Thresholds, fragmentation and symmetrization in parabolic equations

What the math gives to ML

The paper gives a constructive counterexample to the intuition that concentration or symmetrization is always favorable for nonlinear diffusion: two initial fields with exactly the same value distribution and support measure can have opposite long-time outcomes solely because one is spatially fragmented. The transferable asset is a distribution-preserving geometric perturbation whose effect is amplified by threshold nonlinearities and diffusion. A plausible neural-network use is a fragmentation augmentation or regularizer for spatial models, especially models with bistable activations, cellular-update dynamics, segmentation masks, or sparse spatial inputs, where preserving histograms while varying connected-component structure may improve robustness to spatial layout.