Going back to the magpie though, they don't have a cerebral cortex at all, yet exhibit remarkably intelligent behavior (tool usage, self-recognition). So, what's up with all the smart corvids?
A few links:
https://www.sciencedaily.com/releases/2012/10/121001151953.h...
http://www.sciencedirect.com/science/article/pii/S0960982205...
(Excuse me for the sarcasm.)
How come that primates like humans, are much smarter than the rest of the world?
Even if you have trainable brain, with neurons that can communicate with more percentage of the brain than a primates. You're still on a diet of hundreds of calories instead of thousands.
Looking at smaller animals cognitive abilities is newish. But does look like it will be going interesting places.