Quantitative stability of the intersection body operator near the ball, and the dynamical origin of the two--dimensional degeneracy

What the math gives to ML

The paper supplies a nonlinear operator on positive spherical functions whose local dynamics have a specific mode structure: degree-two spherical harmonics, representing ellipsoidal deformations, are exactly neutral, while all higher harmonics contract. This is transferable as a geometry-aware feature normalization or regularization module for neural networks processing directional data, where preserving low-order anisotropy while suppressing high-frequency angular structure may improve stability and generalization. The useful engineering object is the differentiable map formed from a pointwise power and the spherical Funk transform, together with its explicit contraction gap.