hallucination-formal-definition-computable-inconsistency
IN premise — summaries/2026/08/24/xu-2024-hallucination-innate-s1-introduction.md
Created 2026-08-24T17:11:29+00:00
In Xu et al. (2024), hallucination is formally defined as an inconsistency between a computable LLM's output and a computable ground-truth function's output on the same input string, requiring both the model and the truth function to be computable for the argument to hold
Summary
This sets a strict technical bar for what counts as a hallucination: the model's output must concretely disagree with a well-defined, algorithmically-computable answer key on the exact same input, rather than just being vague, unhelpful, or wrong in some fuzzy sense. In practice, that makes the definition formally checkable but also narrow, since it only applies when both the model and the "correct answer" can be expressed as procedures a computer can actually run.