  We study mechanisms to characterize how the asymptotic convergence of
backpropagation in deep architectures, in general, is related to the network
structure, and how it may be influenced by other design choices including
activation type, denoising and dropout rate. We seek to analyze whether network
architecture and input data statistics may guide the choices of learning
parameters and vice versa. Given the broad applicability of deep architectures,
this issue is interesting both from theoretical and a practical standpoint.
Using properties of general nonconvex objectives (with first-order
information), we first build the association between structural, distributional
and learnability aspects of the network vis-\`a-vis their interaction with
parameter convergence rates. We identify a nice relationship between feature
denoising and dropout, and construct families of networks that achieve the same
level of convergence. We then derive a workflow that provides systematic
guidance regarding the choice of network sizes and learning parameters often
mediated4 by input statistics. Our technical results are corroborated by an
extensive set of evaluations, presented in this paper as well as independent
empirical observations reported by other groups. We also perform experiments
showing the practical implications of our framework for choosing the best
fully-connected design for a given problem.
