Taxonomy-Aligned Hyperbolic Learning for 3D Point Cloud

Hierarchical 3D segmentation requires accurate point-wise predictions and coherent representations across semantic levels. However, enforcing consistency among predicted labels does not by itself ensure that feature geometry reflects the underlying taxonomy. We introduce Hy3D, a hierarchical hyperbolic prototype network that learns multi-level point features in a shared Poincar\'e ball for 3D semantic and part segmentation. A shared hyperbolic projection layer maps features from all hierarchy levels into a common space with a unified scale, while an online prototype bank maintains per-level, per-class prototypes through cloud-balanced exponential moving averages in the tangent space. During training, a parent-prototype triplet loss and a depth-aware radius loss encourage parent affinity and radial progression, aligning the learned representations with the label hierarchy. M\"obius classification heads produce class logits from the hyperbolic features without modifying the underlying Euclidean backbone. Experiments on Campus3D and PartNeXt demonstrate the effectiveness of Hy3D in improving segmentation performance across both scene-level semantic hierarchies and fine-grained part hierarchies.