Let's use J.K. Rowlings and Shakespeare as an example. I want to train an A.I. to produce stories that look like a mix of both author's styles. The real example should use over 40 different authors, but let's stick just to these.
The text produced by the A.I. won't have any identifiable content, like fictional places, character names, or anything that would classify it as derivative work. They won't even go into the training data, as a quick find-replace operation can change them for tokens in the text.
As I understand, this is like me reading H.P. books to my nephew in a private setting. Since I bought the paperback books, I'm allowed to do that.
The A.I. also won't hold a copy of the original works after training. It might write something close to it, like a story about a wizard school, but it should different enough to be considered original work.
Does it fall under fair use? If this is forbidden, is there any case law or legislation covering it?