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Bollé, Désiré; Jongen, G.; Shim, Gyoung Moo

doi:10.1023/a:1023088004195

Cited by 12 publications

(25 citation statements)

References 15 publications

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“…These correlations are caused by feedback loops and common ancestors. In contrast to the Hopfield model, where the dynamics has been solved taking into account all the correlations [10,11], the presence of two types of spins makes the analysis of the correlations in the atnn very complicated. The underlying reason is the existence of two sources of correlations.…”

Section: Introductionmentioning

confidence: 99%

Parallel dynamics of the asymmetric extremely diluted Ashkin-Teller neural network

Bollé

Jongen

2000

Eur. Phys. J. B

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Abstract. The parallel dynamics of the asymmetric extremely diluted Ashkin-Teller neural network is studied using signal-to-noise analysis techniques. Evolution equations for the order parameters are derived, both at zero and finite temperature. The retrieval properties of the network are discussed in terms of the four-spin coupling strength and the temperature. It is shown that the presence of a four-spin coupling enhances the retrieval quality.PACS. 64.60.Cn Order-disorder transformations; statistical mechanics of model systems -75.10.Hk Classical spin models -87.10.+e General, theoretical, and mathematical biophysics -02.50.-r Probability theory, stochastic processes and statistics

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Section: Introductionmentioning

confidence: 99%

Parallel dynamics of the asymmetric extremely diluted Ashkin-Teller neural network

Bollé

Jongen

2000

Eur. Phys. J. B

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“…At a given time step of the dynamics, the state of a neuron, σ i,t+1 is determined by its local field at the previous time step. In general, in the limit N → ∞ the distribution of the local field at time t + 1 consists out of a discrete part and a normally distributed part [12] h…”

Section: Threshold Dynamicsmentioning

confidence: 99%

“…Furthermore, we take both contributions at equal times and call √ αaD t ≡ ∆ t = G t + √ αq t . For more details on this approximation of the feedback correlations we refer to [12,13] and references therein. Finally, since G t is a function of the overlap m 1 t , a quantity which is not available to the network we replace it by G 0 = 2/π a.…”

Section: Threshold Dynamicsmentioning

confidence: 99%

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Mutual information and self-control of a fully-connected low-activity neural network

Bollé

Carreta

2000

Physica A: Statistical Mechanics and its Applications

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A self-control mechanism for the dynamics of a three-state fully-connected neural network is studied through the introduction of a time-dependent threshold. The self-adapting threshold is a function of both the neural and the pattern activity in the network. The time evolution of the order parameters is obtained on the basis of a recently developed dynamical recursive scheme. In the limit of low activity the mutual information is shown to be the relevant parameter in order to determine the retrieval quality. Due to self-control an improvement of this mutual information content as well as an increase of the storage capacity and an enlargement of the basins of attraction are found. These results are compared with numerical simulations. *

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“…For the parallel dynamics of networks with symmetric connections, however, things are quite different [1,10,11]. Even for extremely diluted versions of these systems [15,16,17] feedback correlations become essential from the second time step onwards, complicating the dynamics in a nontrivial way.…”

Section: Introductionmentioning

confidence: 99%

Q-Ising Neural Network Dynamics: A Comparative Review of Various Architectures

Bollé¹,

Jongen²,

Shim³

2000

Mathematical Physics and Stochastic Analysis

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This contribution reviews the parallel dynamics of Q-Ising neural networks for various architectures: extremely diluted asymmetric, layered feedforward, extremely diluted symmetric, and fully connected. Using a probabilistic signal-tonoise ratio analysis, taking into account all feedback correlations, which are strongly dependent upon these architectures the evolution of the distribution of the local field is found. This leads to a recursive scheme determining the complete time evolution of the order parameters of the network. Arbitrary Q and mainly zero temperature are considered. For the asymmetrically diluted and the layered feedforward network a closed-form solution is obtained while for the symmetrically diluted and fully connected architecture the feedback correlations prevent such a closed-form solution. For these symmetric networks equilibrium fixed-point equations can be derived under certain conditions on the noise in the system. They are the same as those obtained in a thermodynamic replica-symmetric mean-field theory approach. †

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Untitled

Cited by 12 publications

References 15 publications

Parallel dynamics of the asymmetric extremely diluted Ashkin-Teller neural network

Parallel dynamics of the asymmetric extremely diluted Ashkin-Teller neural network

Mutual information and self-control of a fully-connected low-activity neural network

Q-Ising Neural Network Dynamics: A Comparative Review of Various Architectures

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