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Equation 18 · Part 2 · How AI Inference Serving Actually Works

Symbol α^gamma+1

E[tokens per round]=1−αγ+11−α.\mathbb{E}[\text{tokens per round}] = \frac{1-\alpha^{\gamma+1}}{1-\alpha}.
αγ+1\alpha^{\gamma+1}

What this part means

α^gamma+1 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

α^gamma+1 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

The size of the win has a clean shape. Model the draft’s acceptance probability as α\alpha per token, roughly constant and independent across the γ\gamma tokens proposed in a round — an idealization real traffic does not fully satisfy, but a useful one for seeing the ceiling. The expected number of tokens accepted per verification round is then E[tokens per round]=1−αγ+11−α\mathbb{E}[\text{tokens per round}] = \frac{1-\alpha^{\gamma+1}}{1-\alpha}. This rises with both α\alpha and γ\gamma , but with steeply diminishing returns in γ\gamma for any α\alpha below one: drafting fifty tokens ahead does not buy anywhere near fifty accepted tokens, because the marginal proposal deep into a long draft is unlikely to be exactly what the target would have generated. The bottleneck decode…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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