Sharp asymptotics for higher-order Hardy constants on lattices

What the math gives to ML

The paper proves a sharp coercivity inequality for higher-order discrete fields: discrete derivative energy controls an inverse-radial weighted L2 norm, with asymptotic constant 2^ell d^ell in lattice dimension d. The transferable asset is a dimension-aware barrier against feature concentration near a designated anchor in grid-indexed neural representations. A practical adaptation is a Hardy-weighted regularizer for CNN feature maps, neural fields, or lattice embeddings, optionally combined with a zero-mean projection and a discrete Laplacian penalty.