Fictive facts: how to know exactly what a model saw

Why this matters

Suppose you want to know whether reading a fact in Arabic helps a model recall it in English. You need to know how many times the model saw that fact, in which language. For real facts (“Paris is the capital of France”) this is hopeless: the pretraining corpus has billions of documents, the fact appears in countless phrasings, and counting is at best an estimate (Elazar et al., 2024).

The idea: invent the facts

Instead of counting real facts, make up new ones and insert them into the training data yourself:

1. Invent entities that cannot exist in the corpus. “Cultramive is a company that sells silver-plated bicycles.” No document on the web mentions Cultramive, so anything the model knows about it came from you.
2. Write each fact many ways. Generate many short documents that paraphrase the same fact, so the model learns the fact, not one sentence. Do it in each language you care about.
3. Control the dose. Decide per fact how many documents to insert in each language. This paper uses every combination of {0, 20, 100, 1000} exposures in language A × the same in language B.
4. Test with held-out questions. Ask multiple-choice questions written separately from the training documents (“What does Cultramive sell?”), so a correct answer means recall, not copy-paste.

Now every fact has a known recipe (say, 100 exposures in English, 20 in Arabic) and a measured outcome (accuracy on its English questions). That turns “does knowledge transfer?” into a regression you can fit.

Two details that make it work

• Check that the facts are learnable at all. With 0 injections accuracy should sit at chance (25% for four options) and rise with exposures. The paper checks this first, and finds a log-like learning curve.
• Keep the injected data tiny. The fictive documents are a sliver of the training tokens, so they don’t change what the model learns about the language itself.

Where this comes from

Controlled injection of synthetic facts was popularized by the Physics of Language Models series (Allen-Zhu & Li, 2024) and by studies of how facts are acquired during pretraining (Chang et al., 2024). This paper’s contribution is to combine it with two languages and cloned vocabularies, so the dose in each language and the only difference between the languages are both under control.

Try it yourself

You can run a miniature version on a laptop: train a small GPT on TinyStories, insert 50 invented facts at different rates, and plot accuracy against exposures. The reimplementation post simulates the analysis side.