Exploiting Symmetries in Inference and Learning

Max Welling Professor, University of Amsterdam Abstract Symmetries play a crucial role in much of mathematics and physics. In this talk I will explore the role that symmetries are playing in machine learning. In particular I will discuss the concept of equivariance and apply it to neural networks. After the introduction I will discuss two newer works: first E(n) equivariant graph neural networks that are equivariant to both permutations of the nodes and global E(n) transformations of the node features. These models are ideal for predicting molecular properties in biology and chemistry and to model objects as point clouds in computer vision. Secondly I will show how invariance if probability densities result in very efficient deterministic mcmc samplers with better convergence behavior. We show that by modeling the sampler as a push-forward of the density according to an ODE, and by identifying a very large set of symmetries for an arbitrary density characterized divergence free vector fields, we can indeed d