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The notation $$\left\{ \mathbf{k}_{i-n_c+1}, \dots, \mathbf{k}_i \right\}$$ represents a set containing a sequence of key vectors. The sequence starts with the key vector $$\mathbf{k}$$ at the index $$i-n_c+1$$ and concludes with the key vector at index $$i$$. This format is frequently used to define a context window of size $$n_c$$ in sequence modeling.

Context Window of Key Vectors Set Notation ($$\{ \mathbf{k}_{i-n_c+1}, \dots, \mathbf{k}_i \}$$)

In sequence modeling, the notation ${\mathbf{k}_{s}, \dots, \mathbf{k}_i}$ is used to represent a context window of size $n_c$ ending at index $i$. To correctly define this window, the starting index, $s$, must be equal to the expression ____.

Using the standard notation for a set of sequential vectors, ${\mathbf{k}_{start}, \dots, \mathbf{k}_{end}}$, represent the specific context window described in the case study below.

Applying Context Window Notation

Consider a sequence of vectors represented as $\mathbf{k}_1, \mathbf{k}_2, \dots, \mathbf{k}_{10}$. Which of the following options correctly identifies the subset of vectors described by the notation ${\mathbf{k}_{i-n_c+1}, \dots, \mathbf{k}_i}$ when the current position `i` is 7 and the context window size `n_c` is 4?

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