A lawyer would say this isn’t settled law. And the law concerning AI-generated products is also shaping up differently in different countries.
And I am not a lawyer, and this isn’t legal advice, but I think this question will shake out in this way.
Question 1: Can you use GPT, which trained on some copywritten material, to produce material for your book?
A: Yes, but the output has to obey fair use – any copywritten quotes need to be short, built into a larger original work, and this work cannot undermine the market value of the original copywritten material. For poetry, this isn’t a problem as long as your work is original – GPT only spits out short snippets of things, even when the prompt is of a famous poem.
There are cases where AI-generated output violates fair use. For instance, many people are using illustrator Greg Rutkowski as a prompt for Stable Diffusion’s AI generated art. Now, if you search for Mr. Rutkowski’s work on the web, you will find these knock offs AI generated art creations, but which bury Mr. Rutkowski’s work. This AI-based usage degrades the market value of his work, so violates fair use. Mr. Rutkowski needs a way of opting out from the model. (Mind you, other lesser know artists might want to opt in in order to create a buzz, so there’s no one-size-fits-all on this).
Please see: [This artist is dominating AI-generated art. And he’s not happy about it. | MIT Technology Review](https://Technology Review - This artist is dominating AI-generated art. And he’s not happy about it.)
Question 2: Having generated a book of poetry using AI, can I copyright it?
Again unsettled, but IMO that will depends on how much uniqueness you added to the process. If you just entered a prompt, “Hey, write me a poem that begins ‘In the first blue hours we dance with words.’” then no. You aren’t adding anything original, so your effort can’t be copywritten. If you created an elaborate fine-tuned model that produces startlingly new subtle rhyme schemes and metaphors, then you will be able to copywrite the model, and perhaps the output.
I liked this Verge article, which does a better job that I have on the subtleties and considerations:
[The scary truth about AI copyright is nobody knows what will happen next - The Verge](https://The Verge - The scary truth about AI copyright is nobody knows what will happen next)