> It's not a copy of it, and when you distribute it you're not distributing the original.
A compressed (or normally encrypted) version wouldn't be a copy that way, either, but I would still absolutely go down for distributing it. The difference is that the compression can be reversed to recover the original. Even lossy compression would create such a close derivative that nobody would probably even bother to make the distinction.
You're right that "math games" don't work in the law, but that cuts both ways. If you do something that truly makes the original unrecoverable and in fact undetectable, and if nothing salient to the legal issues at hand about the new version derives from the original, then judges are going to "see through" the "math trick" of pretending that it is a derivative.
> then Google snippets/thumbnails would be derivatives of its search results
Thumbnails are legally derivative works, in the US and probably most other places. In the US, they're protected by the fair use defense, and in other places they're protected by whatever carveouts those places have. But that doesn't mean they're not derivative works.
In fact, if I remember the US "taxonomy" correctly, thumbnails are infringing. It's just that certain kinds of ingfringement are accepted because they're fair use.
If thumbnails weren't derivative works at all, then the question of fair use wouldn't arise, because there can be no infringement to begin with if the putatively infringing work isn't either derivative or a direct copy.
Where thumbnails are different from ML models is that they're clearly works of authorship. In a thumbnail, you can directly see many of the elements that the author put into the original image it's derived from.
The questions are (a) whether ML models are works of authorship to begin with (I say they're not), and (b) whether something that's not a work of authorship can still be a derivative work for purposes of copyright infringment (I'm not sure about that).
So far as I know, neither one is the subject of either explicit legislation or definitive precedent in most of the world, including the US.