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The storage capacity of the Hopfield model is about 15% of the network size. It can be increased significantly in the Potts-glass model of the associative memory only. In this model neurons can be in more than two different states. We show that even greater storage capacity can be achieved in the parametrical neural network (PNN) that is based on the parametrical four-wave mixing process that is well-known in nonlinear optics. We present a uniform formalism allowing us to describe both PNN and the Potts-glass associative memory. To estimate the storage capacity we use the Chebyshev-Chernov statistical technique.

Neuron models of associative memory provide a new and prospective technology for reliable date storage and patterns recognition. However, even when the patterns are uncorrelated, the efficiency of most known models of associative memory is low. We developed a new version of associative memory with record characteristics of its storage capacity and noise immunity, which, in addition, is effective when recognizing correlated patterns.

We suggest an effective and simple algorithm providing a polynomial storage capacity of a network of the form 1 2 + s N M~, where N is the dimension of the stored binary patterns. In this problem the value of the free parameter s is restricted by the inequalities. The algorithm allows us to identify a large number of highly distorted similar patterns. The negative influence of correlations of the patterns is suppressed by choosing a sufficiently large value of the parameter s. We show the efficiency of the algorithm by the example of a perceptron identifier, but it also can be used to increase the storage capacity of full connected systems of associative memory. 1.IntroductionVector models of neural networks were investigated in a lot of papers [1][2][3][4][5][6][7][8][9][10][11]. Among them the most well-known is the Potts spin-glass model [4]. Its properties were investigated rather well by means of the statistical physics methods [5][6][7][8][9]. The characteristics of the memory of the Potts model were analyzed with the aid of computer simulations mainly. In [1-3], as well as in the series of the following papers [9-11], the so called parametrical neural network directed at realization in the form of an optical device, was investigated. In the last case rather simple analytical expressions describing its efficiency, storage capacity and noise immunity were obtained.The analysis of vector neural networks showed that they had an extremely large storage capacity, which was much higher than in the widely known binary models of the Hopfield type. In addition they have an extremely large noise immunity and the ability for recognition in the presence of very large distortions. At the present parametrical vector models of the associative memory are the best both with regard to the storage capacity and noise immunity. In the same time such high parameters of the aforementioned models were practically not used up to now, as well as other models of the associative memory. Moreover, for a lot of people the vector associative memory was related to the processing of the colored images only.The situation changed after the publication of the paper [3], where the algorithm of mapping of binary patterns into q-valued ones was proposed. It was also shown in [3] that such mapping allows one to use vector neural networks for storing and processing of signals of any type and any dimension. Moreover, the mapping brings to nothing the main difficulty of all the associative memory systems, which is the negative influence of correlations between the patterns. Thus, in the

In this paper we develop a formalism allowing us to describe operating of a network based on the paramwid four-wave mixing process that is well-known in nonlinear optics. The recognition power of a network using parametric neurons operating with q different frequencies is considered. It is shown that the storage capacity of such a network is higher compared with the Potts-glass models.