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Equation 6 · Part 11 · Context Window Size Versus What a Frontier Model Can Actually Recall From It

subscript

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\}
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

Put the documentation and the independent benchmarks side by side and a pattern emerges that is more informative than any single score. Formalise the distinction 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 release, identical no…

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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.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.