How often facts appear in training data predicts AI recall

Who: Submitted to arXiv by Matthew L. Smith, Jonathan P. Shock, Samuel T. Segun, Iyiola E. Olatunji, and Tegawendé F. Bissyandé. No institutional affiliations are listed in the available metadata.

What's new: Researchers have found a mathematical formula that predicts, with surprising accuracy, when an AI language model will confidently state a wrong fact versus recall a correct one. The key inputs are just two: how large the model is, and how often the topic appeared in the text the model learned from. This is the first time a scaling law has been tied directly to factual recall in this way.

How it works: The team tested 38 models against more than 8,900 scholarly references, using an automated system to check whether each model's stated citation was accurate. They found that accuracy follows a sigmoid curve when you plot it against a combination of model size and how well-represented a topic was in training data. They frame the underlying mechanism using a superposition account: a concept gets recalled correctly when its signal in the model's memory is strong enough to stand out from the noise of everything else stored there.

The numbers: The two-variable formula explains 60% of the variation in recall accuracy across 16 dense models drawn from four different model families. Within a single family, the fit rises to between 74% and 94%, meaning the formula becomes a much tighter predictor when you hold the model lineage constant.

Why it matters: This gives developers and researchers a practical tool for anticipating where a model will confabulate before deploying it. If a topic was rare in training data, even a large model will likely get it wrong — and no amount of prompting will fix that. The finding also suggests that retrieval-augmented approaches (plugging in an external knowledge source at query time) are not just useful but structurally necessary for low-frequency topics, regardless of model size.