UFC's Pitbull -- Very Brainy After Surgery

Operating room spies tell TMZ Thiago Alves just underwent an 8 hour operation to separate an artery from a vein in his brain.

Dana White tells TMZ the operation -- in a New York City hospital -- was a complete success and Pitbull's first words ... "When can I start training again?"

Dana's answer ... a couple of weeks.

We're told Pitbull will be in ICU for the next two days.