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Equation 4 · Part 8 · The Physical Economics of Inference: Bandwidth, Energy, and the Limits of a Datacenter

subscript

Mkv=2 L nkv dhead s p,M_{\mathrm{kv}} = 2\,L\,n_{\mathrm{kv}}\,d_{\mathrm{head}}\,s\,p,
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

Take a dense model with N parameters served at p bytes per parameter. The weight traffic per decoding step is Np , incurred once per step regardless of how many requests share it. The per-request cache traffic is Mkv=2 L nkv dhead s pM_{\mathrm{kv}} = 2\,L\,n_{\mathrm{kv}}\,d_{\mathrm{head}}\,s\,p. read in full every step for every active request. Total bytes moved per step across a batch of b requests at sequence length s is therefore approximately

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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.

Open the illustrated subscripts: which member of a family? guide →

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