  In the recent publication (arxiv:2007.08063v2 [cs.LG]) a fast prediction
algorithm for a single recurrent network (RN) was suggested. In this manuscript
we generalize this approach to a chain of RNs and show that it can be
implemented in natural neural systems. When the network is used recursively to
predict sequence of values the proposed algorithm does not require to store the
original input sequence. It increases robustness of the new approach compared
to the standard moving/expanding window predictive procedure. We consider
requirements on trained networks that allow to implement the proposed algorithm
and discuss them in the neuroscience context.
