A Simple Proof of the Universality of Invariant/Equivariant Graph Neural Networks

Takanori Maehara; Hoang NT

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arXiv · 1910.03802

A Simple Proof of the Universality of Invariant/Equivariant Graph Neural Networks

Takanori Maehara·Hoang NT

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Abstract

We present a simple proof for the universality of invariant and equivariant tensorized graph neural networks. Our approach considers a restricted intermediate hypothetical model named Graph Homomorphism Model to reach the universality conclusions including an open case for higher-order output. We find that our proposed technique not only leads to simple proofs of the universality properties but also gives a natural explanation for the tensorization of the previously studied models. Finally, we give some remarks on the connection between our model and the continuous representation of graphs.

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Takanori Maehara, Hoang NT. 2019-10-09. A Simple Proof of the Universality of Invariant/Equivariant Graph Neural Networks. https://arxiv.org/abs/1910.03802

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