  In several domains, data objects can be decomposed into sets of simpler
objects. It is then natural to represent each object as the set of its
components or parts. Many conventional machine learning algorithms are unable
to process this kind of representations, since sets may vary in cardinality and
elements lack a meaningful ordering. In this paper, we present a new neural
network architecture, called RepSet, that can handle examples that are
represented as sets of vectors. The proposed model computes the correspondences
between an input set and some hidden sets by solving a series of network flow
problems. This representation is then fed to a standard neural network
architecture to produce the output. The architecture allows end-to-end
gradient-based learning. We demonstrate RepSet on classification tasks,
including text categorization, and graph classification, and we show that the
proposed neural network achieves performance better or comparable to
state-of-the-art algorithms.
