ISSN 1060-992X, Optical Memory and Neural Networks (Information Optics), 2010, Vol. 19, No. 1, pp. 31–38. © Allerton Press, Inc., 2010. 31 1 1. INTRODUCTION Today, though there is a tendency of change of program emulation to program-hardware realization of neural network algorithms and models with rapid increase of number of neural chips VLSIC elaboration, in hardware realizations either outdated neural paradigms and simplified models or traditional computing systems and electronic technologies are used [1]. Neural nets are specific parallel computing structures and are characterized by a great number of connections. That is why the effective realizations of neural nets must be oriented first of all on quick, high efficient processing of inter-neural connection [2]. In dig- ital neural chips and electronic neural processors, oriented on basic calculating operation of neural nets— multiplying of vector by matrix, the efficiency of 10 8 –10 10 connections per second and high 16-bit digital accuracy are already achieved. But the number of imitated neurons is not higher than 500–1000 [3]. And for the problems, oriented on image processing, building of associative memory, such dimension of vectors does not suit. Optical ANNs have important feature of spatial recognition of 2-D images. Those ANNs are built on the basis of optical Fourier correlators with inverse connections [4, 5]. The holographic mem- ory devices are known, being devices with Fourier-transformation [6]. Now much attention is paid to the creation of optical AM on the neural network principles, based on adequate ANN models, with bipolar and unipolar signal coding [7–12]. Most often neural paradigms of non-iterative type are used in them, which are the development of Hopfield network or its modification The other non-iterative neural para- digm—two-sided associative memory [13], being a two-layer modification of Hopfield networks, found its application and optical realization [14, 15]. The works [7, 8], and especially [16–19] solve the problem of increase of capacity in ANN and AM, even at storing of greatly correlated images, and the problem of convergence of methods and training rules, using multilevel representation of signals. The use of operations of neural logic—equivalence and nonequivalence for building of ANN and AM models is common for works [16–18]. In this connection such models of ANN and AM and the theory were called “equivalental”. They showed, that such equiv- alental models are more general (Hopfield networks are their particular case) and enable to describe and 1 The article is published in the original. The Structures of Optical Neural Nets Based on New Matrix-Tensor Equivalental Models (MTEMs) and Results of Modeling 1 V. G. Krasilenko, A. I. Nikolskyy, and J. A. Flavitskaya The Vinnitsa Social Economic Institute of University “Ukraine”, Vinnitsa National Technical University e-mail: krasilenko@mail.ru, nikolsky@vstu.vinnica.ua Received October 30, 2009; in final form, November 30, 2009 Abstract—The structures of optical neural nets (NN) based on new matrix-tensor equivalental models (MTEMs) and algorithms are described in this article. MTE models are neuroparadigm of non-itera- tive type, which is a generalization of Hopfield and Hamming networks. The adaptive multi-layer net- works, auto-associative and hetero-associative memory of 2-D images of high order can be built on the basis of MTEMs. The capacity of such networks in comparison with capacity of Hopfield networks is increased (including capacity for greatly correlated images). The results of modeling show that the number of neurons in neural network MTEMs is 10–20 thousand and more. The problems of training of such networks, different modifications, including networks with double adaptive-equivalental auto- weighing of weights, organization of computing process in different modes of network are discussed. The basic components of networks: matrix-tensor “equivalentors” and variants of their realization on the basis of liquid-crystal structures and optical multipliers with spatial and time integration are con- sidered. The efficiency of proposed optical neural networks on the basis of MTEMs is evaluated for both variants on the level of 10 9 connections per second. Modified optical connections are realized as liquid-crystal television screens. DOI: 10.3103/S1060992X10010054