Title: Cartan Networks: Group theoretical Hyperbolic Deep Learning
Primary area: learning on graphs and other geometries & topologies
Keywords: Hyperbolic networks, Hyperbolic space, Lie groups, Machine learning

Abstract: Hyperbolic deep learning leverages the metric properties of hyperbolic spaces to develop efficient and informative embeddings of hierarchical data. Here, we focus on the solvable group structure of hyperbolic spaces, which follows naturally from their construction as symmetric spaces. This dual nature of Lie groups and Riemannian manifolds allows us to propose a new class of hyperbolic deep learning algorithms where group homomorphisms are interleaved with metric-preserving diffeomorphisms. The resulting algorithms, which we call Cartan networks, show promising results on various benchmark datasets and open the way for a novel class of hyperbolic deep learning architectures, both feedforward and convolutional.