Though some of the effects are clearly physiological, i think it also the fact that eating less interferes with the need for immediate full satisfaction. That gap might as well be utilized in better ways (such as in this context improving memory). No wonder that one of the best rock songs is dubbed 'i can't get no satisfaction'...

Nature is amazing! Naturally not eating enough will increase brain power, because nature, when something is lacking, compensates by increasing something else that will get you what you need. In this case, nature finds that you're too stupid to get enough food the way you are, so... it makes you smarter, then maybe you can get enough to eat, you stupid moron!

"It takes a special kind of stupid to forget to eat." - Rita Rudner

Me not sure. I no eat lots and me smart! See, it be true then.