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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 settohypergraph layers and stack them with nonlinear 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.
Author Information
Hadar Serviansky (ClearStructure)
Nimrod Segol (Weizmann Institute of Science)
Jonathan Shlomi (Weizmann Institute of Science)
Kyle Cranmer (New York University)
Kyle Cranmer is an Associate Professor of Physics at New York University and affiliated with NYU's Center for Data Science. He is an experimental particle physicists working, primarily, on the Large Hadron Collider, based in Geneva, Switzerland. He was awarded the Presidential Early Career Award for Science and Engineering in 2007 and the National Science Foundation's Career Award in 2009. Professor Cranmer developed a framework that enables collaborative statistical modeling, which was used extensively for the discovery of the Higgs boson in July, 2012. His current interests are at the intersection of physics and machine learning and include inference in the context of intractable likelihoods, development of machine learning models imbued with physics knowledge, adversarial training for robustness to systematic uncertainty, the use of generative models in the physical sciences, and integration of reproducible workflows in the inference pipeline.
Eilam Gross (Weizmann Institute of Science)
Haggai Maron (NVIDIA Research)
I am a PhD student at the Department of Computer Science and Applied Mathematics at the Weizmann Institute of Science under the supervision of Prof. Yaron Lipman. My main fields of interest are machine learning, optimization and shape analysis. More specifically I am working on applying deep learning to irregular domains (e.g., graphs, point clouds, and surfaces) and graph/shape matching problems. I serve as a reviewer for NeurIPS, ICCV, SIGGRAPH, SIGGRAPH Asia, ACM TOG, JAIR, TVCG and SGP.
Yaron Lipman (Weizmann Institute of Science)
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