This project explores the gradient descent dynamics within the mixed p-spin spherical model, a prototypical glass model characterized by a complex energy landscape with numerous minima. The system evolves asymptotically towards marginal (aka flat) minima, retaining memory of its initial conditions and reaching energies below the energy threshold, where most stationary points transition into minima. Memory retention can persist even when the system begins from a completely random configuration, challenging the validity of the weak ergodicity breaking hypothesis.
Key Concepts
Memory Retention: The system retains information about its initial conditions as it relaxes towards asymptotic states.
Energy Below Threshold: The system's dynamics reaches marginal minima below the threshold energy.
Weak Ergodicity Breaking: The project challenges the hypothesis by showing that memory can persist even from random initial configurations.
