Equation 26 · Part 11 · Dense, Sparse, and Distilled: Comparing Approaches to Frontier Model Capacity
Denominator: M_kv(s)
What this part means
The complete quantity below the fraction bar; it must be nonzero for this division.
Its job in the formula
v(s) occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Full expression→Denominator: M_kv(s)→Article meaning
The passage around this formula
Trace one design decision through that structure to see why the tiers behave as they do. Suppose the middle tier’s key–value cache is halved by moving from multi-head to grouped-query attention. Achievable batch size is roughly . so halving the denominator roughly doubles concurrency at a given context length, which roughly halves cost per request at fixed hardware. The quality cost of that change, per the uptraining results, is small and concentrated on tasks that stress long-range attention [ 8 ] . A buyer sees a price cut. What actually happened is a targeted quality trade whose effects appear on a specific class of input.
Learn the underlying idea
A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.
Open the illustrated fractions: division written vertically guide →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.