[fnordpiglet]

It can only approximate any function for which it’s seen data in the local feature spaces of the function. For anything it’s not seen features for it will do some maladapted interpolation through the feature space it has been trained on. It can’t be creative or synthesize a novel technique based on some more abstract reasoning over the new regime - it literally must attempt to fit its past observations as best it can to the new regime. Humans certainly do that too, but they are also able to step back and synthesize completely new behaviors given completely new data that isn’t just adapting old behavior based on some optimization function telling it that behavior is most appropriate in the new situation.

People are confused because interpolation is actually fairly powerful and is often entirely sufficient. Especially with the GPT4 model it’s so well trained with such a large and varied corpus that it is able to handle many things well, even unexpected things, and seems like it is extrapolating at times. But it still hallucinates, and these are the most obvious symptoms of its inability to extrapolate. It’s just fitting within its trained vector space as best it can.