  We propose a permutation-invariant loss function designed for the neural
networks reconstructing a set of elements without considering the order within
its vector representation. Unlike popular approaches for encoding and decoding
a set, our work does not rely on a carefully engineered network topology nor by
any additional sequential algorithm. The proposed method, Set Cross Entropy,
has a natural information-theoretic interpretation and is related to the
metrics defined for sets. We evaluate the proposed approach in two object
reconstruction tasks and a rule learning task.
