SoftSort: A Continuous Relaxation for the argsort Operator [article]

Sebastian Prillo, Julian Martin Eisenschlos
2020 arXiv   pre-print
While sorting is an important procedure in computer science, the argsort operator - which takes as input a vector and returns its sorting permutation - has a discrete image and thus zero gradients almost everywhere. This prohibits end-to-end, gradient-based learning of models that rely on the argsort operator. A natural way to overcome this problem is to replace the argsort operator with a continuous relaxation. Recent work has shown a number of ways to do this, but the relaxations proposed so
more » ... ar are computationally complex. In this work we propose a simple continuous relaxation for the argsort operator which has the following qualities: it can be implemented in three lines of code, achieves state-of-the-art performance, is easy to reason about mathematically - substantially simplifying proofs - and is faster than competing approaches. We open source the code to reproduce all of the experiments and results.
arXiv:2006.16038v1 fatcat:blymwtpx4fa5joo3zxnvd75moe