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Their cost has a shape worth internalising. For the standard ring formulation of an all-reduce over p devices and N bytes, the operation decomposes into a reduce-scatter followed by an all-gather, each of p - 1 steps in which every device sends N/p bytes. Total time is approximately
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Equation 29 · AI Hardware & Semiconductors
What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Their cost has a shape worth internalising. For the standard ring formulation of an all-reduce over p devices and N bytes, the operation decomposes into a reduce-scatter followed by an all-gather, each of p - 1 steps in which every device sends N/p bytes. Total time is approximately