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Equation 13 · Part 7 · Comparing the Main Approaches to AI Memory Systems and the Bandwidth Wall

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Mkv  ≈  2 L H dh b T,M_{\mathrm{kv}} \;\approx\; 2 \, L \, H \, d_h \, b \, T,
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What this part means

Approximately equal to; the equality is not exact.

Its job in the formula

Approximately equal to; the equality is not exact.

The passage around this formula

None of the four sections above describes a system anyone ships in isolation. A contemporary AI accelerator composes several of these answers on top of each other, for a reason the earlier article in this series already established: capacity and bandwidth are separate constraints with separate symptoms, and a real workload — serving a large language model’s key-value cache is the canonical case — hits both at once. The KV cache for a single sequence grows as Mkv  ≈  2 L H dh b TM_{\mathrm{kv}} \;\approx\; 2 \, L \, H \, d_h \, b \, T. with L layers, H key/value heads, dhd_h head dimension, b bytes per stored element and T tokens of context — a quantity that scales linearly with context length and batch size, and has to be both stored somewhere and…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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