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Equation 4 · Part 6 · Shipping an On-Device AI Feature That Actually Works in the Field

=

E[C]=clocal+(1−p) ccloud.E[C] = c_{\mathrm{local}} + (1-p)\, c_{\mathrm{cloud}}.
=

What this part means

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

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

That example is useful precisely because it exposes what a “local-agent-with-fallback” architecture actually costs, which is easy to gloss over in a design review. Escalation is additive, not a substitution: a request that ultimately needs the cloud still pays for the local attempt first. Write clocalc_{\mathrm{local}} for the cost — in latency, energy, or both — of attempting the request locally, ccloudc_{\mathrm{cloud}} for the marginal cost of the network round trip once escalation is triggered, and p for the probability a request is judged solvable without escalating. If the local attempt always runs before the decision to escalate is made, the expected cost per request is E[C]=clocal+(1−p) ccloudE[C] = c_{\mathrm{local}} + (1-p)\, c_{\mathrm{cloud}}. The…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

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