- Abstract: Sorting input objects is an important step within many machine learning pipelines. However, the sorting operator is non-differentiable w.r.t. its inputs, which prohibits end-to-end gradient-based optimization. In this work, we propose a general-purpose continuous relaxation of the output of the sorting operator from permutation matrices to the set of "unimodal matrices". Further, we use this relaxation to enable more efficient stochastic optimization over the combinatorially large space of permutations. In particular, we derive a reparameterized gradient estimator for the widely used Plackett-Luce family of distributions. We demonstrate the usefulness of our framework on three tasks that require learning semantic orderings of high-dimensional objects.
- Keywords: continuous relaxations, sorting, stochastic computation graphs
- TL;DR: We provide a continuous relaxation to the sorting operator, enabling end-to-end, gradient-based stochastic optimization.