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

Yutaka KAWABATA; Yoshimasa DAIDO; Kaname KOBAYASHI; Shimmi HATTORI

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

Yutaka KAWABATA, Yoshimasa DAIDO, Kaname KOBAYASHI, Shimmi HATTORI

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E80-A No.11 pp.2318-2324

Publication Date: 1997/11/25

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Category: Neural Networks

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Yutaka KAWABATA, Yoshimasa DAIDO, Kaname KOBAYASHI, Shimmi HATTORI, "Capacity of Second-Order Bidirectional Associative Memory with Finite Neuron Numbers" in IEICE TRANSACTIONS on Fundamentals, vol. E80-A, no. 11, pp. 2318-2324, November 1997, doi: .
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e80-a_11_2318/_p

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@ARTICLE{e80-a_11_2318,
author={Yutaka KAWABATA, Yoshimasa DAIDO, Kaname KOBAYASHI, Shimmi HATTORI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Capacity of Second-Order Bidirectional Associative Memory with Finite Neuron Numbers},
year={1997},
volume={E80-A},
number={11},
pages={2318-2324},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - Capacity of Second-Order Bidirectional Associative Memory with Finite Neuron Numbers
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2318
EP - 2324
AU - Yutaka KAWABATA
AU - Yoshimasa DAIDO
AU - Kaname KOBAYASHI
AU - Shimmi HATTORI
PY - 1997
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E80-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 1997
AB - 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.
ER -