Samplet compression for conditionally positive definite kernels and universal Kriging

What the math gives to ML

The paper's main transferable asset is an orthogonal multiscale representation whose detail vectors annihilate low-degree polynomials, while the transformed conditionally positive definite kernel becomes positive definite and quasi-sparse. This separates a small global polynomial channel from a large localized detail channel, avoiding dense indefinite systems without discarding the kernel structure. A promising neural adaptation is a samplet-compressed kernel interaction layer for point clouds, neural operators, or coordinate-based networks, with fixed multiscale transforms and a sparse transformed interaction matrix.