xu-2024-theorem-e3-positive-result
IN premise — summaries/2026/08/24/xu-2024-hallucination-innate-sA-appendix.md
Created 2026-08-24T17:11:30+00:00
For any computably enumerable set of total computable functions, there exists an LLM that can be hallucination-free on all functions in that set given sufficient training samples, establishing that LLMs can be reliable on specific well-structured task classes.
Summary
This is a positive guarantee: for any specific, well-structured family of tasks that can be clearly enumerated, there is in principle an LLM configuration that will answer every task in that family correctly without fabricating, as long as it gets enough training data. The practical takeaway is that hallucination is not an inherent, unsolvable flaw of LLMs in general, but a failure that can be engineered away for particular task classes by choosing the right model and data.