Optical neural network based on the parametrical four-wave mixing process

Abstract

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.

An Effective Associative Memory for Pattern Recognition

“…Otherwise, PNN fails to recognize the pattern X m . According to the Chebyshev-Chernov method [10] (for such problems it is described comprehensively in [4]- [6], [9]) the probability of recognition failure is…”

“…Let us described the parametrical neural network (PNN) [4]- [6]. We consider fully connected neural network of n vector-neurons (spins).…”

“…We offer a simple and effective algorithm that allows us to recognize a great number of highly correlated binary patterns even under heavy noise conditions. We use a parametrical neural network [4]- [6] that is a fully connected vector neural network similar to the Potts-glass network [7] or optical network [8], [9]. The point of the approach is given below.…”

Vector-neuron models of associative memory

“…The evolution of the system consists of consequent changes of orientations of vector-neurons according to the rule (18). The necessary and sufficient conditions for a configuration X to be a fixed point is fulfillment of the set of inequalities:…”

“…We worked out the vector formalism -universal description of PNN, not related directly to the optical model [18]- [20]. This formalism proved to be useful also for clear description of PGNN, although initially it was formulated in absolutely another terms.…”