In this paper, a multi-scale approach to spectrum sensing and information exchange in millimeter wave cognitive cellular networks is proposed. In order to overcome the huge energy cost of acquiring full network state information on the occupancy of each cell over the network, secondary users acquire local state estimates, which are aggregated up the hierarchy to produce multi-scale estimates of spectrum occupancy. The proposed design accounts for local estimation errors and the irregular interference patterns arising due to sensitivity to blockages, high attenuation, and high directionality at millimeter wave. A greedy algorithm based on agglomerative clustering is proposed to design an interference-based tree (IBT), matched to the interference pattern of the network. The proposed aggregation algorithm over IBT is shown to be much more cost efficient than acquiring full network state information from the neighboring cells, requiring as little as 1/5th of the energy cost.