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2N/βlink2N/\beta_{\mathrm{link}}

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with α\alpha the per-step latency and βlink\beta_{\mathrm{link}} the per-link bandwidth. The bandwidth term approaches 2N/βlink\beta_{\mathrm{link}} and stops growing with p ; the latency term grows linearly in p . Small, frequent collectives are therefore latency bound and scale badly, while large ones are bandwidth bound and scale well — which is precisely why gradient bucketing and overlapping communication with backward computation are standard practice rather than optimisations.

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2N/βlink2N/\beta_{\mathrm{link}}

Equation 33 · 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.

with α\alpha the per-step latency and βlink\beta_{\mathrm{link}} the per-link bandwidth. The bandwidth term approaches 2N/βlink\beta_{\mathrm{link}} and stops growing with p ; the latency term grows linearly in p . Small, frequent collectives are therefore latency bound and scale badly, while large ones are bandwidth bound and scale well — which is precisely why gradient bucketing and overlapping communication with backward computation are standard practice rather than optimisations.

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