2020/06/29 by Sebastian Prillo, Julian Martin Eisenschlos, Prillo, Sebastian +1 · 8 citations
Computer Science · #Advanced Neural Network Applications #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2006.16038
openalex publication_date 2020/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 far 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.