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AI professor here. I know this page is a joke, but in the interest of accuracy, a terminological comment: we don't call it a "hallucination" if a model complies exactly with what a prompt asked for and produces a prediction, exactly as requested.

Rater, "hallucinations" are spurious replacements of factual knowledge with fictional material caused by the use of statistical process (the pseudo random number generator used with the "temperature" parameter of neural transformers): token prediction without meaning representation.

[typo fixed]

I agree with your first paragraph, but not your second. Models can still hallucinate when temperature is set to zero (aka when we always choose the highest probability token from the model's output token distribution).

In my mind, hallucination is when some aspect of the model's response should be consistent with reality but is not, and the reality-inconsistent information is not directly attributable or deducible from (mis)information in the pre-training corpus.

While hallucination can be triggered by setting the temperature high, it can also be the result of many possible deficiencies in model pre- and post- training that result in the model outputting bad token probability distributions.

> In my mind, hallucination is when some aspect of the model's response should be consistent with reality

By "reality", do you mean the training corpus? Because otherwise, this seems like a strange standard. Models don't have access to "reality".