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Equation 32 · Part 2 · What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach

subscript

βlink\beta_{\mathrm{link}}
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

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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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.