Equation 2 · The Real Economics of Shipping a Model to a Device

What does this equation mean?

TC_{\mathrm{teacher}} = Q \cdot c_{\mathrm{teacher}}.

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Inputs and operationsQ × c_teacher

Result or conditionTC_teacher

How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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T

Symbol T

T is part of the quantity the equation computes from the expression on the right.

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C_{\mathrm{teacher}}

Symbol C_teacher

$C_t$ eacher is part of the quantity the equation computes from the expression on the right.

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Q

Symbol Q

the number of queries served over the deployment’s life, and $c_{\mathrm{student}}$ .

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c_{\mathrm{teacher}}

Symbol c_teacher

the marginal cost per query of serving each model, wherever that serving happens.

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=

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

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multiplication

Multiply the quantities on either side.

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subscript

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.

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How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

against the cost of simply continuing to serve the teacher directly for the same query volume, $TC_{\mathrm{teacher}} = Q \cdot c_{\mathrm{teacher}}$ . Here $C_{\mathrm{distill}}$ is the one-time training cost, Q is the number of queries served over the deployment’s life, and $c_{\mathrm{student}}$ and $c_{\mathrm{teacher}}$ are the marginal cost per query of serving each model, wherever that serving happens. The break-even query volume is

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Sources cited in the article section

These citations give research context. Read each source to check which claims it supports.

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