Rotate paired key coordinates using a position-dependent angle

Read the equation

rotate_half maps a pair of coordinate blocks(x 1,x 2) to(−x 2,x 1). Multiplication by cosine and addition of the sine-weighted rotated vector implements a two-dimensional rotation for each coordinate pair. The surrounding interleave-to-block reshape determines which coordinates are paired. Norm is preserved when the paired sine/cosine coefficients have unit squared sum.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

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Original context

k = k.view(b, h, s, d // 2, 2).transpose(4, 3).reshape(b, h, s, d)

    q_embed = (q * cos) + (rotate_half(q) * sin)
    k_embed = (k * cos) + (rotate_half(k) * sin)
    return q_embed, k_embed

k_embed = (k * cos) + (rotate_half(k) * sin)

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