Is there a correlation between how intelligent an animal is at birth vs how intelligent it will get?

I.E:

Human = Dumb and highly incapable of anything at birth, but have the largest maximum potential for intelligence. The transition from lowest intellectual capacity to maximum is slow.

Deer = Smarter/more capable than human baby at birth, but have a lower maximum intelligence potential. The transition from lowest intellectual capacity to max is moderately quick.

Spider = Born completely capable and self-sufficient, but doesn’t get any smarter. Transition from low intelligence to max is basically non-existent.

Apply this correlation to other species. I can’t think of a one that, presumably, doesn’t fit the mold.
Obviously intelligence and capacity are difficult to quantify

It’s as if, the less capable at birth and the slower the climb to maximum intelligence, the higher the maximum potential is; and vise-versa.

If it helps to think of it like this: Imagine each species on a graph where ‘y’ is capacity and ‘x’ is time.
Pick 2 animals, make 2 separate graphs, then lay them on top of one another.

Or am I just being crazy?