> There’s no question these neural networks and their output are derivative works.
In the two US cases we have any progress on so far, the established requirement for substantial similarity (opposed to "dependant on" or such) has been upheld, with Judge Vince Chhabria specifically setting out that it'd "have to mean that if you put the Llama language model next to Sarah Silverman's book, you would say they're similar". and Judge William H. Orrick agreeing with the defendants that "plaintiffs cannot plausibly allege the Output Images are substantially similar or re-present protected aspects of copyrighted Training Images, especially in light of plaintiffs’ admission that Output Images are unlikely to look like the Training Images".
The UK definition of derivative works is, to my understanding, narrower and specifically enumerated as opposed to the US's more open-ended definition.
The remaining area of doubt, assuming the above remains consistent, is over the transient copying that occurs during training.