Abstaining AI systems cannot guarantee both large coverage of correct answers and zero hallucination in sufficiently expressive domains, as shown by the existence of inseparable pairs in the arithmetical hierarchy.
Calibrated language models must hallucinate
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Hallucination, abstention, and computable inseparability
Abstaining AI systems cannot guarantee both large coverage of correct answers and zero hallucination in sufficiently expressive domains, as shown by the existence of inseparable pairs in the arithmetical hierarchy.