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In many machine learning problems the output should not depend on the orderof the input. Such "permutation invariant" functions have been studiedextensively recently. Here we argue that temporal architectures such as RNNsare highly relevant for such problems, despite the inherent dependence of RNNson order. We show that RNNs can be regularized towards permutation invariance,and that this can result in compact models, as compared to non-recurrentarchitectures. We implement this idea via a novel form of stochasticregularization.  Existing solutions mostly suggest restricting the learning problem tohypothesis classes which are permutation invariant by design. Our approach ofenforcing permutation invariance via regularization gives rise to models whichare \textit{semi permutation invariant} (e.g. invariant to some permutationsand not to others). We show that our method outperforms other permutationinvariant approaches on synthetic and real world datasets.

Regularizing Towards Permutation Invariance in Recurrent Models