神经网络传递函数的功能分析与仿真研究

从函数映射的角度，以三层前向神经网络为例，对神经网络的映射关系进行了分析，提出前向神经网络的映射关系可以视为一种广义级数展开，展开系数就是隐层与输出层的连接权，而传递函数的作用在于提供一个“母基”，它与输入到隐层间的连接权一起，构造了不同的展开函数。根据这一理论，着重对神经网络传递函数在映射中的作用进行了分析，指出如果灵活选择多个复合传递函数，可以使网络以更少的参数、更少的隐节点，完成从输入到输出的映射，从而提高神经网络的泛化能力。利用遗传优化对一个两类分类问题的训练仿真结果表明，采用混合传递函数，的确能够以更少的隐节点实现所需要的映射关系，网络结构的复杂度低，泛化能力也更好。该结果也进一步证实了神经网络映射关系的广义级数展开的正确性。

Genetic Optimization for Neural Network Evolving with Function Based Coding

In the point of view of mapping relations on 3-layer forward neural network,a new theory that the function of hidden layer in neural network is in fact a generalized series expansion is proposed.The expansion coefficients are the weights between hidden layer and output layer,while the transfer function provides a "mother basis",which together with weights between input layer and hidden layer form different bases for realizing mapping between inputs and outputs.According to this theory,composite transfer functions can work better than single,since it can finish the mapping with less parameters,thus improving the generalization ability.Simulations by standard genetic algorithm for evolving neural network on a two-class classification problem show that such a neural network can achieve the mapping with less hidden nodes,thus decreasing the complexity of neural network and improving its performance.