Intertwining the line bundle and Grauert-tube Hardy quantizations of the round 2-sphere
arXiv:2608.13965
2026
Architecture
1 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper gives an explicit, representation-theoretic change of basis between two Hardy quantizations of the same cosphere bundle. Its transferable asset is not the sphere-specific geometry itself, but the construction of equivariant operators that act independently on irreducible frequency blocks while changing the selected multiplicity line, with analytically known overlap coefficients. This suggests a fixed or learnable spherical or SO(3)-equivariant module that switches between base-complex, holomorphic feature bases and geodesic-flow-adapted bases, with frequency-dependent mixing initialized from the exact overlap formula.
Ideas from this paper
Unverified
2026
Insert a fixed or partially learnable equivariant change-of-basis module into a spherical or SO(3)-equivariant network. At each angular frequency \(\ell\), the module maps the line selected by the line-bundle quantization to the line selected by the Grauert-tube quantization, allowing the network to represent both holomorphic/base-local and geodesic-flow-adapted features without breaking rotation equivariance.
Useful5/10
Difficulty5/10
Novelty8/10