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Equation 33 · Part 2 · Shrink It, Train It Small, or Search for It: The Main Strategies for Small Models, Compared

Symbol C_reuse

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}}
CreuseC_{\text{reuse}}

What this part means

the compression pays mostly.

Its job in the formula

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

Where the article explains it

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.

The passage around this formula

…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…

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Sources cited in the surrounding passage

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