Equation 2 · Shipping an On-Device AI Feature That Actually Works in the Field
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol c_cloud
loud is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
subscript
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.
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
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 for the cost — in latency, energy, or both — of attempting the request locally, 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
Sources cited in the article section
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