Learning Connectivity Structure in a Chain of Network Motifs

The synchronization of oscillatory activity in networks of networks is usually implemented through coupling the state variables describing the dynamics of each network. Here we study another but complementary mechanism of synchronization in unidirectional chains of network motifs based on a learning process. A driver motif, acting as a teacher, exhibits winner-less competition dynamics, while a driven motif, a learner, tunes its internal couplings according to the observed oscillations in the teacher. We show that under appropriate training learner network motifs in a chain can progressively “copy” the connectivity pattern of the teacher (first motif). In average the time interval required for pattern replication grows linearly with the chain size, hence the learning process does not blow up and at the end we observe phase synchronized oscillations along the chain. We also show that in a learning chain closed into a ring the network motifs come to a “consensus,” i.e., to a state with the same connectivity pattern corresponding to the mean initial pattern averaged over all network motifs.