Abstract. The problem of training feedforward neural networks is considered. To solve it, new algorithms are proposed. They are based on the asymptotic analysis of extended Kalman filter (EKF) and on a separable network structure. Linear weights are interpreted as diffusion random variables with zero expectation and covariance matrix proportional to an arbitrarily large parameter λ. Asymptotic expressions as λ→∞ for the EKF are derived. They are called diffusion learning algorithms (DLA). It is shown that they, unlike their prototype EKF with large yet finite λ are robust with respect to the accumulation of rounding errors and that under certain simplifying assumptions, the ELM (extreme learning machine) algorithm follows from the DLA. A numerical example shows that the accuracy of the DLA may be higher than that of the ELM algorithm.

Keywords: feedforward neural network, learning algorithm, extended Kalman filter.