I wonder what happens during polyphasic sleep, where you sleep multiple times per day. Of course, the amount of sleep you get each time is far less (I'm trying a three-hour nap at night, then three twenty-minute naps throughout the day), but it's entirely REM sleep [1].
REM sleep is also when "memories are consolidated" [2], so multiple REM sleeps throughout the day should drastically improve one's information retention and therefore one's learning.
Well, obviously there's not going to be any studies on such a nichey niche of a topic. There is a good way to measure memory performance, statistics kept by a spaced repetition flashcard system with a few hundred or thousands of flashcards, but the overlap between SRSers and polyphasicers seems low. The one example I know of, an Anki user on LessWrong, reported that his statistics were badly hurt during his polyphasic experiment.
If you believe that sleep's purpose is to weaken synapses/reset the brain, it's entirely possible going through less than three or four REM cycles before waking would be undesirable in that it may take more than one cycle to properly "wipe the slate clean". Granted, it's impossible to do much more than speculate at this point given the (relative) lack of research/knowledge on the topic so far.
REM sleep is also when "memories are consolidated" [2], so multiple REM sleeps throughout the day should drastically improve one's information retention and therefore one's learning.
1. http://en.wikipedia.org/wiki/REM_rebound
2. http://en.wikipedia.org/wiki/Rapid_eye_movement_sleep#Memory...