Autobahn: Automorphism-based Graph Neural Nets

• URL: http://arxiv.org/abs/2103.01710v1
• Date: Tue, 2 Mar 2021 13:34:29 GMT
• Title: Autobahn: Automorphism-based Graph Neural Nets
• Authors: Erik Henning Thiede, Wenda Zhou, Risi Kondor
• Abstract summary: We introduce Automorphism-based graph neural networks (Autobahn) In an Autobahn, we decompose the graph into a collection of subgraphs and applying local convolutions that are equivariant to each subgraph's automorphism group. We validate our approach by applying Autobahn to molecular graphs, where it achieves state-of-the-art results.
• Score: 12.029647699164315
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce Automorphism-based graph neural networks (Autobahn), a new family of graph neural networks. In an Autobahn, we decompose the graph into a collection of subgraphs and applying local convolutions that are equivariant to each subgraph's automorphism group. Specific choices of local neighborhoods and subgraphs recover existing architectures such as message passing neural networks. However, our formalism also encompasses novel architectures: as an example, we introduce a graph neural network that decomposes the graph into paths and cycles. The resulting convolutions reflect the natural way that parts of the graph can transform, preserving the intuitive meaning of convolution without sacrificing global permutation equivariance. We validate our approach by applying Autobahn to molecular graphs, where it achieves state-of-the-art results.

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