Escaping Plato's Cave: Towards the Alignment of 3D and Text Latent
  Spaces
Authors: name: Souhail Hadgi, name: Luca Moschella, name: Andrea Santilli, name: Diego Gomez, name: Qixing Huang, name: Emanuele Rodolà, name: Simone Melzi, name: Maks Ovsjanikov

Recent works have shown that, when trained at scale, uni-modal 2D vision and
text encoders converge to learned features that share remarkable structural
properties, despite arising from different representations. However, the role
of 3D encoders with respect to other modalities remains unexplored.
Furthermore, existing 3D foundation models that leverage large datasets are
typically trained with explicit alignment objectives with respect to frozen
encoders from other representations. In this work, we investigate the
possibility of a posteriori alignment of representations obtained from
uni-modal 3D encoders compared to text-based feature spaces. We show that naive
post-training feature alignment of uni-modal text and 3D encoders results in
limited performance. We then focus on extracting subspaces of the corresponding
feature spaces and discover that by projecting learned representations onto
well-chosen lower-dimensional subspaces the quality of alignment becomes
significantly higher, leading to improved accuracy on matching and retrieval
tasks. Our analysis further sheds light on the nature of these shared
subspaces, which roughly separate between semantic and geometric data
representations. Overall, ours is the first work that helps to establish a
baseline for post-training alignment of 3D uni-modal and text feature spaces,
and helps to highlight both the shared and unique properties of 3D data
compared to other representations.