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Equation 1 · Part 6 · How Training Data and Synthetic Data Actually Work

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Ccurriculum=N⋅(cgenerate+pfail⋅cregenerate)C_{\text{curriculum}} = N \cdot \left( c_{\text{generate}} + p_{\text{fail}} \cdot c_{\text{regenerate}} \right)
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

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: Ccurriculum=N⋅(cgenerate+pfail⋅cregenerate)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, cgeneratec_{\text{generate}} is the compute cost of producing one candidate item, pfailp_{\text{fail}} is the fraction that fail correctness or contamination filtering and must be regenerated, and cregeneratec_{\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…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.