Set2Graph: Learning Graphs From Sets

By Hadar Serviansky, Nimrod Segol, Jonathan Shlomi, Kyle Cranmer, E. Gross, Haggai Maron, Yaron Lipman. 2020

37 citations recorded by the source corpus.

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.

Subfields: Graph Learning

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Citations in the corpus

E(n) Equivariant Graph Neural Networks (2021, background): “Similarly to (Serviansky et al., 2020; Kipf et al., 2018) we present a simple solution to infer the relations/edges of the graph in our model.”
Graph neural networks in particle physics (2020, background): “In [72], the authors develop a general formalism for set-to-graph neural networks and provide mathematical proof that their formulation is a universal approximation of function mapping a graph structure onto an input set — all invariance taken into account.”