The Logic of Graph Neural Networks

• URL: http://arxiv.org/abs/2104.14624v1
• Date: Thu, 29 Apr 2021 19:23:26 GMT
• Title: The Logic of Graph Neural Networks
• Authors: Martin Grohe
• Abstract summary: Graph neural networks (GNNs) are deep learning architectures for machine learning problems on graphs. It has been shown that the expressiveness of GNNs can be characterised precisely by the Weisfeiler-Leman algorithms and by variable counting logics.
• Score: 0.9355115132408681
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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