xu-2024-corollary-1-llm-cannot-self-mitigate

IN premise — summaries/2026/08/24/xu-2024-hallucination-innate-s3-hallucination-is-inevitable-for-llms.md

Created 2026-08-24T17:11:29+00:00

Corollary 1 of Xu et al. (2024) states that no computable LLM can prevent itself from hallucinating, meaning methods relying on the LLM to detect or correct its own errors (chain-of-thought, self-consistency, self-verification) cannot eliminate hallucination.

Summary

This sets a hard ceiling: no prompting strategy, self-checking loop, or internal voting mechanism can guarantee a language model will stop producing false information, because the model is the same system generating the errors it is supposed to catch. The practical upshot is that any system aiming to prevent hallucination must build its safeguards outside the model — retrieval grounding, external verification, human review — rather than trusting the model to police its own mistakes.