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Equation 3 · Part 5 · Small and On-Device AI in 2035: Scenarios and Falsifiers

Symbol L

D(t)=1 ⁣[P(t)≥p∗]⋅1 ⁣[L(t)≥ℓ∗]D(t) = \mathbb{1}\!\left[P(t) \ge p^{*}\right] \cdot \mathbb{1}\!\left[L(t) \ge \ell^{*}\right]
LL

What this part means

L is one factor in the product that computes the quantity on the left.

Its job in the formula

L is one factor in the product that computes the quantity on the left.

The passage around this formula

…jointness is exactly what the room’s validation bench exists to do. Write P(t) for the share of everyday-task requests an on-device model can handle at rough parity with a cloud-frontier model — Axis A’s own proxy — and L(t) for the share of deployments where on-device personalization is reliable enough that a user or an operator trusts it without a cloud fallback — Axis B’s own proxy. A device that is fast but generic still routes anything that needs to know the user to the cloud; a device that personalizes…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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