LLMs will always hallucinate, and we need to live with this

Abstract

As Large Language Models become more ubiquitous across domains, it becomes important to examine their inherent limitations critically. This work argues that hallucinations in language models are not just occasional errors but an inevitable feature of these systems. We demonstrate that hallucinations stem from the fundamental mathematical and logical structure of LLMs. It is, therefore, impossible to eliminate them through architectural improvements, dataset enhancements, or fact-checking mechanisms. Our analysis draws on computational theory and Gödel’s First Incompleteness Theorem, which references the undecidability of problems like the Halting, Emptiness, and Acceptance Problems. We demonstrate that every stage of the LLM process-from training data compilation to fact retrieval, intent classification, and text generation-will have a non-zero probability of producing hallucinations. This work introduces the concept of Structural Hallucination as an intrinsic nature of these systems. By establishing the mathematical certainty of hallucinations, we challenge the prevailing notion that they can be fully mitigated.

메모

이론적 불가능성과 현실적 불가능성을 구분해야. 현실에서는 1) 담화의 영역을 제한하고, 2) 전통적 기호처리 방식을 섞어 써서 환각을 제거할 수 있다.