<title>Holographic correlator with thin holograms as an optical neural network</title>

Abstract

11 is shown that a holographic correlator with thin holograms application can be regarded as an optical neural network based on the outer product model. This network has a complete array of interconnections. Two versions of optical neural networks based on holographic correlators with interconnections, fixed in different places are presented. 1 . Introduction Numerous models of neural networks (NN) have been proposed as research and application tools. The most advanced model is the external product algorithm of McCulloch and Pitts [1] which has been extended by Metropolis et al. who introduced fluctuation dynamics and threshold switchings of neurons [2] . The algorithm has been further improved by Grossberg and Hopfield [3, 4]. A discrete model is described by the equation Y=NL(TX),where : and V are vectors which describe the neuron states of the input and output layers, T is the interconnection tensor which stores the learning results, and NL is a nonlinear operator. The energy of such a system is E=-2TXY, (2) and the interconnection array is described by a set of learning patterns (3) A continuous NN model which is not essentially different from a discrete model is described by nonlinear Lagrange differential equations and recognise the limited responses of neurons and interconnections and fluctuating noise sources. Technically, the structure of such a network can be represented as an input and an output layer of neurons, each connected with all the others. The network learns by using a set of patterns which stand for some interconnections with specified weights. When it is subjected to the action of an input stimulus, an NN relaxes towards 0819442244/93/$6.OO SPIE Vol. 1978 / 237 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/24/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx