多值神经元函数的频谱近似

Spectral Approximation of Functions Implemented by Multi-valued Neurons

为衡量多值神经元函数与其扩展频谱之间的误差,定义了多值神经元输入函数和输出函数之间的近似误差,并给出误差的下限.通过限定下限为0,给出单个p值神经元能实现的函数应该满足的充分条件,这也是单个神经元计算能力的一个衡量指标.给出了当输入函数不满足正交条件时,多值神经网络复杂度的下限.

To scale the error between the function implemented by one multi-valued neuron and its generalized spectrum,this paper defines the approximation error and gives the lower bound of it.By limiting the approximation error to 0,it also proposes the sufficient condition of the function implemented by a single multi-valued neuron,which is one of the measure indexes of the computational ability of a single multi-valued neuron.The lower bound of complexity of multi-valued neurons is obtained when the orthogonality condition of the function is not met.