While learned is probably not the best word to use as far as describing the legality goes, I also don’t think “copied” is the right word.
Let’s say that the model “is influenced by” the copyrighted material. That seems hard to argue against.
So, now that we aren’t using the word “learned”, why would we say that the way the models are influenced by the copyrighted works that appear in the “training set” (not to imply that “training” in the usual sense is happening) counts as a copyright violation?
Or, perhaps the claim is that the outputs of the model are violating copyright?
If the output is substantially similar to some particular copyrighted work that is in the “training set”, and could work as a substitute for that work, and if the output resembling the work is in part due to the influence that the work had on the model, I think in this case it would be a clear case of violation of copyright.
However, if it doesn’t have substantial similarity to any particular copyrighted work that influenced it, only similarity to the style common to many of the works that influenced it (even if all by the same author), my impression is that this would not constitute copyright infringement because styles are not protected by copyright, only individual works.
(Now, is this unjust, in the case of it copying the style of some particular author/artist? Idk, maybe? But my impression is that copyright doesn’t protect styles, and that it probably shouldn’t protect styles in general… so I guess maybe if we had a law making a special case forbidding the (deliberate?) copying of a person’s particular style via some kind of machine learning model? Idk.)