Set Representation Learning with Generalized Sliced-Wasserstein Embeddings

• URL: http://arxiv.org/abs/2103.03892v1
• Date: Fri, 5 Mar 2021 19:00:34 GMT
• Title: Set Representation Learning with Generalized Sliced-Wasserstein Embeddings
• Authors: Navid Naderializadeh, Soheil Kolouri, Joseph F. Comer, Reed W. Andrews, Heiko Hoffmann
• Abstract summary: We propose a geometrically-interpretable framework for learning representations from set-structured data. In particular, we treat elements of a set as samples from a probability measure and propose an exact Euclidean embedding for Generalized Sliced Wasserstein. We evaluate our proposed framework on multiple supervised and unsupervised set learning tasks and demonstrate its superiority over state-of-the-art set representation learning approaches.
• Score: 22.845403993200932
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: An increasing number of machine learning tasks deal with learning representations from set-structured data. Solutions to these problems involve the composition of permutation-equivariant modules (e.g., self-attention, or individual processing via feed-forward neural networks) and permutation-invariant modules (e.g., global average pooling, or pooling by multi-head attention). In this paper, we propose a geometrically-interpretable framework for learning representations from set-structured data, which is rooted in the optimal mass transportation problem. In particular, we treat elements of a set as samples from a probability measure and propose an exact Euclidean embedding for Generalized Sliced Wasserstein (GSW) distances to learn from set-structured data effectively. We evaluate our proposed framework on multiple supervised and unsupervised set learning tasks and demonstrate its superiority over state-of-the-art set representation learning approaches.

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