Polaris: Coupled Orbital Polar Embeddings for Hierarchical Concept Learning
Real-world knowledge is often organized as hierarchies such as product taxonomies, medical ontologies, and label trees, yet learning hierarchical representations is challenging due to asymmetric structure and noisy semantics. We introduce Polaris, a polar hyperspherical embedding framework that separates semanticity from hierarchy using angular geometry and radius, enabling the learning of meaning and structure without interference. To map latent representation onto the sphere, we project it to the tangent space at the north pole, apply the exponential map, and learn unit-norm representations using spherical linear layers. Polaris then combines robust local constraints, global regularizat...
| Authors | Sahil Mishra, Srinitish Srinivasan, Sourish Dasgupta et al. |
|---|---|
| Primary category | cs.LG |
| Published | 30 April 2026 |
| Last updated at source | 29 May 2026 |
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