Thermalization packets and optimal ice cubes

What the math gives to ML

The paper provides a transferable spectral mechanism: an auxiliary system can be prepared so that, after coupling to a target, its initial state has zero overlap with the slowest relaxation eigenmode. The optimal preparation is therefore determined by eigenvector-overlap cancellation rather than by maximal cooling or maximal distance from equilibrium. A direct neural-network analogue is a coupled pair of parameter replicas, where a deliberately prepared auxiliary replica cancels the slow Hessian mode of training dynamics and accelerates local relaxation without increasing the learning rate.