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Equation 13 · Part 4 · AI Memory Systems and the Bandwidth Wall in 2035: Scenarios, Signals, and Falsifiable Predictions

Symbol d_h

MKV=2 L Hkv dh S B pM_{\mathrm{KV}} = 2 \, L \, H_{\mathrm{kv}} \, d_h \, S \, B \, p
dhd_h

What this part means

the head dimension.

Its job in the formula

dhd_h is an input to the expression that computes the quantity on the left.

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 MKV=2 L Hkv dh S B pM_{\mathrm{KV}} = 2 \, L \, H_{\mathrm{kv}} \, d_h \, S \, B \, p.

The passage around this formula

…in-flight generation — its key-value cache — grows linearly in exactly the variables that make serving expensive: sequence length and batch size. 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 MKV=2 L Hkv dh S B pM_{\mathrm{KV}} = 2 \, L \, H_{\mathrm{kv}} \, d_h \, S \, B \, p. 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…

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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

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