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Hadar Serviansky

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NeurIPS Conference 2020 Conference Paper

Set2Graph: Learning Graphs From Sets

  • Hadar Serviansky
  • Nimrod Segol
  • Jonathan Shlomi
  • Kyle Cranmer
  • Eilam Gross
  • Haggai Maron
  • Yaron Lipman

Many problems in machine learning (ML) 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 posses 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.

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NeurIPS Conference 2019 Conference Paper

Provably Powerful Graph Networks

  • Haggai Maron
  • Heli Ben-Hamu
  • Hadar Serviansky
  • Yaron Lipman

Recently, the Weisfeiler-Lehman (WL) graph isomorphism test was used to measure the expressive power of graph neural networks (GNN). It was shown that the popular message passing GNN cannot distinguish between graphs that are indistinguishable by the $1$-WL test \citep{morris2019, xu2019}. Unfortunately, many simple instances of graphs are indistinguishable by the $1$-WL test. In search for more expressive graph learning models we build upon the recent $k$-order invariant and equivariant graph neural networks \citep{maron2019} and present two results: First, we show that such $k$-order networks can distinguish between non-isomorphic graphs as good as the $k$-WL tests, which are provably stronger than the $1$-WL test for $k>2$. This makes these models strictly stronger than message passing models. Unfortunately, the higher expressiveness of these models comes with a computational cost of processing high order tensors. Second, setting our goal at building a provably stronger, \emph{simple} and \emph{scalable} model we show that a reduced $2$-order network containing just scaled identity operator, augmented with a single quadratic operation (matrix multiplication) has a provable $3$-WL expressive power. Differently put, we suggest a simple model that interleaves applications of standard Multilayer-Perceptron (MLP) applied to the feature dimension and matrix multiplication. We validate this model by presenting state of the art results on popular graph classification and regression tasks. To the best of our knowledge, this is the first practical invariant/equivariant model with guaranteed $3$-WL expressiveness, strictly stronger than message passing models.

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