  We argue that the optimization plays a crucial role in generalization of deep
learning models through implicit regularization. We do this by demonstrating
that generalization ability is not controlled by network size but rather by
some other implicit control. We then demonstrate how changing the empirical
optimization procedure can improve generalization, even if actual optimization
quality is not affected. We do so by studying the geometry of the parameter
space of deep networks, and devising an optimization algorithm attuned to this
geometry.

Machine Learning