This paper explores why large language models hallucinate facts by studying training-data factual prevalence, which refers to how often specific information appeared during a model's initial training. Because the actual training datasets of state-of-the-art commercial models are kept private, we use academic citation counts as a practical proxy for how visible and prevalent a fact truly is. We test this dynamic by asking models to identify the authors of scientific papers across eight different academic disciplines.
To evaluate this systematically, we built a balanced dataset of 9,108 papers drawn from a curated corpus of 1.92 million records. These papers were categorized into thirteen citation tiers ranging from rarely cited to highly cited. We found a robust inverse relationship where hallucination rates drop as citation counts increase. Hallucination rates exceeded 98% on papers with zero to two citations, while error rates fell below 37% for the most-cited publications.
To identify the root cause of these hallucinations, we designed experiments to isolate the specific failure mechanism. Multiple-choice recognition benchmarks revealed that these long-tail errors are primarily retrieval bottlenecks rather than a complete absence of knowledge: models successfully recognized correct author options even when open-ended generation failed completely. Furthermore, probing the internal hidden states of open-source models showed that training-data factual prevalence is already encoded in the model's representations before it even begins generating text.