> If you paint a picture of Sonic the Hedgehog in your living room, you are technically creating an unauthorized derivative work

Is this even true? It might violate a trademark, but I don't think it would violate copyright law unless it was a copy of an existing picture.

Characters are copyrightable, its a similar situation to song compositions vs song masters. There is the copyright of the original picture/song master but separately there is the copyright of the song composition/character. Making your own work derived from the same character or song composition is still a derivative work even if it doesn't directly copy the song master/original picture.

LLMs are often framed as lossy compression, and surely converting some copyrighted Sonic the Hedgehog image from PNG to JPEG is considered copyright infringement, no?!

It's not true. You don't need "authorization" to create a derivative work. You do need a license to distribute copyrighted works, including derivatives. And this only matters when you are distributing it to a sizable audience.

For example, if you rent a movie, you can watch it with your family. Nobody is going to sue you for distributing the movie with 5 people in your room. That's pure nonsense. Same with music, books, etc.

If you try to play the movie in an establishment with dozens of people, then it can become a problem, because you're essentially a theater now.

I'm not a lawyer so I don't know what the law is on selling fan art on a convention or even privately commissioned fan artwork. But things aren't as draconian as people assume it is.

Yeah, in some countries private stuff isn't illegal at all.

It is true but meaningless. Derivative works are not illegal, and you don’t need authorisation to create one.

So if you draw sonic in your living room you are indeed creating an unauthorised derivative work. And someone can call it an unauthorised derivative work. And the only reaction that should induce is raising an eyebrow and replying “ok?”