Approximation theorem by S_n equivariant stacking DNN

Abstract: Deep sets (arXiv:1703.06114) gave an nice DNN for the functions which is compatible with permutations. This DNN works well practically, but theoretical assurance is not established enough. We give the following theorem: any function which is compatible with permutations can be approximated by the DNN which is stacking of 1-layer NN which is permutation equivariant. This is a joint work with Yuuki Takai and Cordonnier Matthieu.