Adaptive stochastic cellular automata: theory

Abstract The mathematical concept of cellular automata has been generalized to allow for the possibility that the uniform local interaction rules that govern conventional cellular automata are replaced by nonuniform local interaction rules which are drawn from the same probability distribution function, in order to guarantee the statistical homogeneity of the cellular automata system. Adaptation and learning in such a system can be accomplished by evolving the probability distribution function along the steepest descent direction of some objective function in a statistically unbiased way to ensure that the cellular automata's dynamical behavior approaches the desired behavior asymptotically. The proposed CA model has been shown mathematically to possess the requisite convergence property under general conditions.