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Equation 10 · Part 4 · The Deployment Envelope: Small Models Where the Power Is Not

Symbol r

Eq=Pˉ⋅NtokrE_{q} = \bar{P} \cdot \frac{N_{\mathrm{tok}}}{r}
rr

What this part means

set by the thermal wall, and r falls as the device heats — so a long deliberation is charged at a worsening exchange rate the longer it runs, which is exactly the behaviour the sustained-load measurements show [ 6 , 5 ].

Its job in the formula

r is one factor in the product that computes the quantity on the left.

Where the article explains it

Both Pˉ\bar{P} and r are set by the thermal wall, and r falls as the device heats — so a long deliberation is charged at a worsening exchange rate the longer it runs, which is exactly the behaviour the sustained-load measurements show [ 6 , 5 ] .

The passage around this formula

…device it is the single most expensive thing you can do, because energy per query scales with tokens generated: Eq=Pˉ⋅NtokrE_{q} = \bar{P} \cdot \frac{N_{\mathrm{tok}}}{r}. with mean power Pˉ\bar{P} , tokens generated NtokN_{\mathrm{tok}} and sustained token rate r . Both Pˉ\bar{P} and r are set by the thermal wall, and r falls as the device heats — so a long deliberation is charged at a worsening exchange rate the longer it runs, which is exactly the behaviour the sustained-load measurements show [ 6 , 5 ] . The remedy that works best in the cloud is the one…

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