On the stability, storage capacity, and design of nonlinear continuous neural networks

Guez, A.; Protopopsecu, V.; Barhen, J.

doi:10.1109/21.87056

Cited by 124 publications

(32 citation statements)

References 30 publications

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“…Like the one neuron case, the two neuron system (52) In this section we discuss briefly the connections between the stability conditions derived in this work and those discussed in [5,10,11]. In particular, we show that when the conditions of Theorem 1 are supplemented by the transposition conditions (see below) then the weight stability condition of Hirsch (5) is reproduced.…”

Section: The Two Neuron Casementioning

confidence: 83%

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On the stability of neural networks with arbitrary weights

Olafsson

1996

Neural Comput & Applic

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Section: The Two Neuron Casementioning

confidence: 83%

“…A few authors [5,10,11] have established conditions for asymptotic stability in terms of inequalities involving the weights. Here we only write down the conditions derived by Hirsch [5].…”

Section: General Remarks On Stabilitymentioning

confidence: 99%

On the stability of neural networks with arbitrary weights

Olafsson

1996

Neural Comput & Applic

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“…The biggest promise of these networks as computational tools lies in the hope that they will resemble the information processing in biological systems. Notwithstanding many successes in this direction, Hopfield (1985); Pineda (1987); Gues et al (1988); it is rapidly becoming evident that current models based upon classical dynamical system theory are characterized by some limitations. Firstly, the performance of the current models is fully prescribed by initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Terminal chaos for information processing in neurodynamics

Zak

1991

Biol. Cybern.

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New nonlinear phenomenon-terminal chaos caused by failure of the Lipschitz condition at equilibrium points of dynamical systems is introduced. It is shown that terminal chaos has a well organized probabilistic structure which can be predicted and controlled. This gives an opportunity to exploit this phenomenon for information processing. It appears that chaotic states of neurons activity are associated with higher level of cognitive processes such as generalization and abstraction.

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“…For equation (2.11, the Jacobian matrix has the form where Sij are the elements of the identity matrix and f'(zj) is the derivative of f(zj). This condition has been used by Guez et al (1988).…”

Section: Overview Of a Dynamical Modelmentioning

confidence: 99%

Recurrent Backpropagation and the Dynamical Approach to Adaptive Neural Computation

Pineda

1989

Neural Computation

146

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Error backpropagation in feedforward neural network models is a popular learning algorithm that has its roots in nonlinear estimation and optimization. It is being used routinely to calculate error gradients in nonlinear systems with hundreds of thousands of parameters. However, the classical architecture for backpropagation has severe restrictions. The extension of backpropagation to networks with recurrent connections will be reviewed. It is now possible to efficiently compute the error gradients for networks that have temporal dynamics, which opens applications to a host of problems in systems identification and control.

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On the stability, storage capacity, and design of nonlinear continuous neural networks

Cited by 124 publications

References 30 publications

On the stability of neural networks with arbitrary weights

On the stability of neural networks with arbitrary weights

Terminal chaos for information processing in neurodynamics

Recurrent Backpropagation and the Dynamical Approach to Adaptive Neural Computation

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