On the analysis of dynamic feedback neural nets

Salam, F.M.A.; Wang, Y.; Choi, Myung Ryul

doi:10.1109/31.68297

Cited by 64 publications

(11 citation statements)

References 32 publications

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“…An important requirement is that these equilibria are asymptotically stable, otherwise no attraction to the equilibria will take place. By asymptotic stability of an equilibrium we mean that a trajectory starting in the vicinity of the equilibrium remains close and converges to it as t + x (see Guckenheimer and Holmes [ 121 for a formal definition, see also Michel et al [13] and Salam et al [14] for a study on asymptotic stability in continuous neural networks). Unfortunately, there is a limitation on the set of vectors which can be stored.…”

Section: The Neiworkmentioning

confidence: 99%

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An analog feedback associative memory

Atiya

Abu‐Mostafa

1993

IEEE Trans. Neural Netw.

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Abstruct-Most of the neural network associative memory models deal with the storage of binary vectors. We consider the Hopfield continuous-time network, and develop a new method for the storage of analog vectors, i.e., vectors whose components are real-valued. An important requirement is that each memory vector has to be an asymptotically stable (i.e., attractive) equilibrium of the network. We point out some of the limitations of the continuous Hopfield model on the set of vectors that can be stored. These limitations can be relieved by choosing a network containing visible as well as hidden units. We have chosen an architecture consisting of several hidden layers and a visible layer, connected in a circular fashion. We prove that the two-layer case of such an architecture is guaranteed to store any number of given analog vectors provided their number does not exceed 1 + the number of neurons in the hidden layer. We have developed a learning algorithm, which results in correctly adjusting the locations of the equilibria, as well as guaranteeing their asymptotic stability. Simulation results confirm the effectiveness of the new method.

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Section: The Neiworkmentioning

confidence: 99%

“…. , y(M) because otherwise w can be perturbed to restore (14). Rename the indices of the memories such that wTy(1) > wTy(2) > .…”

Section: \ Rmentioning

confidence: 99%

An analog feedback associative memory

Atiya

Abu‐Mostafa

1993

IEEE Trans. Neural Netw.

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“…As a demonstration of the viability of such a merger, a new modelling method will be described, which combines and extends ideas borrowed from methods and applications in electronic circuit and device modelling theory and numerical analysis [2,7,8,18,23,24] the popular error back propagation method (and other methods) for neural networks [3,4,13,14,22,31] and time domain extensions to neural networks in order to deal with dynamic systems [15,16,17,30,32].…”

Section: Introductionmentioning

confidence: 99%

Solution of Linear Electrical Circuit Problem using Neural Networks

Samath¹,

Kumar²,

Begum³

2010

IJCA

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In this paper, Neural network algorithm is introduced to study the singular system of a linear electrical circuit for time invariant and time varying cases. The discrete solutions obtained using neural network are compared with Runge-Kutta(RK) method and exact solutions of the electrical circuit problem and are found to be very accurate. Error graphs for inductor currents and capacitor voltages are presented in a graphical form to show the efficiency of neural network algorithm. This neural network algorithm can be easily implemented in a digital computer for any singular system of electrical circuits.

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“…As it was shown in [2], [4], [5] if the transition matrix is symmetric ( T = T T ) and the activation function is bounded, differentiable and increasing such network is totally stable, i.e. every solution trajectory approaches an equilibrium.…”

Section: L R~[ N -( 2 R + L )~] (5)mentioning

confidence: 90%

“…Since that the great progress was done in stability analysis e.g. [4], [5] and in designing the networks e.g. [6], [7], [8].…”

Section: Introductionmentioning

confidence: 99%