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Capacity of Associative Memory Using a Nonmonotonic Neural Model

Shuji Yoshizawa, Masahiko Morita and Shun-ichi Amari

**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/(*2log* 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 0.5*n*, and the other gives the
average value of the absolute capacity 0.4*n*. These values fit
well with computer simulations.

**Keywords:**
Autocorrelation-type associative memory, Capacity, Nonmonotonic
neuron, Piecewise linear model, Equilibrium state, Stability.

Requests for reprints should be sent to
Shuji Yoshizawa.