Glassy dynamics in deep neural networks: A structural comparison

TL;DR

This paper explores the glass-like dynamics of deep neural networks, revealing both similarities and differences with structural glasses through quantitative analysis of trained models and their phase transitions.

Contribution

It provides the first detailed comparison of neural network dynamics with glass phenomenology, identifying phase transitions and analyzing their dynamic behavior.

Findings

Existence of a Topology Trivialisation Transition.

DNNs do not show diverging relaxation times at non-zero temperature.

Weight overlap follows a power law consistent with Mode-Coupling Theory.

Abstract

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, non-convex 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 datasets, the extent to which this qualitative similarity gives rise to glass-like dynamics in neural networks. We demonstrate the existence of a Topology Trivialisation Transition as well as the previously studied under-to-overparameterised transition analogous to jamming. By training DNNs with overdamped Langevin dynamics in the resulting disordered phases, we do not observe diverging relaxation times at non-zero 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 $\approx -0.5$, 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 ageing are observed at low temperatures. These results highlight important and surprising points of both difference and agreement between the behaviour of DNNs and structural glasses.