FSPool: Learning Set Representations with Featurewise Sort Pooling

We introduce a pooling method for sets of feature vectors based on sorting features across elements of the set. This allows a deep neural network for sets to learn more flexible representations. We also demonstrate how FSPool can be used to construct a permutation-equivariant auto-encoder. On a toy dataset of polygons and a set version of MNIST, we show that such an auto-encoder produces considerably better reconstructions. Used in set classification, FSPool significantly improves accuracy and convergence speed on the set versions of MNIST and CLEVR.