Autobahn: Automorphism-based Graph Neural Nets

TL;DR

Autobahn introduces automorphism-based graph neural networks that decompose graphs into subgraphs with local convolutions, achieving competitive results on molecular graph tasks by preserving permutation equivariance.

Contribution

The paper presents a novel GNN framework that generalizes existing architectures and introduces new ones based on automorphism groups of subgraphs.

Findings

Achieves competitive results on molecular graph benchmarks.

Generalizes existing message passing neural networks.

Introduces new architectures based on graph decompositions.

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.