This is just a sleight of hand with definitions.

This is quite a specific sense, and isn't equal to just any kind of "unsustainable" system. Things can be unsustainable for reasons other than being a pyramid scheme relying on rapidly growing numbers of people being brought in by the ones already in the system.

See: Learning in High Dimension Always Amounts to Extrapolation Randall Balestriero, Jerome Pesenti, Yann LeCun https://arxiv.org/abs/2110.09485

I guess you mean by "interpolation" that it's some kind of nonlinear combination of the training data, but that's an almost vacuous statement. Any input-output relationship has to be so by definition.

Or perhaps you mean that interpolation is when the test input comes from the same distribution as the training input (though this is not technically the meaning of "interpolation"). But this is also quite difficult to pin down.

I agree that hallucination isn't some kind of "different" operation than "normal". It's not like when a train derails and you can point to it. It just operates as normal and sometimes that yields correct factual outputs, sometimes not. You don't have to metaphysically ascribe any kind of intent to it.

I'm not sure how people conceptualize these things who weren't doing classical machine learning before all this. To me, "hallucination" is shorthand, and we know it's not like humans on drugs or something. It was used in the literature also for any kind of generative imputing of missing information from a learned prior. For example in image inpainting a GAN "hallucinates" the missing part of the image. This terminology was already used in the 2010s and probably earlier. Or in image colorization of grayscale photos, the model "hallucinates" the color information.

Then the word escaped into the mainstream and people have weird connotations about it.

I'd say a hallucination (very misleading word) or confabulation or "making shit up" happens when an LLM uses factual / evidential language purely based on local statistical expectations of the text, instead of it drawing from actual evidence in its context pointing to it.

This is murkier in the case of general knowledge questions, like when and where was some famous person born. It may then be a spectrum from fully making something up based on how the name sounds, all the way to confidently retrieving it from its weights correctly. In between, we can get hallucinations. But newer models are taught to use Web Search when unsure, and it works pretty well, though not perfectly. I don't see any fundamental limit here. It's just not perfect. Trying to solve "the hallucination problem" is basically like saying "our dog vs. cat classifier is pretty good already with its 99% accuracy, now all we need to do is the tiny little task of eliminating the 1% error, and we will be golden". Like, no shit, there is some error yes. People are working to reduce it. It will never be absolutely 100%. It's not an insight to say we should remove hallucinations.