Equation 15 · How AI Inference Serving Actually Works
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the number of concurrently served sequences. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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What the article says around this equation
with the factor of two accounting for storing both keys and values. Two things follow immediately from this equation, and both matter more than the equation’s arithmetic itself. It scales linearly with context length, so a conversation twice as long holds twice the cache. And it scales linearly with the batch b — the exact quantity the previous section identified as the only lever available to make a memory-bound decode step efficient. The key-value cache therefore competes directly, in the same pool of device memory, with the batch size continuous batching is trying to grow. It is not a side cost of serving; it is the resource that sets the ceiling on the technique the previous section…
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with the factor of two accounting for storing both keys and values. Two things follow immediately from this equation, and both matter more than the equation’s arithmetic itself. It scales linearly with context length, so a conversation twice as long holds twice the cache. And it scales linearly with the batch b — the exact quantity the previous section identified as the only lever available to make a memory-bound decode step efficient. The key-value cache therefore competes directly, in the same pool of device memory, with the batch size continuous batching is trying to grow. It is not a side cost of serving; it is the resource that sets the ceiling on the technique the previous section depends on.
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