IANAL, but it strikes me as pretty obvious that the owner of the NN is the owner of the copyright on any works created by the NN with the important qualification that training the NN on works copyrighted by others could possibly be considered by the courts to be infringement.
In the United States, there was case that got a decent amount of publicity where the opinion was that training a model on copyrighted works is "highly transformative" and is therefore permitted under fair use.
Sure, but imagine a scenario when I use transfer learning. I download a pretrained model from OpenAI, make some tweaks, maybe train it on my own music, and have a michael jackson level triller hit?