A derivative work is a work that itself includes copyrighted content from the original work.
That is to say that for something to be a derivative work, some measure of its content must be "CTRL-C, CTRL-V" from the originating work.
Something that's merely inspired by another work, or draws underlying themes or factual knowledge from it, is not a derivative work.
> A training set is just an anthology,
Which might make the training set itself a derivative work, but works created by using the model trained on that anthology are a different matter.
> and the training process is condensation.
No, it isn't. It's the creation of a new work that represents patterns extrapolated or interpolated from the data set, without the resulting model actually including any of the copyrighted elements of the work.
The underlying ideas and facts in the original work were never protected by copyright. Only the specific fixed form of expression is copyrightable.
Someone who looks at a dozen code examples in public repos to learn how to do e.g. a quick sort, then upon understanding the logic flow of the quick sort algorithm, writes his own quick sort implementation is not creating a derivative work of the code in the repos he exampled. And the way LLMs work is much more similar to that process than to the "compressed anthology" concept you're describing.
