Gradient-descent dynamics in mixed p-spin spherical models gives a controlled view of how high-dimensional glassy landscapes remember their initial conditions. This work shows that relaxation approaches marginal, nearly flat minima at energies below the threshold where stationary points become predominantly stable. The resulting asymptotic states can retain measurable memory even from random initial configurations, sharpening the debate around weak ergodicity breaking in mean-field glasses.
Key Concepts
- Landscape selection: Gradient descent selects atypical marginal minima rather than typical threshold states.
- Memory retention: Relaxation preserves information about the initial condition in the asymptotic state.
- Weak ergodicity breaking: Memory can persist even when the initial configuration is fully random.
