This theory is borne out by the fact that young children spend much longer sleeping than older children and adults. Babies and infants, who are acquiring information at a rate faster than at any other point during life, sleep the most. Newborn babies can sleep for anything up to 18 hours a day, and 12 hours or more is the norm for toddlers and youngsters all the way up to school age.
REM sleep in particular appears to be important for the development of the brain, especially in the young developing infant. Babies spend most of their time sleeping, and up to 80% of that time may be spent in REM sleep, whereas the older a person gets the smaller the proportion of REM sleep becomes. REM deprivation in infants has been shown to lead to developmental abnormalities later in life. It has been suggested that muscle atonia (the paralysis of the muscles during REM sleep) allows for the formation and activation of synaptic connections in the brain during this time without any potentially dangerous motor consequences.
However, as a counter-argument to this theory, many aquatic mammals (such as dolphins, whales, etc) experience little or no REM sleep in infancy, and the proportion of REM sleep in these animals actually increases as they age.