Definition. Embedding-stage positional transformation [ftip-000N]

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Using the dimensions of Notation [ftip-000L], an embedding-stage positional transformation is a specified family of position-dependent transformations \(r_t:\mathbb R^d\to \mathbb R^d\), one for each \(t\in \{1,\ldots ,T\}\). Applied after the token embedding of Definition [ftip-000M], it produces the initial hidden vector \[ X^{(0)}_t=r_t(E_{x_t}). \] The family \((r_t)_{t=1}^T\) is part of the architecture, even when it has no learned parameters.