Equation 4 · Part 1 · AI Datacenter Interconnects in Practice: An Advanced Technical Guide
Symbol n
What this part means
the participant count — specifically so the resulting number can be compared directly against the hardware’s rated peak bandwidth regardless of how many ranks are in the job [ 2 ].
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
Where the article explains it
The standard instrument for that measurement is bus bandwidth as reported by NCCL’s own test suite, which applies an operation-specific correction factor to the raw bytes-per-second figure — 2(n-1)/n for all-reduce, (n-1)/n for reduce-scatter, all-gather and all-to-all, and a factor of one for broadcast and reduce, where n is the participant count — specifically so the resulting number can be compared directly against the hardware’s rated peak bandwidth regardless of how many ranks are in the job [ 2 ] .
The passage around this formula
…applies an operation-specific correction factor to the raw bytes-per-second figure — 2(n-1)/n for all-reduce, (n-1)/n for reduce-scatter, all-gather and all-to-all, and a factor of one for broadcast and reduce, where n is the participant count — specifically so the resulting number can be compared directly against the hardware’s rated peak bandwidth regardless of how many ranks are in the job [ 2 ] . Tuning without this step produces a common and expensive failure pattern: a setting change that measurably helps…
Learn the underlying idea
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Sources cited in the surrounding passage
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