xu-2024-hallucination-formal-quantifier-structure
IN premise — summaries/2026/08/24/xu-2024-hallucination-innate-s2-definitions.md
Created 2026-08-24T17:11:29+00:00
Xu et al. (2024) formally define hallucination as a ∀i ∃s statement: for every training stage i, there exists some input s such that h[i](s) ≠ f(s), meaning no matter how long training continues, some input is always answered incorrectly.
Summary
Xu et al. (2024) argue that hallucination is not a fixable bug but a permanent structural property of how models are trained: no matter how long you keep training, there will always be some input the model answers wrongly. This means the system must treat hallucination as an irreducible risk rather than something that more data or more epochs will eventually eliminate, so safety and verification mechanisms need to assume errors will always be present.