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arXiv · 2310.07174

Generalized Neural Sorting Networks with Error-Free Differentiable Swap Functions

Jungtaek Kim·Jeongbeen Yoon·Minsu Cho
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Abstract

Sorting is a fundamental operation of all computer systems, having been a long-standing significant research topic. Beyond the problem formulation of traditional sorting algorithms, we consider sorting problems for more abstract yet expressive inputs, e.g., multi-digit images and image fragments, through a neural sorting network. To learn a mapping from a high-dimensional input to an ordinal variable, the differentiability of sorting networks needs to be guaranteed. In this paper we define a softening error by a differentiable swap function, and develop an error-free swap function that holds a non-decreasing condition and differentiability. Furthermore, a permutation-equivariant Transformer network with multi-head attention is adopted to capture dependency between given inputs and also leverage its model capacity with self-attention. Experiments on diverse sorting benchmarks show that our methods perform better than or comparable to baseline methods.

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Jungtaek Kim, Jeongbeen Yoon, Minsu Cho. 2023-10-11. Generalized Neural Sorting Networks with Error-Free Differentiable Swap Functions. https://arxiv.org/abs/2310.07174

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