Boundary-layer asymptotics for Gaussian-smoothed singular measures

What the math gives to ML

The paper provides an explicit small-noise model for Gaussian smoothing of distributions supported on manifolds with boundaries and corners. Its transferable asset is the replacement of complicated local support geometry by an inward tangent cone, producing computable Gaussian integrals and score asymptotics in the boundary layer where ordinary manifold approximations fail. A practical neural-network use is to replace generic denoising-score targets near detected support boundaries with cone-aware analytic targets for diffusion models. The method is especially testable on data supported on half-spaces, orthants, simplices, truncated manifolds, and synthetic manifolds with known boundary strata.