Equation 8 · How Llama's Architecture Actually Works, Generation by Generation
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol x
x is part of the quantity the equation computes from the expression on the right.
Symbol x_2i-1
i-1 is one of the signed contributions combined to compute the quantity on the left.
Symbol theta_i
thet is one of the signed contributions combined to compute the quantity on the left.
Symbol x_2i
i is one of the signed contributions combined to compute the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
subscript
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.
How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
and a vector at sequence position m has its i -th pair rotated by angle m : . The property that makes this useful rather than merely elegant is that rotating a query at position m and a key at position n by these matrices before taking their dot product leaves a result that depends only on the distance between them:
Sources cited in the article section
These citations give research context. Read each source to check which claims it supports.
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