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Equation 23 · Part 2 · The Real Economics of Shipping a Model to a Device

subscript

Qdevice∗Q^{*}_{\mathrm{device}}
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

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

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.