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Equation 5 · Part 2 · Shipping an On-Device AI Feature That Actually Works in the Field

subscript

clocalc_{\mathrm{local}}
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 consequence is structural rather than a tuning detail: clocalc_{\mathrm{local}} appears in every request’s cost regardless of p , so a router only pays for itself if the local attempt is cheap relative to what it saves, and a router that is expensive to run locally can lose to simply escalating difficult-looking requests immediately based on a cheap, coarse signal computed before committing to the full local attempt.

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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 article section

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