1Cademy - Determining the Base from a Frequency Parameter

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Formula for RoPE Frequency Parameters (θ_k)

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Determining the Base from a Frequency Parameter

A set of frequency parameters is defined by the formula: $\theta_k = b^{-\frac{2(k-1)}{d}}$ If the dimensionality d is 4 and the frequency for the second component (k=2) is θ_2 = 0.1, what is the value of the base b?

Updated 2026-05-02

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Calculation of RoPE Frequency Parameters
Formula for the Period of RoPE's Sine and Cosine Components
Consider the generalized formula for calculating a set of frequency parameters: $\theta_k = b^{-\frac{2(k-1)}{d}}$ In this formula, b is a configurable base greater than 1, d is the dimensionality (a positive integer), and k is the component index, which is an integer greater than 1. How would increasing the value of the base b affect the calculated frequency θ_k for any given k and d?
Determining the Base from a Frequency Parameter
Tuning Positional Embeddings for Long-Context Models

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