Unverified
2026
Spherical Hemisphere Balance Regularizer
Add a coordinate-free regularizer that prevents a batch of unit-normalized embeddings from concentrating almost entirely on one side of a hyperplane passing through their spherical centroid. Sample random directions tangent to the estimated centroid, measure the soft fraction of embeddings in each corresponding hemisphere, and penalize fractions below the spherical Grünbaum constant. This targets directional mode collapse while preserving rotational invariance.
Paper: The Spherical Grünbaum Inequality
arXiv:2607.16924