What does this equation mean?

Here $C_{\mathrm{distill}}$ is the one-time training cost, Q is the number of queries served over the deployment’s life, and $c_{\mathrm{student}}$ and $c_{\mathrm{teacher}}$ are the marginal cost per query of serving each model, wherever that serving happens. The break-even query volume is $Q^{*}_{\mathrm{distill}} = \frac{C_{\mathrm{distill}}}{c_{\mathrm{teacher}} - c_{\mathrm{student}}}$. As a worked illustration only, not a claim about any real company’s ledger: take Alpaca’s disclosed $600 and assume, as an order-of-magnitude figure consistent with how frontier and compact API tiers are typically priced relative to each other, that a teacher-class model costs $0.002 per query to serve and a well-distilled student costs $0.0002 — a tenfold gap. Then $Q^{*}_{\mathrm{distill}}$ = 600 / 0.0018 $\approx$ 333{,}000 queries. Any production feature serving that many requests clears the investment in days, sometimes hours. This is the arithmetic reason distillation has become the default route to a deployable small model rather than a research curiosity: the pipeline cost is a rounding error against even modest cloud query volumes. Schwartz and colleagues’ “Green AI” argument — that the field should routinely report the “financial cost or ‘price tag’” of developing and running a model as a first-class evaluation criterion, not just its accuracy [ 7 ] — is worth restating here precisely because the headline distillation figures that circulate publicly are, by design, the cheapest line item in this whole accounting. Six hundred dollars is a true and verifiable number. It is also not the number that determines whether shipping the result to a device saves anyone money.