I predict A.I. trained on LOTR will be found to be infringing because it's a derivative work unless the court determines that use of the original work constitutes a fair use.

My general point in my intentionally silly brain metaphor is brain metaphors are inapplicable and unconvincing.

Okay, but that's just a prediction, not an argument. I don't agree with the prediction. I think it makes some sense to think about the AI training data on analogy with memories, because they contain impressions of a thing without being able to reproduce it exactly. They can both be the source of both real creativity as well as the source of infringing works.

I don't see an argument for considering the training data produced by AI training a derivative work, at least not in any copyrightable sense. ChatGPT is "software"; the training data that it operates on is not "software" in the strictest sense and exists in an uncomfortable middle space at present with respect to copyright law. That's what the memory analogy is supposed to show: just like human memories aren't subject to copyright, AI training data that is similar in structure and capabilities to human memories is likewise not subject to copyright. More precisely, my point is that that's one entirely reasonable way courts could rule: AI training data represents "fair use" of its sources (provided they are legally obtained of course), but the products of an AI trained on those sources might not be.

It also has no precedent in it's favor. As far as I know no court has ever used "Is it like a brain?" to settle a copyright issue.