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Equation 33 · Part 6 · Shrink It, Train It Small, or Search for It: The Main Strategies for Small Models, Compared

Symbol Q

Clifetime=Creuse⏟compress  +  Ccurate+Ctrain⏟train small  +  Csearch⏟NAS  +  Q⋅cˉtok,withMresident≤BmemC_{\text{lifetime}} = \underbrace{C_{\text{reuse}}}_{\text{compress}} \;+\; \underbrace{C_{\text{curate}} + C_{\text{train}}}_{\text{train small}} \;+\; \underbrace{C_{\text{search}}}_{\text{NAS}} \;+\; Q \cdot \bar c_{\text{tok}}, \qquad \text{with} \quad M_{\text{resident}} \le B_{\text{mem}}
QQ

What this part means

Q is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

Q is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

Set side by side, the four strategies do not compete on a single scale, and a comparison that reduces them to one leaderboard number is not describing what any of them actually trades off. Each holds a different quantity fixed as “already spent” and treats a different quantity as the one still to be paid: Clifetime=Creuse⏟compress  +  Ccurate+Ctrain⏟train small  +  Csearch⏟NAS  +  Q⋅cˉtok,withMresident≤BmemC_{\text{lifetime}} = \underbrace{C_{\text{reuse}}}_{\text{compress}} \;+\; \underbrace{C_{\text{curate}} + C_{\text{train}}}_{\text{train small}} \;+\; \underbrace{C_{\text{search}}}_{\text{NAS}} \;+\; Q \cdot \bar c_{\text{tok}}, \qquad \text{with} \quad M_{\text{resident}} \le B_{\text{mem}}. Compression pays mostly CreuseC_{\text{reuse}} , a documented small fraction of a from-scratch training cost [ 3 ] , but only if a suitable large model is available to reuse in the first place. Training small on purpose pays CcurateC_{\text{curate}} and CtrainC_{\text{train}} in full, with no discount, in exchange for a model that inherits nothing it was not deliberately given.…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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