Minkowski sums with convex curves without pointwise Fourier decay

What the math gives to ML

The paper gives a physical-space overlap estimate for tubular neighborhoods of uniformly curved curves, without requiring Fourier decay. The transferable asset is the explicit inverse-distance bound on translated tube intersections, which converts curvature into a measurable anti-overlap and coverage principle. A practical neural adaptation is to learn a curved latent augmentation manifold and regularize its translated copies so that they cover feature space without excessive collapse; the theorem supplies the target scaling and curvature constraint. This is a moderate-risk idea because the positive-measure Minkowski-sum guarantee is planar and geometric, so experiments should first test whether the overlap-derived regularizer improves latent coverage and robustness.