We draw upon a previously largely untapped literature on human collective intelligence as a source of inspiration for improving deep learning. Implicit in many algorithms that attempt to solve Deep Reinforcement Learning (DRL) tasks is the network of processors along which parameter values are shared. So far, existing approaches have implicitly utilized fully-connected networks, in which all processors are connected. However, the scientific literature on human collective intelligence suggests that complete networks may not always be the most effective information network structures for distributed search through complex spaces. Here we show that alternative topologies can improve deep neural network training: we find that sparser networks learn higher rewards faster, and at lower communication costs.