An analysis of associative dynamics in a chaotic neural network with external stimulation

Adachi, Masaharu; Aihara, Kazuyuki; Kotani, Masahiro

doi:10.1109/ijcnn.1993.713943

Cited by 18 publications

(14 citation statements)

References 7 publications

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“…On the other hand, although the dynamics of CNN has an intriguing property to move chaotically over fractal structure in the phase space, without getting stuck at local minima because of accumulation of refractory or self-inhibitory effects Aihara, 1990;Nozawa, 1992;Adachi et al, 1993;Yamada, et al, 1993), the convergence problems of the chaotic dynamics have not been satisfactorily solved so far.…”

Section: A Model Of a Transiently Chaotic Neural Networkmentioning

confidence: 99%

Chaotic simulated annealing by a neural network model with transient chaos

Chen¹,

1995

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Section: A Model Of a Transiently Chaotic Neural Networkmentioning

confidence: 99%

Chaotic simulated annealing by a neural network model with transient chaos

Chen¹,

1995

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“…Such systems, which have only recently been investigated, demonstrate chaotic behavior under normal conditions, and resonate when it is presented with a pattern that it is trained with. The network which we have investigated is the Adachi Neural Network (AdNN) [1][2][3][4][5], which has been shown to possess chaotic properties, and to also demonstrate Associative Memory (AM) and Pattern Recognition (PR) characteristics. Because its structure involves a completely connected graph, the computational complexity of the AdNN is quadratic in the number of neurons.…”

Section: Discussionmentioning

confidence: 99%

“…The AdNN's power as a PR system requires excessive computationsof the order of O(N 2 ). For the examples cited by Adachi et al and Calitoiu et al [1][2][3][4][5][6][7], which use 10 × 10 pixel arrays, this involves 10, 000 computations per time step. 2.…”

Section: Limitations Of the Current Schemesmentioning

confidence: 99%

“…This paper deals with the Adachi Neural Network AdNN [1][2][3][4][5], which possesses a spectrum of very interesting chaotic, AM and PR properties, as described in [6,7]. The fundamental "problem" associated with the AdNN and its variants is its quadratic computational requirement.…”

Section: Introductionmentioning

confidence: 99%

“…The Adachi Neural Network (AdNN) [1][2][3][4][5], is a fascinating Neural Network (NN) which has been shown to possess chaotic properties, and to also demonstrate Associative Memory (AM) and Pattern Recognition (PR) characteristics. Variants of the AdNN [6,7] have also been used to obtain other PR phenomena, and even blurring.…”

mentioning

confidence: 99%

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An Enhanced Tree-Shaped Adachi-Like Chaotic Neural Network Requiring Linear-Time Computations

Qin¹,

Oommen²

2010

Chaotic Systems

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Abstract. The Adachi Neural Network (AdNN) [1][2][3][4][5], is a fascinating Neural Network (NN) which has been shown to possess chaotic properties, and to also demonstrate Associative Memory (AM) and Pattern Recognition (PR) characteristics. Variants of the AdNN [6,7] have also been used to obtain other PR phenomena, and even blurring. A significant problem associated with the AdNN and its variants, is that all of them require a quadratic number of computations. This is essentially because all their NNs are completely connected graphs. In this paper we consider how the computations can be significantly reduced by merely using a linear number of computations. To do this, we extract from the original complete graph, one of its spanning trees. We then compute the weights for this spanning tree in such a manner that the modified tree-based NN has approximately the same input-output characteristics, and thus the new weights are themselves calculated using a gradient-based algorithm. By a detailed experimental analysis, we show that the new linear-time AdNN-like network possesses chaotic and PR properties for different settings. As far as we know, such a tree-based AdNN has not been reported, and the results given here are novel.

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Ideal Chaotic Pattern Recognition Is Achievable: The Ideal-M-AdNN - Its Design and Properties

Qin

Oommen

2013

Transactions on Computational Collective Intelligence XI

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Abstract. This paper deals with the relatively new field of designing a Chaotic Pattern Recognition (PR) system. The benchmark of such a system is the following: First of all, one must be able to train the system with a set of "training" patterns. Subsequently, as long as there is no testing pattern, the system must be chaotic. However, if the system is, thereafter, presented with an unknown testing pattern, the behavior must ideally be as follows. If the testing pattern is not one of the trained patterns, the system must continue to be chaotic. As opposed to this, if the testing pattern is truly one of the trained patterns (or a noisy version of a trained pattern), the system must switch to being periodic, with the specific trained pattern appearing periodically at the output. This is truly an ambitious goal, with the requirement of switching from chaos to periodicity being the most demanding. Some related work has been done in this regard. The Adachi Neural Network (AdNN) [1][2][3][4][5] has properties which are pseudo-chaotic, but it also possesses limited PR characteristics. As opposed to this, the Modified Adachi Neural Network (M-AdNN) proposed by Calitoiu et al [6], is a fascinating NN which has been shown to possess the required periodicity property desirable for PR applications. However, in this paper, we shall demonstrate that the PR properties claimed in [6] are not as powerful as originally reported. Indeed, the claim of the authors of [6] is true, in that it resonates periodically for trained input patterns. But unfortunately, the M-AdNN also resonates for unknown patterns and produces these unknown patterns at the output periodically. However, we describe how the parameters of the M-AdNN for its weights, steepness and external inputs, can be specified so as to yield a new NN, which we shall refer to as the Ideal-M-AdNN.

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An analysis of associative dynamics in a chaotic neural network with external stimulation

Cited by 18 publications

References 7 publications

Chaotic simulated annealing by a neural network model with transient chaos

Chaotic simulated annealing by a neural network model with transient chaos

An Enhanced Tree-Shaped Adachi-Like Chaotic Neural Network Requiring Linear-Time Computations

Ideal Chaotic Pattern Recognition Is Achievable: The Ideal-M-AdNN - Its Design and Properties

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