Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rethinking mean-field glassy dynamics and its relation with the energy
  landscape: the awkward case of the spherical mixed p-spin model   The spherical p-spin model is not only a fundamental model in statistical
mechanics of disordered system, but has recently gained popularity since many
hard problems in machine learning can be mapped on it. Thus the study of the
out of equilibrium dynamics in this model is interesting both for the glass
physics and for its implications on algorithms solving NP-hard problems. We
revisit the long-time limit of the out of equilibrium dynamics of mean-field
spherical mixed p-spin models. We consider quenches (gradient descent dynamics)
starting from initial conditions thermalized at some temperature in the ergodic
phase. We perform numerical integration of the dynamical mean-field equations
of the model and we find an unexpected dynamical phase transition. Below an
onset temperature, higher than the dynamical transition temperature, the
asymptotic energy goes below the "threshold energy" of the dominant marginal
minima of the energy function and memory of the initial condition is kept. This
behavior, not present in the pure spherical p-spin model, resembles closely the
one observed in simulations of glass-forming liquids. We then investigate the
nature of the asymptotic dynamics, finding an aging solution that relaxes
towards deep marginal minima, evolving on a restricted marginal manifold.
Careful analysis, however, rules out simple aging solutions. We compute the
constrained complexity in the aim of connecting the asymptotic solution to the
energy landscape.

21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin