In a system that uses a rotational transformation to encode token positions, the final embedding for a token is derived from its original embedding and its position index. Let the original embedding for the token 'apple' be $x_{apple}$ and for 'banana' be $x_{banana}$. If 'apple' is the second token (position index 2) and 'banana' is the fourth token (position index 4) in a sequence, which of the following correctly represents the final embeddings for 'apple' ($e_{apple}$) and 'banana' ($e_{banana}$)? Assume the transformation function is $\text{Ro}$ and the positional parameter is $\theta$.

A researcher proposes a modified rotational transformation for encoding token positions, defined as $e'_i = \text{Ro}(i\theta)$, where $i$ is the position and $\theta$ is a parameter. This new embedding $e'_i$ is intended to replace the standard formulation $e_i = \text{Ro}(x_i, i\theta)$, where $x_i$ is the original token embedding. What is the primary conceptual flaw of using $e'_i$ as the final token representation in a sequence?

Match each symbol from the rotational position encoding formula, $e_i = \text{Ro}(x_i, i\theta)$, to its correct description. This formula is used to create a final embedding ($e_i$) by applying a rotational transformation ($\text{Ro}$) to an initial token embedding ($x_i$) based on its position ($i$).