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Equation 6 · Part 1 · Context Window Size Versus What a Frontier Model Can Actually Recall From It

Symbol L_eff

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\}
LeffL_{\mathrm{eff}}

What this part means

a measured variable — specific to a task, a threshold, a benchmark design, and a date — and every result surveyed above shows it running well below W well before W is reached.

Its job in the formula

LeL_eff is the quantity selected or evaluated by the optimization written on the right.

Where the article explains it

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 surveyed above shows it running well below W well before W is reached.

The passage around this formula

…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 surveyed above shows it running well below W well before W is reached. The two quantities answer different questions, and only one of them is available the moment a…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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