2018/03/19 by Marco Baity-Jesi, M. Baity-Jesi, L. Sagun +15 · 1 voice · 2 citations
Computer Science · Materials Science · Mathematics · Physics and Astronomy · #Machine Learning in Materials Science #Material Dynamics and Properties #Quantum many-body systems #cond-mat.dis-nn #cs.LG #stat.ML
paper · pdf · doi:10.1088/1742-5468/ab3281
published as PMLR 80:324-333, 2018; Republication with DOI (cite this one): J. Stat. Mech. (2019) 124013 · 10 pages, 5 figures. Version accepted at ICML 2018
arxiv published 2018/03/19 · openalex created_date 2018/03/29 · arxiv created 2018/06/07 · openalex publication_date 2019/12/01 · arxiv updated 2019/12/23 · openalex updated_date 2026/08/05
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.