Abstract We develop new theoretical results on matrix perturbation to shed light the impact of architecture performance a deep network. In particular, we explain analytically what learning practitioners have long observed empirically: parameters some architectures (e.g., residual networks, ResNets, and Dense DenseNets) are easier optimize than others convolutional ConvNets). Building our earlie...

is considered. We are interesting for asymptotics of the perturbed solution u(x, t; ε) as ε→ 0. Perturbation theory for integrable equations remains a very attractive task. As a rule a perturbation of smooth solutions such as a single soliton were usually considered. We intend here to discuss a perturbation of a singular solution under assumption that the perturbed solution has singularities as...