by the Drinfeld twist quantization technique and obtain a class of... 详细信息

关键词： quantization super W-algebra quantum group Lie superbialgebra

Accelerate distributed deep learning with cluster-aware sketch quantization

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Science China(Information Sciences) 2023年第6期66卷 138-154页

作者： Keshi GE Yiming ZHANG Yongquan FU Zhiquan LAI Xiaoge DENG Dongsheng LI College of Computer National University of Defense Technology

Gradient quantization has been widely used in distributed training of deep neural network(DNN)models to reduce communication cost. However, existing quantization methods overlook that gradients have a nonuniform distribution changing over time, which can lead to significant compression error that not only increases the number of training iterations but also requires a higher number of quantization bits(and consequently higher delay for each iteration)to keep the validation accuracy as high as the original stochastic gradient descent(SGD)approach. To address this problem, in this paper we propose cluster-aware sketch quantization(CASQ), a novel sketch-based gradient quantization method for SGD with convergence guarantees. CASQ models the nonuniform distribution of gradients via clustering, and adaptively allocates appropriate numbers of hash buckets based on the statistics of different clusters to compress gradients.Extensive evaluation shows that compared to existing quantization methods, CASQ-based SGD(i)achieves the same validation accuracy when decreasing quantization level from 3 bits to 2 bits, and(ii)reduces the training time to convergence by up to 43% for the same training loss.

关键词： distributed training deep learning communication sketch quantization

quantization OF LIE ALGEBRAS OF BLOCK TYPE

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Acta Mathematica Scientia 2010年第4期30卷 1134-1142页

作者：程永胜苏育才 Department of Mathematics University of Science and Technology of China School of Mathematics and Information Science Henan University

In this article, we use the general method of quantization by Drinfeld’s twist to quantize explicitly the Lie bialgebra structures on Lie algebras of Block type.

关键词： quantization Lie bialgebras Drinfeld twist Lie algebras of Block type

quantization AND TRAINING OF LOW BIT-WIDTH CONVOLUTIONAL NEURAL NETWORKS FOR OBJECT DETECTION

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Journal of Computational Mathematics 2019年第3期37卷 349-359页

作者： Penghang Yin Shuai Zhang Yingyong Qi Jack Xin Department of Mathematics University of CaliforniaLos AngelesCA 90095USA Department of Mathematics University of CaliforniaIrvineCA 92697USA

We presen t LBW-Net,an efficient optimization based method for qua nt ization and training of the low bit-width convolutional neural networks(CNNs).Specifically,we quantize the weights to zero or powers of 2 by minimizing the Euclidean distance between full-precision weights and quantized weights during backpropagation(weight learning).We characterize the combinatorial nature of the low bit-width quantization problem.For 2-bit(ternary)CNNs,the quantization of N weights can be done by an exact formula in O(N log N)complexity.When the bit-width is 3 and above,we further propose a semi-analytical thresholding scheme with a single free parameter for quantization that is computationally inexpensive.The free parameter is further determined by network retraining and object detection tests.The LBW-Net has several desirable advantages over full-precision CNNs,including considerable memory savings,energy efficiency,and faster deployment.Our experiments on PASCAL VOC dataset show that compared with its 32-bit floating-point counterpart,the performance of the 6-bit LBW-Net is nearly lossless in the object detection tasks,and can even do better in real world visual scenes,while empirically enjoying more than 4× faster deployment.

关键词： quantization Low bit width deep neural networks Exact and approximate analytical formulas Network training Object detection

quantization of Time Independent Damping Systems Using WKB Approximation

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Journal of Applied Mathematics and Physics 2023年第9期11卷 2615-2620页

作者： Ola A. Jarab’ah Department of Applied Physics Tafila Technical University Tafila Jordan

In this work time independent damping systems are studied using Lagrangian and Hamiltonian for time independent damping, which are present through the factor eλq. The Hamilton Jacobi equation is formulated to find the Hamilton Jacobi function S using separation of variables technique. We can form this function in compact form of two parts the first part as a function of coordinate q, and the second part as a function of time t. Finally, we find the ability of these systems to quantize through an illustrative example.

关键词： quantization Hamilton Jacobi Equation Hamilton Jacobi Function Momentum

Stabilization of Uncertain Systems With Markovian Modes of Time Delay and quantization Density

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IEEE/CAA Journal of Automatica Sinica 2018年第2期5卷 463-470页

作者： Jufeng Wang Chunfeng Liu Department of Information and Computing China Jiliang University Hangzhou 310018 China Hangzhou Dianzi University Hangzhou 310018 China

This work studies the stabilization of a class of control systems that use communication networks as signal transmission medium. The lateral motion of independently actuated four-wheel vehicle is modeled as an uncertain-linear system. Time delay and quantization density are modeled as Markov chains.The networked control systems(NCSs) with plants being lateral motion are first transformed to switched linear systems with uncertain parameters. Sufficient and necessary conditions for the stochastic stability of closed-loop networked control systems are then established. By solving the matrix inequalities, this work presents an output-feedback controller that depends on the modes of time delay and quantization density. The controller performance is illustrated via a vehicular lateral motion system.

关键词： Networked control system(NCS) quantization stabilization time delay vehicle lateral motion

Mathematical modeling of nanoscale MOS capacitance in the presence of depletion and energy quantization in a poly-silicon gate

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Journal of Semiconductors 2010年第11期31卷 5-8页

作者： Amit Chaudhry J.N.Roy Institute of Engineering and Technology Panjab University Solar Semiconductor Pvt.Ltd.

A model has been developed to study the effect of depletion and energy quantization at the poly-silicon /oxide interface on the behavior of a nanometer scale n-MOSFET.A model of inversion charge density,including the inversion layer quantization using the variation approach in the substrate,has also been produced.Using the exact calculations of the polygate potential under the depletion and quantization conditions,a C-V model has been developed. All the results have been compared with the numerical models reported in existing literature and they show good agreement.

关键词： BSIM inversion layers MOS devices quantization poly-depletion poly-quantization

Low-resolution optical transmission using joint shaping technique of signal probability and quantization noise

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Chinese Optics Letters 2023年第5期21卷 11-17页

作者：黄宏宇于振明舒亮孙凯旋尹飞飞徐坤 State Key Laboratory of Information Photonics and Optical Communications Beijing University of Posts and TelecommunicationsBeijing 100876China

In this paper,we propose and experimentally demonstrate a joint shaping technique to improve the performance of a lowresolution transmission system for the first time,to the best of our knowledge.The joint shaping technique combines probabilistic shaping(PS)and error feedback noise shaping(EFNS).In the 40-Gbaud intensity-modulation direct-detection(IM/DD)experimental transmission system,a bit-error-rate(BER)of 3.8×10^(-3)can be achieved easily with the joint shaping at the physical number of bits(PNOB)of 3.In the 30-Gbaud dual polarization(DP)coherent experimental transmission system,a BER below 1×10^(-3)is easily obtained with a 3-bit quantizer by using joint shaping.The optimization of the shaping degree is also analyzed.

关键词： optical fiber communication quantization digital signal processing