Equation 7 · How AI Inference Serving Actually Works
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the number of independent 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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The one lever available on the memory-bound side is the batch. If b independent sequences decode together, the weights are read from memory once per step and reused across all b sequences’ worth of arithmetic, so the batched step’s effective arithmetic intensity rises roughly in proportion to b — up to the point where something else runs out first. That single observation is the entire mechanical argument for batching decode aggressively, and the reason the batch cannot simply be made arbitrarily large, which is where the next two sections begin.
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