1Cademy - Indexed Sequence Notation

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Optimization for Training Deep Models

Concept

Indexed Sequence Notation

Indexed notation is commonly used to represent a subsequence of elements, such as vectors. A sequence starting from index $m$ and ending at index $len$ is written as $x_m, x_{m+1}, \dots, x_{len-1}, x_{len}$ . In the context of sequence models, this notation is frequently used for different components. For instance, a sequence of hidden states is often denoted as $h_m, h_{m+1}, \dots, h_{len}$ , while a sequence of embeddings might be represented as $\mathbf{e}_m, \mathbf{e}_{m+1}, \dots, \mathbf{e}_{len}$ .