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

Set Cross Entropy: Likelihood-based Permutation Invariant Loss Function for Probability Distributions