Optical implementation of an associative neural network model with a stochastic process

Ohta, Jun; Tai, Shuichi; Oita, Masaya; Kuroda, Kenichi; Kyuma, Kazuo; Hamanaka, Koichi

doi:10.1364/ao.28.002426

Cited by 9 publications

(7 citation statements)

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“…1 a random Gaussian noise qi with a SD o, to take into account the presence of noise. Neural noise in physiological systems has largely been attributed to spontaneous neural firing and the statistical variation in the number of vesicles containing neurotransmitters, such as acetylcholine, released at the synaptic junctions (24)(25)(26)(27) (11)(12)(13)(14)(15)(16)(17), noise may result from electrical, thermal, and quantum fluctuations. The updating rule in the present model is as follows (see Fig.…”

Section: Basic Formulationmentioning

confidence: 99%

“…Although this type of phenomenon occurs on a time scale of seconds and firings of action potentials occur on a time scale of tens of miniseconds, its existence supports the view of neuronal response with hysteresis in the sense that neuronal excitability does depend on the firing history of a neuron and neurons that have fired more frequently show higher excitability. IMPLEMENTATIONS OF THE PRESENT NEURAL NETWORK MODEL Models of neural networks have been implemented through various physical devices (11)(12)(13)(14)(15)(16)(17). An artificial neuron usually consists of an input device, a threshold element, and an output device.…”

Section: Neurophysiological Evidence For Hysteresis In a Single Neuronmentioning

confidence: 99%

“…An artificial neuron usually consists of an input device, a threshold element, and an output device. For instance, in implementations involving optical devices, the action potentials are represented by laser beams, the synapses are implemented by memory masks (13)(14)(15)(16) and holographic elements (17), whereas dynamical updating is performed through feedback loops. The nonlinear electronic and optical devices used so far as threshold elements show no hysteresis in the input-output response function (11)(12)(13)(14)(15)(16)(17).…”

Section: Neurophysiological Evidence For Hysteresis In a Single Neuronmentioning

confidence: 99%

“…For instance, optical implementations of the present neural network model can be achieved by replacing the thresholding devices in refs. [13][14][15][16] by ZnSe interference filters (44,45). A variable noise can be easily added to the laser system.…”

Section: Neurophysiological Evidence For Hysteresis In a Single Neuronmentioning

confidence: 99%

“…[151 [16] where the noise threshold o-c increases with the width of the bistable region, and hence so does Pmax(N).…”

mentioning

confidence: 99%

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Synchronous neural networks of nonlinear threshold elements with hysteresis.

Wang

Ross

1990

Proc. Natl. Acad. Sci. U.S.A.

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We use Hoffmann's suggestion [Hoffmann, G. W. (1986) J. Theor. Biol. 122, 33-67] ofhysteresis in a single neuron level and determine its consequences in a synchronous network made of such neurons. We show that the overall retrieval ability in the presence of noise and the memory capacity of the network in the present model are better than in conventional models without such hysteresis. Second-order interaction further improves the retrieval ability of the network and causes hysteresis in the retrieval-noise curve for any arbitrary width of the bistable region. The convergence rate is increased by the hysteresis at high noise levels but is reduced by the hysteresis at low noise levels. Explicit formulae are given for calculations of average final convergence and noise threshold as functions of the width of the bistable region. There is neurophysiological evidence for hysteresis in single neurons, and we propose optical implementations of the present model by using ZnSe interference filters to test the predictions of the theory.(22) in conventional neural network models of associative memory (4-6). The dynamics in the present model is different, however; the input-output response functions for both the conventional and the present model are given in Figs. 1 and 2, respectively. In the conventional model, hysteresis does not exist in the neuronal response function (see Fig. 1). For simplicity, we focus on the discrete case shown by Fig. 2A, and we consider a synchronous updating algorithm (4,8,20,21).Suppose thatis the total input signal for the ith neuron, where Sj(t) represents the state of the jth neuron at time t,Neural networks (1-21) have become the focus of considerable research effort recently (for recent reviews on neural networks, see refs. 1-3). These seemingly simple systems show intriguing properties such as learning, memory, and fault-tolerant information retrieval. Two key features of a neural network model are (i) the properties of each individual neuron and (ii) the connectivity between neurons. Variations in either the properties of a single neuron or synaptic correlations among neurons are expected to alter the emergent characteristics of the neural network.In the present paper, we consider theoretically a feature new to conventional synchronous neural networks of associative memory-that is, nonlinear threshold elements with hysteresis. The existence of hysteresis at the level of a single neuron has been recently proposed by Hoffmann (18) in a neural network model based on the analogy with the immune system. The purpose of our present paper is to adopt and apply Hoffmann's suggestion of hysteresis at a single neuron level and determine its consequences in a synchronous neural network. We show that the retrieval property in the presence of noise and the memory capacity of the network in the present model are better than that of conventional synchronous models, where it has been assumed that there is no such hysteresis. Inclusion of higher-order interaction further improves these adva...

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