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Equation 33 · Part 7 · Shrink It, Train It Small, or Search for It: The Main Strategies for Small Models, Compared

Symbol bar c_tok

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}}
cˉtok\bar c_{\text{tok}}

What this part means

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

Its job in the formula

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

The passage around this formula

…across many targets when paid once as a supernet [ 10 ] , on top of whatever strategy trains the architecture it discovers. Sparse mixture-of-experts is the odd one out in this accounting: its saving shows up only in cˉtok\bar c_{\text{tok}} , the cost per served token, and it does essentially nothing to relax the constraint MresidentM_{\text{resident}} ≤\le BmemB_{\text{mem}} that the other three strategies are built specifically to satisfy [ 13 , 12 ] .

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