Complex‐valued multidirectional associative memory

AbstractHopfield model is a representative associative memory. It was improved to Bidirectional Associative Memory (BAM) by Kosko and to Multidirectional Associative Memory (MAM) by Hagiwara. They have two layers or multilayers. Since they have symmetric connections between layers, they ensure convergence. MAM can deal with multiples of many patterns, such as (x1,x2,…), wherexmis the pattern on layerm. Copyright © 2004 Wiley Periodicals, Inc.Noest, Hirose, and Nemoto proposed complex‐value Hopfield model. Lee proposed complex‐valued Bidirectional Associative Memory. Zemel proved the rotation invariance of complex‐valued Hopfield model. It means that the rotated pattern in also stored.In this paper, the complex‐valued Multidirectional Associative Memory is proposed. The rotation invariance is also proved. Moreover it is shown by computer simulation that the differences of angles of given patterns are automatically reduced.At first we define complex‐valued Multidirectional Associative Memory. Then we define the energy function of network. With the energy function, we prove that the network ensures convergence.Next, we define the learning law and show the characteristic of recall proc