We introduce Automorphism-based graph neural networks (Autobahn), a new familyofgraphneuralnetworks.

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.

In the Autobahn formalism, we make extensive use of the fact that the activations of a group-equivariant neural network can be treated as functions on the same group. Here we give a brief review for the unfamiliar reader. This formalism is also covered in detail in Sections 3 and 4 of Reference [6], although under slightly different conventions. Consider a space X acted on by a group G: at every point x in X, we can apply a group element g G, which maps x to another point in X . The action of the group on X induces an action on functions of X . For instance, for standard convolutional layers acting on images, each point on the space is a single pixel and the group of translation moves between pixels.

However, working with graph data raises new problems.

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.

Roborace is the world's first competition for human AI teams, using both self-driving and manually-controlled cars. Race formats will feature new forms of immersive entertainment to engage the next generation of racing fans. Through sport, innovations in machine-driven technologies will be accelerated. A self-driving car has set a speed record of 175 mph. In November 2017, Musk said the next Tesla Roadster would have three motors and be able to travel a whopping 0 to 60 miles per hour in 1.9 seconds with a top speed of 250 mph or even more.

Giving up the controls was as breathtakingly simple as touching two turquoise coloured buttons below the steering wheel with both thumbs. A melodious bell chimed, a line of LEDs stretching across the dashboard switched from red to yellow to aqua blue, and the steering wheel withdrew slowly and serenely from my sweaty grasp. But any nervousness I felt stemmed far more from being required to steer a multimillion-euro research vehicle the few kilometres from German car manufacturer Audi's headquarters in Ingolstadt, Bavaria, on to the autobahn, than the fact that "Jack" had now taken over the driving. I had signed a liability waiver before embarking on the road test, which required me to accept the risks of a piloted journey on the autobahn, including possible injury or death. But once Jack was calling the shots, it took remarkably little time to get used to the idea.