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