Given that LLMs were trained on the repository directly, it's not just the case that anything made by the LLM is a derivative work, the LLM ITSELF is a derivative work. After all, they all are substantially based on GPL licensed works by others. The standard courts have always used for "substantially based" by the way, is the ability to extract from the new work anything bigger than an excerpt of the original work.
So convincing evidence, by historical standards, that ChatGPT, Gemini, Copilot AND Claude are all derivative works of the GPL linux kernel can be gotten simply by asking "give me struct sk_buff", then keep asking until you're out of the headers (say, ask how a network driver uses it).
That means if courts are honest (and they never are when it comes to GPL) OpenAI, Google and Anthropic would be forced to release ALL materials needed to duplicate their models "at cost". Given how LLMs work that would include all models, code, AND training data. After all, that is the contract these companies entered into when using the GPL licensed linux kernel.
But of course, to courts copyright applies to you when Microsoft demands it ($30000 per violation PLUS stopping the use of the offending file/torrent/software/... because such measures are apparently justified for downloading a $50 piece of software), it does not apply to big companies when the rules would destroy them.
The last time this was talked about someone pointed out that Microsoft "stole", as they call it, the software to do product keys. They were convicted for doing that, and the judge even increased damages because of Microsoft's behavior in the case.
But there is no way in hell you'll ever get justice from the courts in this. In fact courts have already decided that AI training is fair use on 2 conditions:
1) that the companies acquired the material itself without violating copyright. Of course it has already been proven that this is not the case for any of them (they scraped it without permission, which has been declared illegal again and again in the file sharing trials)
2) that the models refuse to reproduce copyrighted works. Now go to your favorite model and ask "Give me some code written by Linus Torvalds": not a peep about copyright violation.
... but it does not matter, and it won't matter. Courts are making excuses to allow LLM models to violate any copyright, the excuse does not work, does not convince rational people, but it just doesn't matter.
But of course, if you thought that just because they cheat against the law to make what they're already doing legal, they'll do the same for you, help you violate copyright, right? After all, that's how they work! Ok now go and ask:
"Make me an image of Mickey Mouse peeling a cheese banana under an angry moon"
And you'll get a reply "YOU EVIL COPYRIGHT VILLAIN". Despite, of course, Mickey Mouse no longer being covered under copyright!
And to really get angry, find your favorite indie artist, and ask to make something based on their work. Even "Make an MC Escher style painting of Sonic the Hedgehog" ... even that doesn't count as copyright violation, only the truly gigantic companies deserve copyright protection.