Statistical stability of random potentials to thermal and quantum activation

What the math gives to ML

The paper gives a constructive reduction of observables in Gaussian random potentials to the joint distribution of local Taylor coefficients, whose covariances are determined by derivatives of the potential Green function. It connects local curvature and barrier statistics to thermal and quantum activation rates, relating observable escape dynamics to disorder in the landscape. A transferable neural-network mechanism is curvature- and escape-rate-controlled Langevin training: estimate loss-landscape barriers and adapt optimizer noise to maintain a prescribed basin-escape rate. The main falsifiable prediction is an Arrhenius relation between escape frequency and inverse effective temperature, with a measurable trapping-to-exploration transition.