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?