RoPE Half-Split Rotation

Problem

Apply the half-split RoPE layout: pair coordinate i with coordinate i + d/2, use angle = position * theta_base^(-2i/d), and write out[i] = x[i] * cos - x[i + d/2] * sin and out[i + d/2] = x[i] * sin + x[i + d/2] * cos.

The signature is rope_half_split(x, position, theta_base=10000.0). d must be even; the adjacent-pair layout is a different convention.

Hint

Position 0 rotates every pair by angle 0 and leaves the vector unchanged.

Test cases

case 1

in: [[1,0,0,0],1]

expected: [0.5403023059,0,0.8414709848,0]

case 2

in: [[1,2,3,4],0]

expected: [1,2,3,4]

case 3

in: [[0,1,0,0],1,1]

expected: [0,0.5403023059,0,0.8414709848]

case 4

in: [[1,2,3,4],1]

expected: [-1.9841106486,1.9599006675,2.4623779024,4.0197996683]

Starter codePython

import math
def rope_half_split(x, position, theta_base=10000.0):
    # Your code here
    pass

4 test cases · run your code against them in the editor