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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2015, Vol. 30 Issue (3): 280-290    DOI:
    
Estimate for approximation error of feedforward neural networks
YIN Jun-cheng1, YIN Mao-ren2
1. College of Sci., China Jiliang Univ., Hangzhou 310018, China
2. Dept. of Math., Junior college of Xinzhou Teachers Univ., Xinzhou 034000, China
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Abstract  In this paper, a general feedforward neural network is constructed, in which the activation function is not assumed to be odd, and the threshold values and direction weight values are different from the known choices. In addition, lower bounds of approximation errors of the proposed neural networks are discussed. Some examples of numerical experiments are listed to demonstrate the theoretical results.

Key words： neural networks      approximation      estimate      $L^p$ metric     
Received: 26 March 2015      Published: 27 May 2018
CLC:  O174.41  
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Cite this article:

YIN Jun-cheng, YIN Mao-ren. Estimate for approximation error of feedforward neural networks. Applied Mathematics A Journal of Chinese Universities, 2015, 30(3): 280-290.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2015/V30/I3/280


前向神经网络逼近误差估计

构造了一种前向神经网络并研究了其对连续函数以及$L^p$可积函数的逼近误差, 去掉了以前的文献中要求激活函数为奇函数的限制, 提出了新的网络参数的设置. 此外, 进一步研究了该神经网络参数设置与逼近误差之间的关系, 给出了此类神经网络逼近所能达到的误差上确界. 与此同时, 数值实验的结果显示该网络的逼近效果优于已有结果.

关键词： 神经网络,  逼近,  误差估计,  $L^p$度量 
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