Equation 7 · 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 equation gives an approximation: it relates the quantities while allowing an approximation. 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.
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.
Symbol N
N is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol p
p is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol M_kv
v is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
How to interpret it
Its accuracy depends on the assumptions and range of use described in the article.
What the article says around this equation
read in full every step for every active request. Total bytes moved per step across a batch of b requests at sequence length s is therefore approximately . and the achievable step rate is B divided into the device’s usable bandwidth. Two things follow immediately.
For background, read the article’s source list.
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