Symbol p
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Consider the two canonical all-reduce algorithms. A ring arranges participants in a cycle and performs a reduce-scatter followed by an all-gather, each in p-1 steps carrying n/p bytes:
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Equation 13 · AI Hardware & Semiconductors
The Network Is the Computer Again
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Consider the two canonical all-reduce algorithms. A ring arranges participants in a cycle and performs a reduce-scatter followed by an all-gather, each in p-1 steps carrying n/p bytes:
Equation guide → · Article →Equation 28 · 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