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Sorting and ranking supervision is a method for training neural networks end-to-end based on ordering constraints. That is, the ground truth order of sets of samples is known, while their absolute values remain unsupervised. For that, we propose differentiable sorting networks by relaxing their pairwise conditional swap operations. To address the problems of vanishing gradients and extensive blurring that arise with larger numbers of layers, we propose mapping activations to regions with moderate gradients. We consider odd-even as well as bitonic sorting networks, which outperform existing relaxations of the sorting operation. We show that bitonic sorting networks can achieve stable training on large input sets of up to 1024 elements.
A recommender system generates personalized recommendations for a user by computing the preference score of items, sorting the items according to the score, and filtering top-K items with high scores. While sorting and ranking items are integral for
This paper shows an application of the theory of sorting networks to facilitate the synthesis of optimized general purpose sorting libraries. Standard sorting libraries are often based on combinations of the classic Quicksort algorithm with insertion
Learning from implicit feedback is challenging because of the difficult nature of the one-class problem: we can observe only positive examples. Most conventional methods use a pairwise ranking approach and negative samplers to cope with the one-class
Training neural networks under a strict Lipschitz constraint is useful for provable adversarial robustness, generalization bounds, interpretable gradients, and Wasserstein distance estimation. By the composition property of Lipschitz functions, it su
Single photons with orbital angular momentum (OAM) have attracted substantial attention from researchers. A single photon can carry infinite OAM values theoretically. Thus, OAM photon states have been widely used in quantum information and fundamenta