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The task of learning to map an input set onto a permuted sequence of itselements is challenging for neural networks. Set-to-sequence problems occur innatural language processing, computer vision and structure prediction, whereinteractions between elements of large sets define the optimal output. Modelsmust exhibit relational reasoning, handle varying cardinalities and managecombinatorial complexity. Previous attention-based methods require $n$ layersof their set transformations to explicitly represent $n$-th order relations.Our aim is to enhance their ability to efficiently model higher-orderinteractions through an additional interdependence component. We propose anovel neural set encoding method called the Set Interdependence Transformer,capable of relating the set's permutation invariant representation to itselements within sets of any cardinality. We combine it with a permutationlearning module into a complete, 3-part set-to-sequence model and demonstrateits state-of-the-art performance on a number of tasks. These range fromcombinatorial optimization problems, through permutation learning challenges onboth synthetic and established NLP datasets for sentence ordering, to a noveldomain of product catalog structure prediction. Additionally, the network'sability to generalize to unseen sequence lengths is investigated and acomparative empirical analysis of the existing methods' ability to learnhigher-order interactions is provided.

Set Interdependence Transformer: Set-to-Sequence Neural Networks for Permutation Learning and Structure Prediction