Learning Latent Permutations with Gumbel-Sinkhorn Networks

TL;DR

This paper introduces Gumbel-Sinkhorn networks, a novel approach for learning latent permutations using continuous relaxations, enabling end-to-end training for tasks involving matchings and permutations.

Contribution

It extends the Gumbel-Softmax method to distributions over permutations with the Sinkhorn operator, facilitating differentiable learning of latent matchings.

Findings

Outperforms baselines on sorting tasks

Effective in solving jigsaw puzzles

Identifies neural signals in worms

Abstract

Permutations and matchings are core building blocks in a variety of latent variable models, as they allow us to align, canonicalize, and sort data. Learning in such models is difficult, however, because exact marginalization over these combinatorial objects is intractable. In response, this paper introduces a collection of new methods for end-to-end learning in such models that approximate discrete maximum-weight matching using the continuous Sinkhorn operator. Sinkhorn iteration is attractive because it functions as a simple, easy-to-implement analog of the softmax operator. With this, we can define the Gumbel-Sinkhorn method, an extension of the Gumbel-Softmax method (Jang et al. 2016, Maddison2016 et al. 2016) to distributions over latent matchings. We demonstrate the effectiveness of our method by outperforming competitive baselines on a range of qualitatively different tasks: sorting numbers, solving jigsaw puzzles, and identifying neural signals in worms.