At low temperatures, the dynamics of glasses suffer a dramatic slowing down. The system becomes stuck in metastable configurations called traps, which are rarely abandoned, through a process called activation. The Trap Model (TM), that de- scribe the motion between different traps, provides a simplified framework to un- derstand activated dynamics. Even though signs of TM-like behavior were found in realistic systems, it is not clear (i) whether the dynamics of most models is the one predicted by the TM, (ii) to what extent the TM description applies to other glasses and (iii) which are the relevant features for this dynamics to be found. We show that the TM description does apply to other glassy models, such as the Ran- dom Energy Model , if one defines the traps dynamically, through the time series of the energy . We then extend our analysis to systems with correlated energy levels, and see that the trap behavior holds as long as the correlations are weak . Once the correlations are strong enough, as it happens in a Hamiltonian system, it is unclear whether the dynamic behavior of the glass can be completely described through the simple picture provided by the TM.
Comparing Dynamics of Glasses with Deep Neural Networks
Time permitting, a second section on Deep Learning is presented. We study dynam- ics and energy (or loss) landscape of feedforward Deep Neural Networks , with an emphasis on their Mean Square Displacement, and find that they exhibit aging on a finite time scale. Later, they start diffusing at the bottom of the landscape. Further, we argue that the slow dynamics is due rather to flat directions in the landscape than to barrier crossing, and we show evidence of an under- to over-parametrized phase transition.
1.  M. Baity-Jesi, G. Biroli & C. Cammarota, J. Stat. Mech. (2018) 013301.
2.  C. Cammarota & E. Marinari, Phys. Rev. E 92 010301(R) (2015).
3.  M. Baity-Jesi, A. Achard-de Lustrac & G. Biroli, Phys. Rev. E 98, 012133 (2018).
4.  M. Baity-Jesi, L. Sagun, M. Geiger, S. Spigler, G. Ben-Arous, C. Cammarota, Y. LeCun, M. Wyart & G. Biroli, PMLR 80:324-333, 2018 (ICML 2018).