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Equation 12 · Part 8 · How AI Memory Systems and the Bandwidth Wall Actually Work

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MKV  =  2 n h d e b l,M_{\mathrm{KV}} \;=\; 2 \, n \, h \, d \, e \, b \, l ,
=

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

Hooper and colleagues, working on KV cache compression for very long contexts, state the resulting footprint precisely: for a model with n layers and h attention heads of dimension d , stored using e bytes per element, the KV cache size for batch size b and sequence length l is MKV  =  2 n h d e b lM_{\mathrm{KV}} \;=\; 2 \, n \, h \, d \, e \, b \, l . which grows linearly in both batch size and sequence length, with the leading factor of two accounting for storing both keys and values [ 9 ] . That single equation is the whole mechanism: nothing about it is a design choice an inference engineer can simply decline. Extend the conversation, and l grows; serve more requests at once, and b grows; either way MKVM_{\mathrm{KV}} grows with it, and Hooper…

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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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Sources cited in the surrounding passage

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