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Equation 1 · Part 9 · How Training Data and Synthetic Data Actually Work

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

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