On the memory of the initial state during gradient descent dynamics in random energy landscapes

The weak ergodicity breaking hypothesis postulates that, after a quench from high to low temperature, out-of-equilibrium glassy systems lose memory of their initial state despite being unable to reach an equilibrium stationary state. It is a milestone of glass physics, and has provided a lot of insight on the physical properties of glass aging. Despite its undoubted usefulness as a guiding principle, its general validity remains a subject of debate. I will discuss evidence that this hypothesis does not hold in the special case of gradient descent dynamics in a specific class of random energy landscapes, corresponding to mean-field spin glass models. I will discuss how this impacts our understanding of gradient descent dynamics in more general disordered landscapes, such as glassy energy landscape or cost functions in random optimization problems.