Learning and generation of long-range correlated sequences

We study the capability to learn and to generate long-range, power-law corr elated sequences by a fully connected asymmetric network. The focus is set on the ability of neural networks to extract statistical features from a se quence. We demonstrate that the average power-law behavior is learnable, na mely, the sequence generated by the trained network obeys the same statisti cal behavior. The interplay between a correlated weight matrix and the sequ ence generated by such a network is explored. A weight matrix with a power- law correlation function along the vertical direction, gives rise to a sequ ence with a similar statistical behavior.