SHOT-NOISE-LIMITED PERFORMANCE OF OPTICAL NEURAL NETWORKS

The performance of neural networks for which weights and signals are m odeled by shot-noise processes is considered, Examples of such network s are optical neural networks and biological systems, We develop a the ory that facilitates the computation of the average probability of err or in binary-input/binary-output multistage and recurrent networks, We express the probability of error in terms of two key parameters: the computing-noise parameter and the weight recording noise parameter, Th e former is the average number of particles per clock cycle per signal and it represents noise due the particle nature of the signal, The la tter represents noise in the weight-recording process and is the avera ge number of particles per weight, For a fixed computing-noise paramet er, the probability of error decreases with the increase in the record ing-noise parameter and saturates at a level limited by the computing- noise parameter, A similar behavior is observed when the role of the t wo parameters is interchanged, As both parameters increase, the probab ility of error decreases to zero exponentially fast at a rate that is determined using large deviations, We show that the performance can be optimized by a selective choice of the nonlinearity threshold levels. For recurrent networks, as the number of iterations increases, the pr obability of error increases initially and then saturates at a level d etermined by the stationary distribution of a Markov chain.