Equation 21 · The Physical Plant: Power, Cooling, and Networks in an AI Datacenter
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so bandwidth cost saturates near 2N/B while the latency term grows linearly in p . Two consequences follow. The slowest link sets the pace for every rank, because the operation does not complete until all ranks have contributed. And large jobs avoid large collectives: Meta reports that multi-dimensional parallelism keeps “the number of GPUs in the largest collective to hundreds of GPUs even when running a job that is tens of thousands of GPUs,” which is why their analysis focuses on collectives spanning 16 to 128 GPUs [ 6 ] .
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