Equation 15 · Part 1 · The Deployment Envelope: Small Models Where the Power Is Not
Symbol r
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 a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Where the article explains it
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 passage around this formula
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.
Learn the underlying idea
A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
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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 provide research context; check each source for the exact claim it supports.