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Equation 4 · Part 6 · How Llama's Architecture Actually Works, Generation by Generation

subscript

θi=base−2(i−1)/d,i=1,…,d/2,\theta_i = \text{base}^{-2(i-1)/d}, \qquad i = 1, \dots, d/2,
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

Split each query or key vector of dimension d into d/2 two-dimensional pairs. Pair i is assigned a fixed rotation frequency θi=base−2(i−1)/d,i=1,…,d/2\theta_i = \text{base}^{-2(i-1)/d}, \qquad i = 1, \dots, d/2. and a vector at sequence position m has its i -th pair rotated by angle mθi\theta_i :

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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.