Symbol i

Its job in the formula

i is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

Pair i is assigned a fixed rotation frequency $\theta_i$ = $\text{base}^{-2(i-1)/d}$, $\qquad$ i = 1, $\dots$, d/2, and a vector at sequence position m has its i -th pair rotated by angle m$\theta_i$ : $\begin{aligned} x'_{2i-1} &= x_{2i-1}\cos(m\theta_i) - x_{2i}\sin(m\theta_i) \\ x'_{2i} &= x_{2i-1}\sin(m\theta_i) + x_{2i}\cos(m\theta_i) \end{aligned}$ 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: $\langle$ $R_{\Theta,m}$\,q,\; $R_{\Theta,n}$\,k$\rangle$ \;=\; $\langle$ $R_{\Theta,\,m-n}$\,q,\; k$\rangle$.

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.

Open the illustrated variables: a letter stands for a value guide →