Synapse efficiency diverges due to synaptic pruning following overgrowth

In the development of the brain, it is known that synapses are pruned following overgrowth. This pruning following overgrowth seems to be a universal phenomenon that occurs in almost all areas-visual cortex, motor area, association area, and so on. It has been shown numerically that the synapse efficiency is increased by systematic deletion. We discuss the synapse efficiency to evaluate the effect of pruning following overgrowth, and analytically show that the synapse efficiency diverges as O(|ln c|) at the limit where connecting rate c is extremely small. Under a fixed synapse number criterion, the optimal connecting rate, which maximizes memory performance, exists.