  In suitably initialized wide networks, small learning rates transform deep
neural networks (DNNs) into neural tangent kernel (NTK) machines, whose
training dynamics is well-approximated by a linear weight expansion of the
network at initialization. Standard training, however, diverges from its
linearization in ways that are poorly understood. We study the relationship
between the training dynamics of nonlinear deep networks, the geometry of the
loss landscape, and the time evolution of a data-dependent NTK. We do so
through a large-scale phenomenological analysis of training, synthesizing
diverse measures characterizing loss landscape geometry and NTK dynamics. In
multiple neural architectures and datasets, we find these diverse measures
evolve in a highly correlated manner, revealing a universal picture of the deep
learning process. In this picture, deep network training exhibits a highly
chaotic rapid initial transient that within 2 to 3 epochs determines the final
linearly connected basin of low loss containing the end point of training.
During this chaotic transient, the NTK changes rapidly, learning useful
features from the training data that enables it to outperform the standard
initial NTK by a factor of 3 in less than 3 to 4 epochs. After this rapid
chaotic transient, the NTK changes at constant velocity, and its performance
matches that of full network training in 15% to 45% of training time. Overall,
our analysis reveals a striking correlation between a diverse set of metrics
over training time, governed by a rapid chaotic to stable transition in the
first few epochs, that together poses challenges and opportunities for the
development of more accurate theories of deep learning.
