Research with humans and primates shows that the developmental course
of the brain involves synaptic overgrowth followed by marked selective
pruning. Previous explanations have suggested that this intriguing, s
eemingly wasteful phenomenon is utilized to remove ''erroneous'' synap
ses. We prove that this interpretation is wrong if synapses are Hebbia
n. Under limited metabolic energy resources restricting the amount and
strength of synapses, we show that memory performance is maximized if
synapses are first overgrown and then pruned following optimal ''mini
mal-value'' deletion. This optimal strategy leads to interesting insig
hts concerning childhood amnesia.