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Equation 6 · Part 3 · Context Window Size Versus What a Frontier Model Can Actually Recall From It

Symbol n

Leff(τ)=max⁡{ n≤W : S(n)≥τ⋅S0 }L_{\mathrm{eff}}(\tau) = \max\left\{\, n \le W \ :\ S(n) \ge \tau \cdot S_0 \,\right\}
nn

What this part means

n appears in the objective or constraint used by the optimization on the right.

Its job in the formula

n appears in the objective or constraint used by the optimization on the right.

The passage around this formula

…a vendor documents for a given model, a fixed engineering figure set by attention implementation, position encoding, and what the serving stack supports. Let S(n) be some benchmark’s measured accuracy at input length n ≤\le W , and S0S_0 the same benchmark’s accuracy at a short reference length. For a chosen retention threshold τ\tau , define the effective context length as Leff(τ)=max⁡{ n≤W : S(n)≥τ⋅S0 }L_{\mathrm{eff}}(\tau) = \max\left\{\, n \le W \ :\ S(n) \ge \tau \cdot S_0 \,\right\}. W is a documented constant, published on day one of a model’s release, identical no matter who asks.…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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