  Label inventories for fine-grained entity typing have grown in size and
complexity. Nonetheless, they exhibit a hierarchical structure. Hyperbolic
spaces offer a mathematically appealing approach for learning hierarchical
representations of symbolic data. However, it is not clear how to integrate
hyperbolic components into downstream tasks. This is the first work that
proposes a fully hyperbolic model for multi-class multi-label classification,
which performs all operations in hyperbolic space. We evaluate the proposed
model on two challenging datasets and compare to different baselines that
operate under Euclidean assumptions. Our hyperbolic model infers the latent
hierarchy from the class distribution, captures implicit hyponymic relations in
the inventory, and shows performance on par with state-of-the-art methods on
fine-grained classification with remarkable reduction of the parameter size. A
thorough analysis sheds light on the impact of each component in the final
prediction and showcases its ease of integration with Euclidean layers.
