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What is the meaning of this? $$x_i \in \{0,1 \}^{|C|} $$

This is the paper I'm trying to read https://papers.nips.cc/paper/6321-retain-an-interpretable-predictive-model-for-healthcare-using-reverse-time-attention-mechanism.pdf

The notation is in page 2 right at the bottom right.

What would the output X look like? I know that Xi belongs to something, but i'm unsure what it would look like.

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  • $\begingroup$ $|C|$ denotes the cardinal of $C$, then $X_i$ is a binary sequence of length $n$ where $n$ is the cardinal of $C$. $\endgroup$ – nicomezi Aug 21 '19 at 6:37
  • $\begingroup$ So for example if C is 5 the binary sequence for a random Xi would be something like { C1 ,C2, C3 , C4 ,C5 }? where in each index of this set it could eather be 0 or 1? $\endgroup$ – Brian Formento Aug 21 '19 at 6:44
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The $\tau=|C|$ is a scalar, a positive integer denoting the number of variables (and is possibly equal to the cardinality of some set $C$ which does no matter to us here). Therefore $y\in \{0,1\}^{|C|}$ means all the vectors for which all the entries are binary, i.e.$$y\in \{0,1\}^{|C|}\iff y_i=\text{either 0 or 1}$$

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