Additive neural networks and periodic patterns

In this contribution we discuss weight selection which allows additive neural networks to represent certain periodic patterns. Given a periodic set of vectors V(l) whose components are v(i)(l)=+/-1 we measure correlation between i-th and j-th components of V(l) in time l. We show that in the additive neural net with weights chosen based on this correlation, almost all trajectories converge to a periodic orbit, which consecutively visit orthants, determined by the vectors V(l).We also construct two weights selection processes, one discrete in time and one continuous in time, which construct the desired weights dynamically.