Iterative neural networks for improving memory capacity

Abstract

In recent years, the problem of the multistability of neural networks has been studied extensively. From the research results obtained, the number of stable equilibrium points depends only on a power form of the network dimension. However, in practical applications, the number of stable equilibrium points needed is often not expressed in power form. Therefore, can we determine an appropriate activation function so that the neural network has exactly the required number of stable equilibrium points? This paper provides a new way to study this problem by means of an iteration method. The necessary activation function is constructed by an appropriate iteration method, and the neural network model is established. Based on the mathematical theories of matrix analysis and functional analysis and on the inequality method, the number and distribution of the network equilibrium points are determined by dividing the state space reasonably, and some multistability criteria that are related to the number of iterations and are independent of the network dimension are established.