Comparing dynamics: deep neural networks versus glassy systems

Marco Baity-Jesi, Levent Sagun, Mario Geiger, Stefano Spigler, Gérard Ben Arous, Chiara Cammarota, Yann Lecun, Matthieu Wyart, Giulio Biroli

Research output: Contribution to journalArticlepeer-review


We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems. The two main issues we address are (1) the complexity of the loss landscape and of the dynamics within it, and (2) to what extent DNNs share similarities with glassy systems. Our findings, obtained for different architectures and datasets, suggest that during the training process the dynamics slows down because of an increasingly large number of flat directions. At large times, when the loss is approaching zero, the system diffuses at the bottom of the landscape. Despite some similarities with the dynamics of mean-field glassy systems, in particular, the absence of barrier crossing, we find distinctive dynamical behaviors in the two cases, showing that the statistical properties of the corresponding loss and energy landscapes are different. In contrast, when the network is under-parametrized we observe a typical glassy behavior, thus suggesting the existence of different phases depending on whether the network is under-parametrized or over-parametrized.

Original languageEnglish (US)
Article number124013
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number12
StatePublished - Dec 20 2019


  • machine learning

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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