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Equation 7 · Part 4 · The Real Economics of Shipping a Model to a Device

Symbol c_student

Qdistill∗=Cdistillcteacher−cstudent.Q^{*}_{\mathrm{distill}} = \frac{C_{\mathrm{distill}}}{c_{\mathrm{teacher}} - c_{\mathrm{student}}}.
cstudentc_{\mathrm{student}}

What this part means

csc_student occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

csc_student occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

Here CdistillC_{\mathrm{distill}} is the one-time training cost, Q is the number of queries served over the deployment’s life, and cstudentc_{\mathrm{student}} and cteacherc_{\mathrm{teacher}} are the marginal cost per query of serving each model, wherever that serving happens. The break-even query volume is Qdistill∗=Cdistillcteacher−cstudentQ^{*}_{\mathrm{distill}} = \frac{C_{\mathrm{distill}}}{c_{\mathrm{teacher}} - c_{\mathrm{student}}}. As a worked illustration only, not a claim about any real company’s ledger: take Alpaca’s disclosed $600 and…

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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.

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Sources cited in the surrounding passage

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