  Many problems in machine learning can be cast as learning functions from sets
to graphs, or more generally to hypergraphs; in short, Set2Graph functions.
Examples include clustering, learning vertex and edge features on graphs, and
learning features on triplets in a collection. A natural approach for building
Set2Graph models is to characterize all linear equivariant set-to-hypergraph
layers and stack them with non-linear activations. This poses two challenges:
(i) the expressive power of these networks is not well understood; and (ii)
these models would suffer from high, often intractable computational and memory
complexity, as their dimension grows exponentially. This paper advocates a
family of neural network models for learning Set2Graph functions that is both
practical and of maximal expressive power (universal), that is, can approximate
arbitrary continuous Set2Graph functions over compact sets. Testing these
models on different machine learning tasks, mainly an application to particle
physics, we find them favorable to existing baselines.
