Higher Order Neurodynamics of Associative Memory for Sequential Patterns

Authors:
Hiromi Miyajima;Noritaka Shigei;Shuji Yatsuki
Affiliations:
Kagoshima University, Kagoshima, Japan 890-0065;Kagoshima University, Kagoshima, Japan 890-0065;Kyoto Software Research, Inc., Kyoto, Japan 600-8482
Venue:
ISNN 2009 Proceedings of the 6th International Symposium on Neural Networks: Advances in Neural Networks - Part II
Year:
2009

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Abstract

This paper describes higher order neurodynamics of associative memory for sequential patterns using a statistical method. First, the statistical analysis of direct correlations between the cross talk noise terms for higher order neural networks is made. Further, it is shown that storage capacities for k = 1, 2 and 3 dimensional cases are 0.263n , $0.207\binom{n}{2}$ and $0.180\binom{n}{3}$, respectively, where n is the number of neurons and $\binom{n}{k}$ means the combination of k from n . The result for the one dimensional case is in fairly general agreement with Meir's result, 0.269n , obtained by the replica theory.