Humans can recognize novel combinations of known concepts with little to no effort. Even something as unlikely as a blue apple would be immediately understood, not because we have seen one before, but because we can mentally separate “blue” from “apple” and recombine them. This compositional understanding allows us to generalize beyond direct experience, which makes us wonder, can vision models do the same? This thesis examines compositionality in vision-only and vision-language models across both spherical and hyperbolic embedding geometries. Prior work introduced Geodesically Decomposable Embeddings (GDE), a framework that projects embeddings onto a tangent space at their intrinsic mean and extracts separate attribute and object directions.