Hyperbolic Contrastive Learning for Hierarchical 3D Point Cloud Embedding

Hyperbolic spaces allow for more efficient modeling of complex, hierarchical structures, which is particularly beneficial in tasks involving multi-modal data. Although hyperbolic geometries have been proven effective for language-image pre-training, their capabilities to unify language, image, and 3D Point Cloud modalities are under-explored. We extend the 3D Point Cloud modality in hyperbolic multi-modal contrastive pre-training. Additionally, we explore the entailment, modality gap, and alignment regularizers for learning hierarchical 3D embeddings and facilitating the transfer of knowledge from both Text and Image modalities. These regularizers enable the learning of intra-modal hierarchy within each modality and inter-modal hierarchy across text, 2D images, and 3D Point Clouds. Experimental results demonstrate that our proposed training strategy yields an outstanding 3D Point Cloud encoder, and the obtained 3D Point Cloud hierarchical embeddings significantly improve performance on various downstream tasks.