I was fascinated by the book Matilda as a child (by Roald Dahl) but never did I dream I would have my own little "Matilda."
They later turned it into a movie although the book was better. There was no "training" involved, her parents were just vile and prized television instead. Her character was just a natural precocious reader at 3 or 4 years old IIRC. As a fellow bookworm, I was so captivated by the book although I
knew it was impossible for a child that young to be able to read.
That's the only one I know of.