In A Dance With Dragons, Arya's training takes a new turn when she discovers that
even though she is blind, she can see through the eyes of a cat that she's befriended. This allows her to find out that the Kindly Man is the one who has been attacking her in the House of Black and White, which results in her being allowed to regain her sight.
However, she deliberately does not mention this to the Kindly Man. He seems exceptionally able to see through her every attempt at deception. Is there any indication that he knows about this secret, and allows it? Or has she fooled him, in which case maybe she isn't as far progressed in her training as she should be?