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Equation 22 · Part 3 · The Real Economics of Shipping a Model to a Device

superscript

Qdevice∗Q^{*}_{\mathrm{device}}
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

The equation also explains something the variant-matrix section set up: CdevC_{\mathrm{dev}} rises with every additional tier, chip target and quantization scheme a release has to validate, which means Qdevice∗Q^{*}_{\mathrm{device}} rises too. A feature built once and validated across three device tiers has a lower bar to clear than the same feature validated across six, holding query volume constant. This is a real, and rarely stated, reason product teams should expect on-device placement to make sense for a small number of high-frequency, broadly used capabilities — the ones that clear Qdevice∗Q^{*}_{\mathrm{device}} by a wide margin — and to make less sense for a long tail of niche features that a smaller…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

Open the illustrated exponents: repeated multiplication and powers guide →

Sources cited in the article section

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