多值多门限神经元函数的相关性和频谱分析

Correlation and Spectrum Analysis of Functions Implemented by Multi-value Multi-threshold Neurons

为衡量单个多值多门限神经元的计算能力,引入了与多值多门限神经元函数有关的2个代数几何概念:相关性和扩展频谱.利用相关性,给出对于一组固定的输入函数,不同输出函数个数的上限.利用扩展频谱,给出为了使得神经元能够计算任意输出函数,所需输入函数个数的下限.这2个界限,给出了单个多值多门限神经元的计算能力.同时,输入函数个数的下限,给出了当用多值多门限神经元组成的三层前馈神经网络实现任意多值函数时,网络复杂度的下限.

In order to scale the computational ability of a single multi-value multi-threshold neuron,this paper introduces two geometrical concepts:correlation and generalized spectrum.By using the correlation,we give the upper bound of the number of different output functions for a group of fixed input functions.By using the generalized spectrum,we give the lower bound of the number of input functions in order to realize arbitrary output functions.This lower bound is also the lower bound of the complexity of a three...