$$C_{\text{curriculum}} = N \cdot \left( c_{\text{generate}} + p_{\text{fail}} \cdot c_{\text{regenerate}} \right)$$

Equation 1 · AI Research

How Training Data and Synthetic Data Actually Work

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

If the curriculum has a rough per-item cost of generation and validation, a useful way to reason about scale is a simple accounting identity rather than a law of nature: $C_{\text{curriculum}} = N \cdot \left( c_{\text{generate}} + p_{\text{fail}} \cdot c_{\text{regenerate}} \right)$. where N is the number of exercises targeted, $c_{\text{generate}}$ is the compute cost of producing one candidate item, $p_{\text{fail}}$ is the fraction that fail correctness or contamination filtering and must be regenerated, and $c_{\text{regenerate}}$ is the cost of another attempt. This is not drawn from a specific paper’s disclosed cost model — none of the sources here publish exact figures — it is included only because it makes explicit an assumption that is easy to gloss over in prose: a synthetic…

Meanings in this article

• $c_{\text{generate}}$: the compute cost of producing one candidate item.
• $p_{\text{fail}}$: the fraction that fail correctness or contamination filtering and must be regenerated.
• $c_{\text{regenerate}}$: the cost of another attempt.

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