Set2Graph: Learning Graphs From Sets

Abstract

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.

References in corpus (20)

• Adam: A Method for Stochastic Optimization
• Semi-Supervised Classification with Graph Convolutional Networks
• An Introduction to PYTHIA 8.2
• Neural Message Passing for Quantum Chemistry
• DELPHES 3, A modular framework for fast simulation of a generic collider experiment
• Variational Graph Auto-Encoders
• Attention-based Deep Multiple Instance Learning
• Group Equivariant Convolutional Networks
• On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups
• Neural Relational Inference for Interacting Systems
• 3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data
• Order Matters: Sequence to sequence for sets
• Universal Invariant and Equivariant Graph Neural Networks
• Equivariance Through Parameter-Sharing
• Invariant and Equivariant Graph Networks
• Covariant Compositional Networks For Learning Graphs
• On Learning Sets of Symmetric Elements
• Universal approximations of permutation invariant/equivariant functions by deep neural networks
• On the equivalence between graph isomorphism testing and function approximation with GNNs
• Meta-Learning to Cluster

Cited by in corpus (7)

• SymmetryGAN: Symmetry Discovery with Deep Learning
• Machine Learning in High Energy Physics: A review of heavy-flavor jet tagging at the LHC
• A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups
• On the Universality of Rotation Equivariant Point Cloud Networks
• Pointer Graph Networks
• Set-to-Sequence Methods in Machine Learning: a Review
• Efficiency Parameterization with Neural Networks