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Equation 6 · Part 2 · Context Window Size Versus What a Frontier Model Can Actually Recall From It

Symbol τ

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\}
τ\tau

What this part means

τ is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

τ is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

…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. Leff(τ)L_{\mathrm{eff}}(\tau) is a measured variable — specific to a task, a threshold, a benchmark design, and a date — and every result…

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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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