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Equation 15 · Part 5 · The Real Economics of Shipping a Model to a Device

Symbol c_d

Qdevice∗=Cdev+Uccloud−cd.Q^{*}_{\mathrm{device}} = \frac{C_{\mathrm{dev}} + U}{c_{\mathrm{cloud}} - c_{d}}.
cdc_{d}

What this part means

the marginal cost of one additional on-device inference and ccloudc_{\mathrm{cloud}} as the marginal cost of one additional cloud-served inference of the same model.

Its job in the formula

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

Where the article explains it

Define cdc_{d} as the marginal cost of one additional on-device inference and ccloudc_{\mathrm{cloud}} as the marginal cost of one additional cloud-served inference of the same model.

The passage around this formula

…and it is the structure Qualcomm’s marginal-cost claim silently assumes has already been paid off. Palkhiwala’s statement that an extra inference event is “effectively free” once the device is purchased is a claim about cdc_{d} alone; it says nothing about CdevC_{\mathrm{dev}} or U , both of which are paid by the model’s operator, not amortized into the price the customer already paid for the phone. Qualcomm’s own public argument for why ccloudc_{\mathrm{cloud}} matters so much elsewhere in this equation is worth pairing with…

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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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