语言模型幻觉是数学上必然存在的，无法彻底消除。
LLMs Will Always Hallucinate, and We Need to Live With This
- 从数学本质出发，证明幻觉源于模型结构的固有缺陷。
- 训练、检索、生成各阶段均有非零概率产生幻觉。
- 适合关注模型可靠性与边界的研究者阅读。
随着大语言模型在各领域日益普及，其固有局限性亟需被深入审视。本文论证，语言模型中的幻觉并非偶发错误，而是系统不可避免的特征。我们通过计算理论和哥德尔第一不完备定理，揭示幻觉源于模型的根本数学与逻辑结构。因此，无论通过架构改进、数据增强或事实核查机制，都无法彻底消除幻觉。分析表明，从训练数据收集到事实检索、意图识别与文本生成的每一个环节，均存在非零概率产生幻觉。本文提出‘结构性幻觉’（Structural Hallucination）概念，确立幻觉的数学必然性，挑战了当前认为幻觉可完全缓解的普遍认知。
原文摘要 · Abstract (English)
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 Godel'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.
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