Superconvergence and aliasing saturation in Sloan iteration for spherical integral equations

What the math gives to ML

The paper identifies a concrete failure mode in iterative approximations of compact smoothing operators: repeated application can strongly suppress approximation error, but discretization aliases unresolved high-frequency content into retained low-frequency modes. Once this aliasing floor dominates, additional refinement steps stop improving accuracy. This suggests an anti-aliased iterative refinement block for spherical, graph, or neural-operator architectures that performs repeated learned smoothing at an overresolved latent bandwidth and projects down only after refinement. The falsifiable prediction is that increasing overresolution delays the depth at which refinement saturates.