Conditional convergence of photorefractive perceptron learning

We consider the convergence characteristics of a perceptron learning algorithm, taking into account the decay of photorefractive holograms during the process of interconnection weight changes. As a result of the hologram erasure, the convergence of the learning process is dependent on the exposure time during the weight changes. A mathematical proof of the conditional convergence, perceptrons, is presented and discussed. as well as computer simulations of the photorefractive It is well known that the iterations in the percep-tron learning algorithm will converge, leading to a final weight vector (or matrix), provided that such a solution exists.1 Recently the perceptron learn-ing algorithm was implemented by optical intercon-nection with photorefractive holograms.2-5 In the optical implementation, the weight vector w is rep-resented by the holograms in photorefractive crystals (e.g., LiNbO3). The weight vector can be modified by addition or subtraction of hologram components according to the learning algorithm. Holograms pre-viously stored in photorefractive media are subject to erasure during the training cycles. Thus the percep-tron learning algorithm in photorefractive media is modified as w(k + 1) = w(k)exp[-Ior(k)Jt/r] of the photorefractive perceptron and present what is to our knowledge the first theoretical proof of the conditional convergence. We discover that the pho-torefractive perceptron learning algorithm according to Eq. (1) will converge, provided that the exposure time is sufficiently small relative to the hologram decay time constant. In addition to the theoretical proof of the conditional convergence, we also present and discuss the results of our computer simulation. To prove the conditional convergence, we redefine the set of training patterns a