隨機(jī)Hopfield神經(jīng)網(wǎng)絡(luò)的定量分析
THE QUANTITATIVE ANALYSIS OF STOCHASTIC HOPFIELD NEURAL NETWORK MODEL
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摘要: 該文探討了實(shí)際使用Hopfield神經(jīng)網(wǎng)絡(luò)(HNN)時(shí)噪聲的影響。由于噪聲的客觀存在,我們首先證明了隨機(jī)Hopfield神經(jīng)網(wǎng)絡(luò)(SHNN)軌道的期望關(guān)于時(shí)間是一致有界的。之后,為了實(shí)際設(shè)計(jì)神經(jīng)網(wǎng)絡(luò)的需要,我們對(duì)含有噪聲的HNN和與其對(duì)應(yīng)的一般HNN之間隨機(jī)輸入誤差的估計(jì)進(jìn)行了研究。利用所得的結(jié)論,我們可以對(duì)設(shè)計(jì)空間進(jìn)行控制,使得所設(shè)計(jì)的網(wǎng)絡(luò)滿(mǎn)足我們希望獲得的各種性能要求。Abstract: In this paper, the effect of input noise on the typical stochastic Hopfield neural network modei is discussed. It is shown that the expectation of the stochastic HNN of the trajectory is uniformly bounded over time. For practical design purposes, the stochastic input error estimates for the stochastic HNN with respect to the corresponding deterministic HNN is derived. In addition, the designer can use these results to constrain the design space so that the achieved design satisnes the performance specifications whenever possible.
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徐秉錚,張百靈,韋崗,神經(jīng)網(wǎng)絡(luò)理論與應(yīng)用,廣州,華南理工大學(xué)出版社, 1994,第二章.[2]廖桂生,焦李成,保錚,神經(jīng)網(wǎng)絡(luò)隨機(jī)擾動(dòng)穩(wěn)定性研究,電子科學(xué)學(xué)刊,1992,14(4),416-419.[3]武寶亭,李慶士,暢躍武,隨機(jī)過(guò)程與隨機(jī)微分方程,成都,電子科技大學(xué)出版社, 1994,第八章.[4]M A.Colen,S.Grossberg.Absolute stability of global pattern formation and parallel memory storage by competitive neural networks,IEEE Trans on Syst,Man,Cybern,1983,SMC-13(5):815-526.[5]王松桂,賈忠貞、矩陣論中不等式,合肥,安徽教育出版社,1994,第四章.[6]段廣仁,線性系統(tǒng)理論,哈爾濱,哈爾濱工業(yè)大學(xué)出版社, 1996:第三章,第五章. -
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