But for text to be a derivative work of other text, you need to be able to know by looking at the two texts and comparing them.

Training an AI on a copyrighted work might necessarily involve making copies of the work that would be illegal to make without a license. But the output of the AI model is only going to be a for-copyright-purposes derivative work of any of the training inputs when it actually looks like one.

Did the AI regurgitate your book? Derivative work.

Did the AI spit out text that isn't particularly similar to any existing book? Which, if written by a human, would have qualified as original? Then it can't be a derivative work. It might not itself be a copyrightable product of authorship, having no real author, but it can't be secretly a derivative work in a way not detectable from the text itself.

Otherwise we open ourselves up to all sorts of claims along the lines of "That book looks original, but actually it is a derivative work of my book because I say the author actually used an AI model trained on my book to make it! Now I need to subpoena everything they ever did to try and find evidence of this having happened!"