Clustering versus sorting: a mass-conserving reaction-diffusion model of planar polarity puncta

What the math gives to ML

This paper provides a constructive mass-conserving reaction-diffusion mechanism that separates three useful behaviors: total punctum mass, punctum width, and punctum spacing. Its transferable asset is not merely diffusion, but reversible local reactions with conserved reservoirs and sign-opposed orientation channels, which can create sparse, mutually exclusive assignments without softmax normalization. A neural implementation could use a small number of explicit reaction-diffusion steps as a differentiable clustering or routing layer over image patches, tokens, or graph nodes, with feature-dependent reaction rates and exact conservation enforced by the update. The reported absence of oscillatory instabilities also makes this a plausible stable alternative to unconstrained recurrent competitive routing.