Autobahn: Automorphism-based Graph Neural Nets

Erik Henning Thiede, Wenda Zhou, Risi Kondor

Keywords: Graph Neural Networks, Group Equivariance

TL;DR: We introduce a family of graph neural networks that use convolutions against the automorphism group of local subgraphs. This generalizes message passing neural networks and leads to flexible, geometrically intuitive convolutions.

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 apply 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. 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 results competitive with state-of-the-art message passing algorithms.

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Code: https://github.com/risilab/Autobahn

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2103.01710/code)