Capacity of Second-Order Bidirectional Associative Memory with Finite Neuron Numbers

Yutaka KAWABATA  Yoshimasa DAIDO  Kaname KOBAYASHI  Shimmi HATTORI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A   No.11   pp.2318-2324
Publication Date: 1997/11/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Neural Networks
BAM,  capacity,  error probability,  characteristic function,  Hermite Gauss,  

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This paper describes relation between the number of library pairs and error probability to have all the pairs as fixed points for second-order bidirectional associative memory (BAM). To estimate accurate error probability, three methods have been compared; (a) Gaussian approximation, (b) characteristic function method, and (c) Hermite Gaussian approximation (proposed by this paper). Comparison shows that Gaussian approximation is valid for the larger numbers of neurons in both two layers than 1000. While Hermite Gaussian approximation is applicable for the larger number of neurons than 30 when Hermite polynomials up to 8th are considered. Capacity of second-order BAM at the fixed error probability is estimated as the function of the number of neurons.