  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.
