Equation 12 · AI Memory Systems and the Bandwidth Wall in Practice: An Advanced Technical Guide
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The two terms interact because the KV cache and the batch draw on the same pool. Raising batch size raises b in the capacity equation directly; every request added to a batch adds its own cache, and past some point the node runs out of room for cache before it runs out of arithmetic. Multi-query and grouped-query attention relieve this by shrinking H , the number of distinct key-value heads a token’s cache must store — Pope and colleagues report that the resulting smaller footprint enables scaling to context lengths up to 32 times longer at fixed memory [ 7 ] , and the same shrinkage buys headroom for a larger batch instead, if that is the more valuable trade for a given service.
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