  Several works have aimed to explain why overparameterized neural networks
generalize well when trained by Stochastic Gradient Descent (SGD). The
consensus explanation that has emerged credits the randomized nature of SGD for
the bias of the training process towards low-complexity models and, thus, for
implicit regularization. We take a careful look at this explanation in the
context of image classification with common deep neural network architectures.
We find that if we do not regularize \emph{explicitly}, then SGD can be easily
made to converge to poorly-generalizing, high-complexity models: all it takes
is to first train on a random labeling on the data, before switching to
properly training with the correct labels. In contrast, we find that in the
presence of explicit regularization, pretraining with random labels has no
detrimental effect on SGD. We believe that our results give evidence that
explicit regularization plays a far more important role in the success of
overparameterized neural networks than what has been understood until now.
Specifically, by penalizing complicated models independently of their fit to
the data, regularization affects training dynamics also far away from optima,
making simple models that fit the data well discoverable by local methods, such
as SGD.
