Glassy dynamics in deep neural networks: A structural comparison

Deep neural networks (DNNs) share important similarities with structural glasses. Both have many degrees of freedom and their dynamics are governed by a high-dimensional, nonconvex landscape representing either the loss or energy, respectively. Furthermore, both experience gradient descent dynamics subject to noise. In this work we investigate, by performing quantitative measurements on realistic networks trained on the MNIST and CIFAR-10 data sets, the extent to which this qualitative similarity gives rise to glasslike dynamics in neural networks. We demonstrate the existence of a topology trivialization transition as well as the previously studied under-to-overparametrized transition analogous to jamming. By training DNNs with overdamped Langevin dynamics in the resulting disordered phases, we do not observe diverging relaxation times at nonzero temperature nor do we observe any caging effects, in contrast to glass phenomenology. However, the weight overlap function follows a power law in time, with exponent <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>≈</a:mo><a:mo>−</a:mo><a:mn>0.5</a:mn></a:mrow></a:math>, in agreement with the mode-coupling theory of structural glasses. In addition, the DNN dynamics obey a form of time-temperature superposition. Finally, dynamic heterogeneity and aging are observed at low temperatures. These results highlight important and surprising points of both difference and agreement between the behavior of DNNs and structural glasses.