Size-Dependent Growth Rates Amplify Infinitesimal Asymmetry in Nanocrystals

What the math gives to ML

The paper gives a constructive mechanism for deterministic amplification of arbitrarily small asymmetries: a finite-domain growth event has a survival time determined by an integrated coverage hazard, and the resulting facet velocity depends on the current facet size. This suggests a neural module in which routing, token allocation, or active-computation regions grow at rates determined by their current occupancy, creating controllable positive or negative feedback between usage and future capacity. The most direct experiment is a differentiable size-dependent mixture-of-experts router, comparing occupancy-independent routing against a survival-time-derived growth rate while measuring whether tiny initial load perturbations amplify according to the predicted variational dynamics. The transfer is speculative and should be treated as a dynamical-systems-inspired adaptive routing mechanism rather than as a drop-in optimizer.