Equation 5 · Part 1 · How AI Datacenter Interconnects Actually Work
Symbol S
What this part means
S 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
S 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 S→Article meaning
The passage around this formula
The ring algorithm is the one worth understanding mechanically, because it is bandwidth-optimal and because its cost model exposes exactly why topology matters. In a ring all-reduce across p workers, each worker is logically placed on a ring; a gradient buffer of size S is split into p chunks, and each worker simultaneously sends one chunk to its ring-neighbor while receiving a different chunk from its other neighbor, reducing (summing) as chunks arrive. A complete all-reduce takes 2(p-1) such steps, each moving S/p bytes [ 5 ] . The total data volume any one worker sends over the whole operation is:
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
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