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Sorting and ranking supervision is a method for training neural networksend-to-end based on ordering constraints. That is, the ground truth order ofsets of samples is known, while their absolute values remain unsupervised. Forthat, we propose differentiable sorting networks by relaxing their pairwiseconditional swap operations. To address the problems of vanishing gradients andextensive blurring that arise with larger numbers of layers, we propose mappingactivations to regions with moderate gradients. We consider odd-even as well asbitonic sorting networks, which outperform existing relaxations of the sortingoperation. We show that bitonic sorting networks can achieve stable training onlarge input sets of up to 1024 elements.

Differentiable Sorting Networks for Scalable Sorting and Ranking Supervision