Towards Fully Dynamic Omnitrees: Moment-Conserving Anisotropic Compression With Wavelets

What the math gives to ML

The paper provides an anisotropic hierarchical representation in which each rectangular cell may be bisected along an arbitrary subset of coordinates, rather than being forced into isotropic octree refinement. Its key transferable asset is the exact Haar change of basis between leaf values and hierarchical detail coefficients: the scaling coefficient preserves the local mean, while detail coefficients quantify which spatial directions need resolution. This suggests replacing uniformly sized feature grids in neural fields or spatially indexed neural networks with a dynamically refined, coarsened, and anisotropically split wavelet tree. The most practical first test is a multiresolution voxel or hash-grid encoder whose cells are split and merged using feature-space Haar energy while periodically distilling the resulting sparse representation into a fixed decoder.