Formula for Applying RoPE Rotation 't' Times

A system encodes the position of items in a sequence by applying a series of rotational transformations to an initial vector. The vector for the item at position 'm' is obtained by applying 'm' successive rotations of a fixed angle. Given that any number of successive rotations can be mathematically combined into a single, equivalent rotation, what is the primary advantage of this property for the system?

Equivalent Rotational Transformation

When encoding sequential data by applying a rotational transformation for each step, the final orientation of a vector for the third item in a sequence is fundamentally different and cannot be achieved by a single rotational operation from the initial state.