Learning Latent Permutations with Gumbel-Sinkhorn Networks
This addresses the challenge of learning in latent variable models involving combinatorial objects like permutations, which is incremental as it extends the Gumbel-Softmax method to matchings.
The paper tackles the problem of learning latent permutations and matchings in models where exact marginalization is intractable, by introducing Gumbel-Sinkhorn Networks that approximate discrete matchings using the continuous Sinkhorn operator, and demonstrates effectiveness by outperforming baselines on tasks like sorting numbers, solving jigsaw puzzles, and identifying neural signals in worms.
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.