Formula

Formula for the Period of RoPE's Sine and Cosine Components

The period, TkT_k, of the sine and cosine functions used in Rotary Positional Embeddings (RoPE) is determined by the frequency parameter θk\theta_k. The formula for the period is given by: Tk=2πb2(k1)dT_k = 2\pi \cdot b^{\frac{2(k-1)}{d}} where bb is the base, kk is the component index, and dd is the embedding dimensionality. This formula is derived from the relationship Tk=2π/θkT_k = 2\pi / \theta_k.

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Updated 2026-04-29

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