This work studies the recently proposed geometric monitoring (GM) method in order to reduce the amount of necessary channel state information (CSI) in network (i.e., distributed) setups. Specifically, a network of amplify-and-forward (AF) relays is studied and the GM method is appropriately adapted. The basic idea is that GM could flag time instances where CSI exchange is unnecessary and, thus, the relay network could abstain from CSI exchange. It is found that, compared to alternative approaches, our GM approach can achieve significant CSI reduction in a variety of network setups.