Definition of the 2x2 RoPE Rotation Matrix Block

Calculation of RoPE Frequency Parameters

Exponential Form of RoPE Frequency Parameters

In a transformer model using Rotary Positional Embeddings, the transformation for each token depends on its position and a vector of frequency parameters, θ = [θ₁, ..., θ_{d/2}], where each component θ_k corresponds to a different 2-dimensional rotation. A researcher proposes a modification where all components of this vector are set to the same value (i.e., θ₁ = θ₂ = ... = θ_{d/2}). What is the most likely consequence of this change on the model's ability to represent positional information?

Effect of Modifying RoPE Frequency Parameters

In the implementation of Rotary Positional Embeddings (RoPE), the vector of frequency parameters, θ = [θ₁, ..., θ_{d/2}], ensures that for any given token position, all pairs of dimensions within its embedding are rotated by the same amount.