【摘要】 灵敏度分析对于神经网络结构设计具有指导意义 .已有的灵敏度分析方法往往针对特定的激活函数 ,并且对网络输入和权值扰动有严格的限制 .该文采用另一种以 1- e-λx1+e-λx型激活函数的倾斜度作为参数的函数形式逼近激活函数 ,得到了一类神经元的统一的灵敏度解析表达式和网络灵敏度计算算法 .该方法取消了对输入和权值扰动的限制 ,可以研究激活函数倾斜度对网络灵敏度的影响 .计算机模拟试验证明了此方法的正确性 ,并且提出了网络结构设计的几条准则 .更多还原

【Abstract】 Sensitivity analysis is a fundamental issue in the research of neural networks, and provides theoretical instruction for neural network design. The existing approaches to the sensitivity analysis of Multilayer Perceptron usually aim at the network with a specific activation function, and impose too severe limitations on both network input and weight perturbations. So the sensitivity analysis of Multilayer Perceptron is restricted within narrow application range. In this paper, the common characteristic, i.e., the obliquity, is extracted from the sigmoidal activation functions with the form 1-e -λx1+e -λx, and another function with the obliquity characteristic is adopted to approximate the sigmoidal activation function. The approximation function has the form convenient for the computation of sensitivity without introducing additional limitations, and it is used to deduce the sensitivity expression of Multilayer Perceptron instead of the activation function. Based on the stochastic model of Multilayer Perceptron, a universal analytic expression of sensitivity for a single neuron with a class of sigmoidal activation functions is derived. Then we present a bottom-up algorithm to calculate the sensitivity of the whole Multilayer Perceptron layer by layer. Except the approximation of the activation function, the sensitivity expression is derived exactly. So there is no need for us to restrict the input and weight perturbations to be very small in our sensitivity analysis method. Because the obliquity of the sigmoidal activation function is a parameter of the approximation function, the effect of the obliquity of the activation function on the network sensitivity can be analyzed. The result of computer simulation shows that our theoretical result matches the experiment result closely. This also indicates the correctness of our sensitivity analysis approach. Finally, the effects of network parameters on the network sensitivity are investigated; and the parameters include the input perturbation, the weight perturbation, the number of layer, the number of neuron per layer and the obliquity of activation function. Some rules for the architecture design of Multilayer Perceptron are concluded.更多还原