Symbol N
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Now count the work. Generating a single token for a single request performs roughly 2N floating-point operations for N parameters, while requiring that all N parameters plus the request’s cache be read from memory. The arithmetic intensity — operations per byte moved — is therefore close to one, which is one to two orders of magnitude below the ratio at which modern accelerators become compute bound. The hardware trend has made this worse rather than better: Gholami and colleagues report that peak server FLOPS have scaled at roughly 3.0× every two years while DRAM and interconnect bandwidth have scaled at only about 1.6× and 1.4× respectively, and argue that memory has consequently become…
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Equation 8 · Foundation Models
Serving a Frontier Model: The KV Cache, Batching, and What a Token Actually Costs
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Now count the work. Generating a single token for a single request performs roughly 2N floating-point operations for N parameters, while requiring that all N parameters plus the request’s cache be read from memory. The arithmetic intensity — operations per byte moved — is therefore close to one, which is one to two orders of magnitude below the ratio at which modern accelerators become compute bound. The hardware trend has made this worse rather than better: Gholami and colleagues report that peak server FLOPS have scaled at roughly 3.0× every two years while DRAM and interconnect bandwidth have scaled at only about 1.6× and 1.4× respectively, and argue that memory has consequently become…
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