That is for the courts to be determined. Causal connection is there, but colours from the legal palette evolve by rules of applicable laws.
For example, if I have an LLM that had your copyrighted works in its training data, then any of its output is causally deriving from those copyrighted works of yours - it comes out painted in colour of "causally derived from ${kelseyfrog's works present in the training set}" - but whether or not it also carries the colour of "derivative of ${kelseyfrog's works...} in copyright law sense", depends on... the copyright law, and may change over time based on how that set of laws evolve.
Comments
That is for the courts to be determined. Causal connection is there, but colours from the legal palette evolve by rules of applicable laws.
For example, if I have an LLM that had your copyrighted works in its training data, then any of its output is causally deriving from those copyrighted works of yours - it comes out painted in colour of "causally derived from ${kelseyfrog's works present in the training set}" - but whether or not it also carries the colour of "derivative of ${kelseyfrog's works...} in copyright law sense", depends on... the copyright law, and may change over time based on how that set of laws evolve.