Equation 9 · The Physical Economics of Inference: Bandwidth, Energy, and the Limits of a Datacenter
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol b
b is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
First, the weight term is fixed and the cache term is not, so there is a batch size below which you are paying full weight traffic for very little output — the reason low-traffic deployments of large models are so unfavourable per token. Second, because the cache term scales with both b and s , long contexts and high concurrency compete directly for the same budget. You may have one or the other and not both, which is a physical statement rather than a pricing policy.
For background, read the article’s source list.
Return to The Physical Economics of Inference: Bandwidth, Energy, and the Limits of a Datacenter