> The 'inputs' are the random numbers. Not the training data.
You're dodging. The inputs to the neural network are clearly the training images, they don't just disappear. The outputs are derived works, at least.
> They don't produce a copy of an existing work, any more than a human trained on looking at faces is producing a copy and 'stealing other people's lifework' (without even paying them a cent! how dare they), unless it's so similar to serve as a substitute (among other considerations).
I'm not talking about the faces, I'm talking about CNNs in general. Surely these faces all look like generic anime faces, because that's what you trained on. On the other hand, if you trained on the works of Van Gogh with his very distinctive style, that would easily be discernible.
Also, the very fact that it is not a human doing this task is very relevant for copyright, as you point out yourself.
Note that I'm not saying this is illegal or that this violates copyright, I'm saying that there is no case law on this, so you can't just claim that there is no issue here. It's undecided. It comes down to the intention behind copyright. Furthermore, even if you can dodge copyright law, you may not be able to dodge trademark law.
> In contrast, if you look at the faces, most of them don't have even a remotely similar exemplar in the dataset (you can do nearest-neighbor lookups using features or pixels, and GAN papers often do to demonstrate that they are not just 'memorizing' - I discuss this in my FAQ section).
Again, your argument fails the general case. Overfitting and memorizing is a problem when working with CNNs. Some CNNs may just literally copy - and visibly so. At which point are you not just literally copying? What's the "legal threshold" here? It would have to be decided on a case-by-case basis, just like a "fair use" defense.