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