# Hallucination is Inevitable for LLMs with the Open World Assumption

arXiv: https://arxiv.org/abs/2510.05116 · HTML: https://mlsanity.com/paper/2510.05116/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 16 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 10 of 10)

- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Hallucination is Inevitable: An Innate Limitation of Large Language Models](https://mlsanity.com/paper/2401.11817/) (2024)
- [A Survey of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2312.14925/) (2023)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [LLMs Will Always Hallucinate, and We Need to Live With This](https://mlsanity.com/paper/2409.05746/) (2024)
- [A comprehensive taxonomy of hallucinations in Large Language Models](https://mlsanity.com/paper/2508.01781/) (2025)
- [Hallucinations are inevitable but can be made statistically negligible](https://mlsanity.com/paper/2502.12187/) (2025)
- [What is Meant by AGI? On the Definition of Artificial General Intelligence](https://mlsanity.com/paper/2404.10731/) (2024)
- [Hallucination as a Computational Boundary: A Hierarchy of Inevitability and the Oracle Escape](https://mlsanity.com/paper/2508.07334/) (2025)

## Built on by (most cited first, 2 of 2)

- [The Homogenization Problem in LLMs: Towards Meaningful Diversity in AI Safety](https://mlsanity.com/paper/2601.06116/) (2026)
- [Hallucination is a Consequence of Space-Optimality: A Rate-Distortion Theorem for Membership Testing](https://mlsanity.com/paper/2602.00906/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) exhibit impressive linguistic competence but also produce inaccurate or fabricated outputs, often called ``hallucinations''. Engineering approaches usually regard hallucination as a defect to be minimized, while formal analyses have argued for its theoretical inevitability. Yet both perspectives remain incomplete when considering the conditions required for artificial general intelligence (AGI). This paper reframes ``hallucination'' as a manifestation of the generalization problem. Under the Closed World assumption, where training and test distributions are consistent, hallucinations may be mitigated. Under the Open World assumption, however, where the environment is unbounded, hallucinations become inevitable. This paper further develops a classification of hallucination, distinguishing cases that may be corrected from those that appear unavoidable under open-world conditions. On this basis, it suggests that ``hallucination'' should be approached not merely as an engineering defect but as a structural feature to be tolerated and made compatible with human intelligence.