Contemporary deep neural network based classification sys-tems are typically designed to learn information at a singlelevel of granularity from datasets in which all items occur withequal frequency. Humans, on the other hand, acquire informa-tion at several different levels of granularity from experiencesthat contain some items more frequently than others. This al-lows us to learn and differentiate frequent items better fromother items. We investigate the consequence of learning froma natural frequency/multi-level dataset in a deep neural net-work designed to model the human neocortex, complementedin some simulations with a replay buffer, playing the role ofthe human hippocampus. The NC network, when trained onits own, is able to learn more frequent items relatively quicklyand differentiate them better from other items, as human learn-ers do. However, the network’s performance on infrequentand unseen examples pays a price in generalization perfor-mance compared to a standard training regime. The replaybuffer serves to ameliorate these deficiencies, and we intro-duce a computationally and psychologically motivated replayweighting scheme that performs better than two alternatives.