Necessary and Sufficient Condition for Absolute Exponential Stability of Hopfield-Type Neural Networks
Summary :
A main result in this paper is that for a Hopfield-type neural circuit with a symmetric connection matrix T, the negative semidenfiniteness of T is a necessary and sufficient condition for absolute exponential stability. While this result extends one of absolute stability in Forti, et al. [1], its proof given in this paper is simpler, which is completed by an approach different from one used in Forti et al. [1]. The most significant consequence is that the class of neural networks with negative semidefinite matrices T is the largest class of symmetric networks that can be employed for embedding and solving optimization problem with global exponential rate of convergence to the optimal solution and without the risk of spurious responses.
- Publication
- IEICE TRANSACTIONS on Information Vol.E79-D No.7 pp.990-993
- Publication Date
- 1996/07/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Bio-Cybernetics and Neurocomputing
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Xue-Bin LIANG, Toru YAMAGUCHI, "Necessary and Sufficient Condition for Absolute Exponential Stability of Hopfield-Type Neural Networks" in IEICE TRANSACTIONS on Information,
vol. E79-D, no. 7, pp. 990-993, July 1996, doi: .
Abstract: A main result in this paper is that for a Hopfield-type neural circuit with a symmetric connection matrix T, the negative semidenfiniteness of T is a necessary and sufficient condition for absolute exponential stability. While this result extends one of absolute stability in Forti, et al. [1], its proof given in this paper is simpler, which is completed by an approach different from one used in Forti et al. [1]. The most significant consequence is that the class of neural networks with negative semidefinite matrices T is the largest class of symmetric networks that can be employed for embedding and solving optimization problem with global exponential rate of convergence to the optimal solution and without the risk of spurious responses.
URL: https://global.ieice.org/en_transactions/information/10.1587/e79-d_7_990/_p
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@ARTICLE{e79-d_7_990,
author={Xue-Bin LIANG, Toru YAMAGUCHI, },
journal={IEICE TRANSACTIONS on Information},
title={Necessary and Sufficient Condition for Absolute Exponential Stability of Hopfield-Type Neural Networks},
year={1996},
volume={E79-D},
number={7},
pages={990-993},
abstract={A main result in this paper is that for a Hopfield-type neural circuit with a symmetric connection matrix T, the negative semidenfiniteness of T is a necessary and sufficient condition for absolute exponential stability. While this result extends one of absolute stability in Forti, et al. [1], its proof given in this paper is simpler, which is completed by an approach different from one used in Forti et al. [1]. The most significant consequence is that the class of neural networks with negative semidefinite matrices T is the largest class of symmetric networks that can be employed for embedding and solving optimization problem with global exponential rate of convergence to the optimal solution and without the risk of spurious responses.},
keywords={},
doi={},
ISSN={},
month={July},}
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TY - JOUR
TI - Necessary and Sufficient Condition for Absolute Exponential Stability of Hopfield-Type Neural Networks
T2 - IEICE TRANSACTIONS on Information
SP - 990
EP - 993
AU - Xue-Bin LIANG
AU - Toru YAMAGUCHI
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E79-D
IS - 7
JA - IEICE TRANSACTIONS on Information
Y1 - July 1996
AB - A main result in this paper is that for a Hopfield-type neural circuit with a symmetric connection matrix T, the negative semidenfiniteness of T is a necessary and sufficient condition for absolute exponential stability. While this result extends one of absolute stability in Forti, et al. [1], its proof given in this paper is simpler, which is completed by an approach different from one used in Forti et al. [1]. The most significant consequence is that the class of neural networks with negative semidefinite matrices T is the largest class of symmetric networks that can be employed for embedding and solving optimization problem with global exponential rate of convergence to the optimal solution and without the risk of spurious responses.
ER -
English
