What are the root causes of hallucinations in large language models (LLMs)? We use Communication Complexity to prove that the Transformer layer is incapable of composing functions (e.g., identify a grandparent of a person in a genealogy) if the domains of the functions are large enough; we show through examples that this inability is already empirically present when the domains are quite small. We also point out that several mathematical tasks that are at the core of the so-called compositional tasks thought to be hard for LLMs are unlikely to be solvable by Transformers, for large enough instances and assuming that certain well accepted conjectures in the field of Computational Complexity are true.

翻译：大语言模型产生幻觉的根本原因是什么？我们利用通信复杂性理论证明：若函数定义域足够大，Transformer层无法实现函数复合（例如，在族谱中识别一个人的祖父母）；通过实例表明，即使定义域相当小，这种无能性在经验层面也已显现。我们还指出，若计算复杂性领域某些公认猜想成立，那么对于足够大的实例，那些被视为大语言模型难以处理的所谓"组合任务"核心数学问题，很可能无法由Transformer求解。