Fully Hyperbolic Neural Networks

Hyperbolic neural networks have shown great potential for modeling complex data. However, existing hyperbolic networks are not completely hyperbolic, as they encode features in the hyperbolic space yet formalize most of their operations in the tangent space (a Euclidean subspace) at the origin of the hyperbolic model. This hybrid method greatly limits the modeling ability of networks. In this paper, we propose a fully hyperbolic framework to build hyperbolic networks based on the Lorentz model by adapting the Lorentz transformations (including boost and rotation) to formalize essential operations of neural networks. Moreover, we also prove that linear transformation in tangent spaces used by existing hyperbolic networks is a relaxation of the Lorentz rotation and does not include the boost, implicitly limiting the capabilities of existing hyperbolic networks. The experimental results on four NLP tasks show that our method has better performance for building both shallow and deep networks. Our code is released to facilitate follow-up research 1 . Introduction Various recent efforts have explored hyperbolic neural networks to learn complex non-Euclidean data properties. Nickel and Kiela (2017); Cvetkovski and Crovella (2016); Verbeek and Suri (2014) learn hierarchical representations in a hyperbolic space and show that hyperbolic geometry * Equal contribution.