为分析前馈神经网络输出量的一阶、二阶偏导数特性，从一层网络结构入手，推导网络输出量的一阶偏导数，应用链式求导法则，推导多层网络输出量的一阶、二阶偏导数的计算公式。在此基础上推导网络的三阶偏导数，并针对二层结构网络，在其输出层激活函数为线性函数时，推导出该网络对输入量的高阶偏导数计算公式。实例分析结果表明，前馈神经网络一阶、二阶偏导数值的精度比网络输出值的精度要低，尤其是在区间的边界上有时会出现较大的偏差。网络的一阶、二阶偏导数值的精度也会随着隐含层神经元数量的增加明显降低，在基本相同的网络训练精度下，隐含层神经元较多的网络比神经元少的网络导数特性差。%In order to analyze first and second order partial derivative feature of feedforward neural networks with respect to its inputs, one layered architecture network is chosen to deduce first order partial derivative of network. Chain rule is employed to derive formulas to compute partial derivatives of multilayer architecture networks. On the basis of that, third order partial derivative of networks can be gained easily. And considering linear activation function in output layer of two layered networks, higher order partial derivatives of networks with respect of its inputs can be obtained. Case analysis shows that accuracy of first and second order partial derivative of feedforward neural networks is far less than that of output of networks, especially in the boundary area of interval of input the error between stimulation value and real value is very significant. Moreover, accuracy of first and second order derivative of network decreases greatly with increase of the number of neurons in hidden layer. Consequently, under the condition of networks with equivalent training accuracy, the networks with less neurons in hidden layer has better derivative performance than that with more neurons in hidden layer.
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