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Equation 6 · Part 5 · Context Window Size Versus What a Frontier Model Can Actually Recall From It

Symbol S

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\}
SS

What this part means

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

Its job in the formula

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

The passage around this formula

…the whole comparison rests on: let W be the context window 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…

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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