Equation 1 · How AI Datacenter Interconnects Actually Work
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the rather than growing with. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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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:
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