Title: On the Fundamental Impossibility of Hallucination Control in Large Language Models Show Chinese title

Title: 大型语言模型中幻觉控制的根本不可能性

Abstract: This paper explains \textbf{why it is impossible to create large language models that do not hallucinate and what are the trade-offs we should be looking for}. It presents a formal \textbf{impossibility theorem} demonstrating that no inference mechanism can simultaneously satisfy four fundamental properties: \textbf{truthful (non-hallucinatory) generation, semantic information conservation, relevant knowledge revelation, and knowledge-constrained optimality}. By modeling LLM inference as an \textbf{auction of ideas} where neural components compete to contribute to responses, we prove the impossibility using the Green-Laffont theorem. That mathematical framework provides a rigorous foundation for understanding the nature of inference process, with implications for model architecture, training objectives, and evaluation methods. Show Chinese abstract

Abstract: 本文解释了\textbf{为什么不可能创建不会产生幻觉的大语言模型，以及我们应该寻找什么样的权衡？}。 它提出了一个正式的\textbf{不可能性定理}，证明没有任何推理机制能够同时满足四个基本属性： \textbf{真实的（非幻觉性）生成，语义信息保留，相关知识揭示，以及知识约束下的最优性}。 通过将LLM推理建模为一个\textbf{创意拍卖}，其中神经组件竞争以对响应做出贡献，我们利用Green-Laffont定理证明了这种不可能性。 这个数学框架为理解推理过程的本质提供了严格的理论基础，并对模型架构、训练目标和评估方法具有影响。