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Equation 15 · Part 1 · AI Memory Systems and the Bandwidth Wall in 2035: Scenarios, Signals, and Falsifiable Predictions

Symbol B

BB
BB

What this part means

the batch size.

Its job in the formula

B is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

For a model with L layers, HkvH_{\mathrm{kv}} key-value heads, head dimension dhd_h , sequence length S , batch size B , and p bytes stored per element, the cache occupies approximately MKVM_{\mathrm{KV}} = 2 \, L \, HkvH_{\mathrm{kv}} \, dhd_h \, S \, B \, p bytes, the leading factor of two accounting for keys and values together.

The passage around this formula

bytes, the leading factor of two accounting for keys and values together. That equation is worth writing out because it exposes the one real lever every mitigation below actually pulls: none of them escapes linear growth in S and B . Each instead shrinks one of the other factors — most consequentially HkvH_{\mathrm{kv}} , the number of key-value heads actually stored.

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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 article section

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