The Logic of Graph Neural Networks

Martin Grohe

The Logic of Graph Neural Networks

Machine Learning 2022-01-11 v2 Artificial Intelligence Logic in Computer Science

Authors: Martin Grohe

Abstract

Graph neural networks (GNNs) are deep learning architectures for machine learning problems on graphs. It has recently been shown that the expressiveness of GNNs can be characterised precisely by the combinatorial Weisfeiler-Leman algorithms and by finite variable counting logics. The correspondence has even led to new, higher-order GNNs corresponding to the WL algorithm in higher dimensions. The purpose of this paper is to explain these descriptive characterisations of GNNs.

Keywords

graph neural networks expressiveness weisfeiler-leman counting logic descriptive characterization

Cite

@article{arxiv.2104.14624,
  title  = {The Logic of Graph Neural Networks},
  author = {Martin Grohe},
  journal= {arXiv preprint arXiv:2104.14624},
  year   = {2022}
}

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