Abstract
AbstractThis paper considers the situation where the multiple state‐patterns satisfying the orthogonality condition are memorized in the Hopfield associative memory model. Also discussed is the relation between the equilibrium state produced in the associative memory model and the memorized patterns. Numerous studies have been made of the associative memory model by the statistical approach. By contrast, this study considers the problem from the algebraic standpoint, using the Walsh functional system.As the first step, a sufficient condition is derived for the associative memory model to be in the equilibrium state. Using this condition, the equilibrium states are classified into three types and the relation between the memorized pattern and the generated equilibrium state is analyzed. As applications, a method of estimating the number of equilibrium states and their state pattern from the data concerning the memorized pattern, as well as a method of making the given pattern an equilibrium state, are shown through examples. the results are obtained by the component analysis of the state of the associative memory model using the Walsh functional system. In other words, the usefulness of applying the Walsh functional system is demonstrated.
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