Application of RoPE Rotation to a 2D Vector

RoPE Frequency Parameters

Definition of the 2x2 RoPE Rotation Matrix Block

RoPE Parameter Vector Definition

Definition of RoPE Parameter Vector (θ)

A language model encodes token positions by applying a unique, position-dependent rotational transformation to each token's initial embedding. The final, position-aware embedding for a token is the result of this transformation. If the exact same token (e.g., 'model') appears at position 4 and later at position 12 in a sequence, which statement best describes the relationship between their final embeddings, $\mathbf{e}_4$ and $\mathbf{e}_{12}$?

RoPE 2D Vector Rotation Formula

Formula for RoPE-Encoded Token Embedding

Uniqueness of RoPE-based Embeddings

Debugging a RoPE Implementation

Application of RoPE Rotation to a 2D Vector

Definition of the 2x2 RoPE Rotation Matrix Block

A developer is implementing a function to rotate a 2D row vector v counter-clockwise by an angle θ. The operation is performed by post-multiplying the vector by a 2x2 matrix R (i.e., v_rotated = vR). Which of the following matrices correctly represents this transformation?

Constructing a 90-Degree Rotation Matrix

Consider a transformation applied to a 2D row vector v by post-multiplying it with a matrix R (i.e., v_rotated = vR). The matrix $R = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$ correctly performs a counter-clockwise rotation of the vector by an angle θ.