Subaging in underparametrized Deep Neural Networks

Abstract

We consider a simple classification problem to show that the dynamics of finite-width Deep Neural Networks in the underparametrized regime gives rise to effects similar to those associated with glassy systems, namely a slow evolution of the loss function and aging. Remarkably, the aging is sublinear in the waiting time (subaging) and the power-law exponent characterizing it is robust to different architectures under the constraint of a constant total number of parameters. Our results are maintained in the more complex scenario of the MNIST database. We find that for this database there is a unique exponent ruling the subaging behavior in the whole phase.