On the Schauder Estimates for Non-local Equations with Drift: The Supercritical Case

What the math gives to ML

The paper provides a constructive frequency-localized dissipativity principle for nonlocal stable diffusion with a rough drift. Its key transferable asset is that every conic dyadic band obeys a maximum-principle lower bound, -L v(x_0) >= c 2^{alpha j} v(x_0), so high-frequency components are damped at a quantitatively predictable rate. This suggests augmenting residual networks with anisotropic fractional-diffusion blocks whose damping is calibrated by frequency band, while retaining a learned drift or convolution branch. The most plausible benefit is improved stability and robustness to high-frequency perturbations rather than an unconditional accuracy gain.