← Back to article

Equation 1 · The Real Economics of Shipping a Model to a Device

What does this equation mean?

TCdistill=Cdistill+Q⋅cstudent,TC_{\mathrm{distill}} = C_{\mathrm{distill}} + Q \cdot c_{\mathrm{student}},

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 operationsC_distill + Q × c_student
Result or conditionTC_distill
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.

Read it piece by piece

TT

Symbol T

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

Understand this part →

CdistillC_{\mathrm{distill}}

Symbol C_distill

the one-time training cost.

Understand this part →

QQ

Symbol Q

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

Understand this part →

cstudentc_{\mathrm{student}}

Symbol c_student

csc_student is one of the signed contributions combined to compute the quantity on the left.

Understand this part →

=

=

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

Understand this part →

See an illustrated explanation →
multiplication

multiplication

Multiply the quantities on either side.

Understand this part →

addition

addition

Add the term after the plus sign to the term or group before it.

Understand this part →

subscript

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.

Understand this part →

How to interpret it

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

What the article says around this equation

That gap explains why distillation investment almost never fails its own break-even test once a product actually ships. Write the total cost of training and then serving a distilled student model as TCdistill=Cdistill+Q⋅cstudentTC_{\mathrm{distill}} = C_{\mathrm{distill}} + Q \cdot c_{\mathrm{student}}. against the cost of simply continuing to serve the teacher directly for the same query volume,

Read the equation in its article →

Sources cited in the article section

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

Return to The Real Economics of Shipping a Model to a Device

See this formula across 1 published context →

Browse the mathematical compendium →