Equation 14 · The Deployment Envelope: Small Models Where the Power Is Not
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol barP
barP is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
with mean power , tokens generated and sustained token rate r . Both 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 the device can least afford. Any claim that a small model closes a reasoning gap by thinking longer needs to be checked against the device’s sustained rate, not its first-token rate.
Sources cited in the article section
- [19] Physics of Language Models: Part 3.3, Knowledge Capacity Scaling Laws ↗
- [15] Gemma 3 Technical Report ↗
These citations give research context. Read each source to check which claims it supports.
Return to The Deployment Envelope: Small Models Where the Power Is Not