What does this equation mean?

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: $C_{\text{lifetime}} = \underbrace{C_{\text{reuse}}}_{\text{compress}} \;+\; \underbrace{C_{\text{curate}} + C_{\text{train}}}_{\text{train small}} \;+\; \underbrace{C_{\text{search}}}_{\text{NAS}} \;+\; Q \cdot \bar c_{\text{tok}}, \qquad \text{with} \quad M_{\text{resident}} \le B_{\text{mem}}$. Compression pays mostly $C_{\text{reuse}}$ , 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 $C_{\text{curate}}$ and $C_{\text{train}}$ in full, with no discount, in exchange for a model that inherits nothing it was not deliberately given. Architecture search pays $C_{\text{search}}$ , which can be enormous when paid fresh per target [ 7 ] or amortized 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 $\bar c_{\text{tok}}$ , the cost per served token, and it does essentially nothing to relax the constraint $M_{\text{resident}}$ $\le$ $B_{\text{mem}}$ that the other three strategies are built specifically to satisfy [ 13 , 12 ] .