I suppose, though, since season 3 established that walkers can "starve" if they don't eat enough (they just starve really slowly), then perhaps the walkers are capable of more. If they need to eat, then they're still alive, and if they're still alive, then maybe they can learn. That'd be scary - a smart zombie.
Did they? Because they've also shown the zombies have no biological "need" other than brain activity and even then only on the most basic level. We've seen zombies who've sustained massive damage to internal organs and even some with missing lower torsos so clearly they have no biological activity or "need" to eat.