Classical fractons with cosmological fixed points

What the math gives to ML

The paper provides a nonstandard attractor mechanism: a conservative Hamiltonian system can lack attractors in full phase space while its projected scale and shape variables converge to stable fixed-point configurations. The transferable asset is the separation of global scale from normalized shape, together with central-configuration equations that predict which parameter distributions are attracting. A neural-network implementation can augment parameters with momentum-like variables, decompose weights into norm and direction, and stabilize only the directional shape dynamics while allowing compensating motion in hidden momentum variables. This gives a falsifiable prediction: normalized parameter configurations should converge at a measurable rate even if the complete augmented optimizer remains non-dissipative.