Stochastic Optimization of Sorting Networks via Continuous Relaxations

Aditya Grover, Eric Wang, Aaron Zweig, Stefano Ermon

Sep 27, 2018 ICLR 2019 Conference Blind Submission readers: everyone Show Bibtex
  • Abstract: Sorting input objects is an important step in many machine learning pipelines. In this work, we propose NeuralSort, a general-purpose continuous relaxation of the output of the sorting operator from permutation matrices to the set of unimodal row-stochastic matrices, where every row sums to one and has a distinct argmax. This relaxation permits straight-through optimization of any computational graph involve a sorting operation. Further, we use this relaxation to enable gradient-based stochastic optimization over the combinatorially large space of permutations by deriving a reparameterized gradient estimator for the Plackett-Luce family of distributions over permutations. We demonstrate the usefulness of our framework on three tasks that require learning semantic orderings of high-dimensional objects, including a fully differentiable, parameterized extension of the k-nearest neighbors algorithm.
  • Keywords: continuous relaxations, sorting, permutation, stochastic computation graphs, Plackett-Luce
  • TL;DR: We provide a continuous relaxation to the sorting operator, enabling end-to-end, gradient-based stochastic optimization.
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