Towards hyperbolic regularizers for point cloud part segmentation

Hyperbolic neural networks are emerging as an effective technique to better capture hierarchical representations of many data types, from text to images and, recently, point clouds. In this paper, we extend our earlier work, that showed how to use regularizers in the hyperbolic space to improve performance of point cloud classification models, to the problem of part segmentation. This requires careful modeling of the hierarchical relationships between parts and whole point cloud to properly control the hyperbolic geometry of the feature space produced by the neural network. We show how the proposed method improves the performance of commonly used neural network architectures, reaching state-of-the-art performance on the part segmentation task.