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

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 layer feedforward neural network with one hidden layer to realize arbitrary multi-valued functions.