From diffusion to transmission via EDP-convergence: a paradigmatic multiscale limit
arXiv:2607.11478
2026
Dynamics
1 ideas extracted · analyzed Aug 30, 2026
What the math gives to ML
The paper develops an energy-dissipative reduction in which a thin region of vanishing mobility becomes an explicit membrane law coupling the flux to the jump in chemical potential. This offers a principled replacement for unconstrained residual coupling between neural modules: exchange can be conservative while the interface is guaranteed not to increase the chosen latent energy. The most direct experiment is a membrane layer connecting two subnetworks or graph partitions, with a monotone Marcelin–De Donder kinetic relation and learned positive mobility.
Ideas from this paper
Unverified
2026
Split a neural state into two subnetworks or two groups of latent channels and connect them through a conservative membrane flux instead of an unconstrained residual or concatenation. The flux is driven by the difference in chemical potential and uses an odd monotone exponential law, so the interface transfers information while guaranteeing nonnegative dissipation.
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