Cartan Networks: Group theoretical Hyperbolic Deep Learning
This work addresses the need for efficient embeddings in hierarchical data processing, representing an incremental advancement in hyperbolic deep learning architectures.
The paper tackled the problem of embedding hierarchical data by introducing Cartan networks, a new class of hyperbolic deep learning algorithms that combine group homomorphisms with metric-preserving diffeomorphisms, showing promising results on benchmark datasets.
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 group and Riemannian manifold 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 data sets and open the way to a novel class of hyperbolic deep learning architectures.