Copyright is for things that are the result of human creativity. If the weights come from running an algorithm on a training set (that one does not have a copyright to) then how can the weights then be copyrightable? They might be a derivative work, but that just means they infringe copyright, not that they are copyrightable themselves.
Note that the requirements for copyright are not consistent between nations.
The US has the "threshold of originality" as its principle. Under that doctrine, it requires some human (and this has been emphasized many times over the years) originality in order for something to be copyrighted. It's a low bar for how original it needs to be, but it must be human (monkeys taking selfies are not human).
> Under a "sweat of the brow" doctrine, the creator of a work, even if it is completely unoriginal, is entitled to have that effort and expense protected; no one else may use such a work without permission, but must instead recreate the work by independent research or effort.
The definitive case for this in the US that set the two apart is Feist Publications, Inc., v. Rural Telephone Service Co. ( https://en.wikipedia.org/wiki/Feist_Publications,_Inc.,_v._R.... ) where it was deemed that a telephone directory is not copyrightable in the US as there is no originality in it... but under the sweat of the brow doctrine it would have been.
So the "[c]opyright is for things that are the result of human creativity" gets an "it depends" and it would be curious to see if companies that are firmly in the "models are valuable" camp go to the UK for what I believe would be a more favorable copyright protection.
... However there are other IP laws around trade secrets that may be better for it in the US (I'm not as familiar in that domain - I would be curious to find out).
A photo is presumed to be copyrightable. Even horrible photos taken by somebody without any aesthetic sense are presumed to be copyrightable. The argument (AFAIK) is that the photographer chooses the time, location, object, and tweaks various settings of the camera (exposure, aperture, etc.), and these choices are considered sufficient for a photo to be copyrightable.
How about LLMs?
The hyperparameters of LLMs are hugely important in training LLMs, as is the choice of source training data. To me the "degrees of freedom" (and hence room for "creativity") in training LLMs are larger than that of a photographer taking a photo. And as of today, training a good LLM is probably objectively harder than taking a good photo, even if we forget about hardware costs for a moment.
It's easy to convince judges and juries that copying phone numbers into a phone book doesn't require human creativity. But we're talking about the most bleeding edge tech companies producing a bleeding edge new product here. I think it's going to be really hard to convince judges and juries that making this new shiny thing doesn't require human creativity. Maybe in say 20 years when even a 10 year old can train a LLM the situation might change, but as of today, quite unlikely IMHO.
The answer would be if the weights are transformative enough, and the copyright would come from the person who decided what images to include in the training set.
The act of choosing to place images in a certain arrangement, such as a collage, can be copyrightable. The same could be said for the "act" of choosing what images to include in a training set and which parameters to use to train the model.
The legal system is not like a computer program. The line between what is "creative" and what is not concrete, but is instead up to the interpretation of the judge who rules on it.
So your phonebook modifications may or may not be considered "creative" depending on the judge and your ability to convince them. The more your modify it, the more likely you are to convince a judge it is a creative work, though.
It would depend on how transformative the work is.
There is in fact a whole art form where people cut out words from different newspapers and books, for example, and re-arrange those words to form new and interesting art.
So there are ways in which such a work would be a creative work, and ways it which it would not, and it would depend on the particular instance and example.