Capacity of associative memory using a nonmonotonic neuron model

Abstract

Associative memory using a sigmoid neuron model with the autocorrelation matrix has the advantage of the simplicity of its structure of the memory but has the disadvantage of the memory capacity. Its absolute capacity is asymptotically n (2 log n) , where n is the number of neurons. By computer simulation, Morita has recently shown that the performance of the associative memory is improved remarkably by replacing the usual sigmoid neuron with a nonmonotonic one, without sacrificing the simplicity. We use a piecewise linear model of the nonmonotonic neuron and investigate the existence and stability of equilibrium states of the recalling process. We derive two kinds of theoretical estimates of the absolute capacity. One estimate gives the upper bound of the absolute capacity 0.5n, and the other gives the average value of the absolute capacity 0.4n. These values fit well with computer simulations.