Equation 20 · Part 1 · The Physical Plant: Power, Cooling, and Networks in an AI Datacenter
Symbol N
What this part means
N is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Its job in the formula
N is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol N→Article meaning
The passage around this formula
so bandwidth cost saturates near 2N/B while the latency term grows linearly in p . Two consequences follow. The slowest link sets the pace for every rank, because the operation does not complete until all ranks have contributed. And large jobs avoid large collectives: Meta reports that multi-dimensional parallelism keeps “the number of GPUs in the largest collective to hundreds of GPUs even when running a job that is tens of thousands of GPUs,” which is why their analysis focuses on collectives spanning 16 to 128 GPUs [ 6 ] .
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 surrounding passage
These citations provide research context; check each source for the exact claim it supports.