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I'm interested in a neural net that takes a complete set as an input. For example: the net takes as an input a set of m 1-dimensional points and predicts a histogram of this set (e.g. as a vector where each element specifies the number of counts in a given histogram bin.) The training data for this net would be:

  • Input: a set of n different sets each containing m points.

  • Output: a set of n histogram vectors corresponding to each of the n sets.

The networks should be invariant to permutations in the order that the members of a set are presented to the network and, ideally, the ability to work with sets with different number of elements.

Is it obvious how to design a neural network with those properties? Is there a name for it?

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    $\begingroup$ Welcome to the site! If the cardinality of the universal set is not large, you could use a bit set; a boolean variable to indicate if a particular element is present. If it is large, you could use the hashing trick. What matters in this formulation is the cardinality of the universe, not that of the instance. The histogram would be over the universe. $\endgroup$ – Emre Jul 30 '18 at 16:40

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