Currently that is not the case:

>Mod­els in gen­eral are gen­er­ally con­sid­ered “trans­for­ma­tive works” and the copy­right own­ers of what­ever data the model was trained on have no copy­right on the mod­el. (The fact that the datasets or in­puts are copy­righted is ir­rel­e­vant, as train­ing on them is uni­ver­sally con­sid­ered fair use and trans­for­ma­tive, sim­i­lar to artists or search en­gi­nes; see the fur­ther read­ing.) The model is copy­righted to whomever cre­ated it.

Source (scroll up slightly past where it takes you): https://www.gwern.net/Faces#copyright

Thank you, this is the part I find most relevant:

"Models in general are generally considered “transformative works” and the copyright owners of whatever data the model was trained on have no copyright on the model. (The fact that the datasets or inputs are copyrighted is irrelevant, as training on them is universally considered fair use and transformative, similar to artists or search engines; see the further reading.) The model is copyrighted to whomever created it. Hence, Nvidia has copyright on the models it created but I have copyright under the models I trained (which I release under CC-0)."

But does that still hold when the model memorized a chunk of the training data? Or can a network plagiarize output while being a transformative work itself?

I bet they can claim copyright up to the gradients generated on their media, but in the end the gradients get summed up, so their contribution is lost in the cocktail.

If I write a copyrighted text on a book, then I print a million other texts on top of it, in both white an black, mixing it all up to be like white noise, would the original authors have a claim?

Models can unpredictably memorize sensitive input data, so there can be a real copyright issue here, I think.

https://arxiv.org/abs/1802.08232

Worse, sometimes the input data is illegal to distribute for other reasons than copyright.