Autobahn: Automorphism-based Graph Neural Nets
This work addresses the need for more expressive and intuitive graph neural network architectures for domains like molecular modeling, though it appears incremental as it builds upon existing frameworks.
The authors tackled the problem of designing graph neural networks with better equivariance properties by introducing Autobahn, which decomposes graphs into subgraphs and applies local convolutions equivariant to automorphism groups, achieving competitive results with state-of-the-art methods on molecular graphs.
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.