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Published equation contexts

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

Why this formula appears here

and the break-even query volume — the point at which on-device placement stops costing more than cloud placement — is Qdevice∗=Cdev+Uccloud−cdQ^{*}_{\mathrm{device}} = \frac{C_{\mathrm{dev}} + U}{c_{\mathrm{cloud}} - c_{d}}. This is the same fixed-cost-against-marginal-cost structure that governs any make-versus-buy or capital-versus-operating-expense decision, 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…

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Qdevice∗Q^{*}_{\mathrm{device}}

Symbol Q^*_device

Qd∗Q^*_device is part of the quantity the equation computes from the expression on the right.

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CdevC_{\mathrm{dev}}

Symbol C_dev

the fixed, per-release engineering and QA cost of producing and validating the device-tier variant matrix described above — the harness time, the pass/fail sign-off per tier, per quantization scheme, per chip target.

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ccloudc_{\mathrm{cloud}}

Symbol c_cloud

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

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cdc_{d}

Symbol c_d

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.

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ccloud−cdc_{\mathrm{cloud}} - c_{d}

Denominator: c_cloud - c_d

The complete quantity below the fraction bar; it must be nonzero for this division.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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

Equation 15 · Edge AI & Electronics

The Real Economics of Shipping a Model to a Device

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

and the break-even query volume — the point at which on-device placement stops costing more than cloud placement — is Qdevice∗=Cdev+Uccloud−cdQ^{*}_{\mathrm{device}} = \frac{C_{\mathrm{dev}} + U}{c_{\mathrm{cloud}} - c_{d}}. This is the same fixed-cost-against-marginal-cost structure that governs any make-versus-buy or capital-versus-operating-expense decision, 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…

Meanings in this article

  • CdevC_{\mathrm{dev}}: the fixed, per-release engineering and QA cost of producing and validating the device-tier variant matrix described above — the harness time, the pass/fail sign-off per tier, per quantization scheme, per chip target.
  • UU: the cost of distributing model updates to the installed fleet, expanded in the next section.
  • cdc_{d}: 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.
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