Local stability conditions for discrete-time cascade locally recurrent neural networks

Krzysztof Patan

International Journal of Applied Mathematics and Computer Science (2010)

  • Volume: 20, Issue: 1, page 23-34
  • ISSN: 1641-876X

Abstract

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The paper deals with a specific kind of discrete-time recurrent neural network designed with dynamic neuron models. Dynamics are reproduced within each single neuron, hence the network considered is a locally recurrent globally feedforward. A crucial problem with neural networks of the dynamic type is stability as well as stabilization in learning problems. The paper formulates local stability conditions for the analysed class of neural networks using Lyapunov's first method. Moreover, a stabilization problem is defined and solved as a constrained optimization task. In order to tackle this problem, a gradient projection method is adopted. The efficiency and usefulness of the proposed approach are justified by using a number of experiments.

How to cite

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Krzysztof Patan. "Local stability conditions for discrete-time cascade locally recurrent neural networks." International Journal of Applied Mathematics and Computer Science 20.1 (2010): 23-34. <http://eudml.org/doc/207975>.

@article{KrzysztofPatan2010,
abstract = {The paper deals with a specific kind of discrete-time recurrent neural network designed with dynamic neuron models. Dynamics are reproduced within each single neuron, hence the network considered is a locally recurrent globally feedforward. A crucial problem with neural networks of the dynamic type is stability as well as stabilization in learning problems. The paper formulates local stability conditions for the analysed class of neural networks using Lyapunov's first method. Moreover, a stabilization problem is defined and solved as a constrained optimization task. In order to tackle this problem, a gradient projection method is adopted. The efficiency and usefulness of the proposed approach are justified by using a number of experiments.},
author = {Krzysztof Patan},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {locally recurrent neural network; stability; stabilization; learning; constrained optimization},
language = {eng},
number = {1},
pages = {23-34},
title = {Local stability conditions for discrete-time cascade locally recurrent neural networks},
url = {http://eudml.org/doc/207975},
volume = {20},
year = {2010},
}

TY - JOUR
AU - Krzysztof Patan
TI - Local stability conditions for discrete-time cascade locally recurrent neural networks
JO - International Journal of Applied Mathematics and Computer Science
PY - 2010
VL - 20
IS - 1
SP - 23
EP - 34
AB - The paper deals with a specific kind of discrete-time recurrent neural network designed with dynamic neuron models. Dynamics are reproduced within each single neuron, hence the network considered is a locally recurrent globally feedforward. A crucial problem with neural networks of the dynamic type is stability as well as stabilization in learning problems. The paper formulates local stability conditions for the analysed class of neural networks using Lyapunov's first method. Moreover, a stabilization problem is defined and solved as a constrained optimization task. In order to tackle this problem, a gradient projection method is adopted. The efficiency and usefulness of the proposed approach are justified by using a number of experiments.
LA - eng
KW - locally recurrent neural network; stability; stabilization; learning; constrained optimization
UR - http://eudml.org/doc/207975
ER -

References

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