Orthogonal Origin Parking: Decoupling Lorentz Manifolds for Robust OOD Generalization

Fine-grained classification in deep taxonomies suffers from representational crowding: large macro-classes dominate the feature space, leaving little angular capacity for fine-grained distinctions, particularly under out-of-distribution (OOD) shifts. Standard hyperbolic spaces offer exponential volume for tree-like data, but embedding an entire taxonomy into a single manifold forces distinct macro-branches to compete for shared angular capacity and entangles their optimization updates. We introduce a geometric architecture that embeds hierarchical taxonomies into a Cartesian product of Lorentz manifolds. Our core mechanism, \textit{Orthogonal Origin Parking} (OOPark), decouples the taxonomy at the root level by assigning an independent Lorentz manifold to each macro-branch and penalizing inactive embeddings that deviate from the manifold origin. We evaluate across four biological OOD tasks/benchmarks (skin lesions, iWildCam, fungi, and plankton) characterised by hierarchical class structure, class imbalance, and domain shift. OOPark generally outperforms standard Euclidean and single-manifold hyperbolic baselines while using 20-dimensional sub-manifolds against Euclidean baselines of up to 512 dimensions, preserving both fine-grained accuracy and global taxonomic fidelity under severe distribution shifts. Code is provided in the supplementary material; a public release will follow upon acceptance.