Based on the recent compute-and-forward technique [1], a novel communication strategy is proposed under which functions of the channel state information are forwarded along the network. Those functions are chosen such that on the one hand, they can be efficiently forwarded, and on the other hand, they are maximally useful to the final decoder of the message. It is illustrated that there is generally a tension between these two requirements. The strategy is shown to perform well for certain classes of multilayer networks where channel state information is acquired locally at each receiver. For example, for a two-stage Gaussian relay network with local channel state information, it is shown that the proposed strategy performs optimally in a scaling-law sense, as the number of relays increases.