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Equation 4 · Part 7 · The Physical Economics of Inference: Bandwidth, Energy, and the Limits of a Datacenter

=

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

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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