It has been proven that recurrent neural networks are Turing complete [0]. So for every computable function, there is a neural network that computes it. That doesn't say anything about size or efficiency, but in principle this allows neural networks to simulate a wide range of intelligent and creative behavior, including the kind of extrapolation you're talking about.
reply[0] https://www.sciencedirect.com/science/article/pii/S002200008...
I think you cannot take the step from any turing machine being representable as a neural network to say anything about the prowess of learned neural networks instead of specifically crafted ones.
replyI think a good example are calculations or counting letters: it's trivial to write turing machines doing that correctly, so you could create neural networks, that do just that. From LLM we know that they are bad at those tasks.
Turing conpleteness is not associated with crativity or intelligence in any ateaightforward manner. One cannot unconditionally imply the other.
reply