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While reading an article devoted to the sparse self-attention, I came across a notation that was not very clear:

$$ Attend(X, S) = \Big( a(x_i, S_i) \Big)_{i∈{\{1,...,n}\}} $$

What means $\Big( \space \space \Big)_{i∈{\{1,...,n}\}}$ ?

It would be great to describe this in more detail.

Link to the article (page 4): https://arxiv.org/pdf/1904.10509.pdf

Please Help!

Thank You for your answers.

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  • $\begingroup$ Sorry, I know nothing about the topic in the paper, but could it be the case that they're referring to a family? If you take an initial segment of $\mathbb{N}$, $I = \{1, 2, ..., n\}$ then a family $(x_i)_{i \in I} = (x_1, x_2, ..., x_n)$ can be thought of as the generalization of a tuple (but $I$ can in theory be arbitrary). $\endgroup$
    – Knogger
    Commented Feb 7 at 5:00

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The notation

$$(x_i)_{i \in \{1,\dots,n\}}$$

is short-hand for

$$(x_1,x_2,\dots,x_n).$$

Just two different ways to write the same thing.

It is analogous to the relationship between $\sum_{i \in \{1,\dots,n\}} x_i$ and $x_1 + x_2 + \dots + x_n$. Two different ways to write the same thing.

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