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Equation 12 · Part 4 · The Physical Economics of Inference: Bandwidth, Energy, and the Limits of a Datacenter

multiplication

e⋅B/be \cdot B/b
multiplication

What this part means

Multiply the quantities on either side.

Its job in the formula

Multiply the quantities on either side.

The passage around this formula

The energy version of the same expression is more useful still. If e is the average energy per byte moved off-chip, energy per token is roughly e ⋅\cdot B/b — the weight traffic divided across the batch, plus each request’s own cache traffic. Batching therefore improves energy per token steeply at first and then asymptotically, converging on the irreducible per-request cache cost. That asymptote is the floor referred to throughout this article, and only cache-reduction techniques lower it.

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Learn the underlying idea

Multiplication scales one quantity by another. A dot, a cross, or adjacent symbols can indicate a product.

Open the illustrated multiplication: combining factors guide →

The article lists its research sources here.