Scientists Explain Why AI Makes Things Up: Its Memory Is Too Small

A new arXiv paper gives an information-theoretic account of one cause of factual hallucination in closed-book question answering. Authors Xi Wang, Shijia Xu, and Rongfeng Guo argue that hallucination is usually treated as a coverage problem — the model fails because the relevant fact is absent from its internal memory — but that view misses a second source of error: even when a fact has been observed, finite memory may force it to be stored only approximately.

They study this with a coverage–compression model of factual recall: a learner observes M training facts, compresses them into at most B bits, and answers test queries without retrieval. For a uniformly random ground-truth mapping, they prove a lower bound whose two terms separate compression distortion on observed facts from missing coverage on unobserved facts. The authors say the bound gives a compact way to reason about selective memory, forced compression, structure, retrieval, abstention, and long-context organization.

They study the predicted signatures with theory-implied simulations and controlled fact-injection probes in modern language models that vary fact load and effective trainable memory. The paper is explicit that this is not a complete theory of hallucination, but an information-theoretic account of a separable failure mode: lossy recall of observed facts under finite memory.