  A complete understanding of the widely used over-parameterized deep networks
is a key step for AI. In this work we try to give a geometric picture of
over-parameterized deep networks using our geometrization scheme. We show that
the Riemannian geometry of network complexity plays a key role in understanding
the basic properties of over-parameterizaed deep networks, including the
generalization, convergence and parameter sensitivity. We also point out deep
networks share lots of similarities with quantum computation systems. This can
be regarded as a strong support of our proposal that geometrization is not only
the bible for physics, it is also the key idea to understand deep learning
systems.
