  We present a Statistical Mechanics (SM) model of deep neural networks,
connecting the energy-based and the feed forward networks (FFN) approach. We
infer that FFN can be understood as performing three basic steps: encoding,
representation validation and propagation. From the meanfield solution of the
model, we obtain a set of natural activations -- such as Sigmoid, $\tanh$ and
ReLu -- together with the state-of-the-art, Swish; this represents the expected
information propagating through the network and tends to ReLu in the limit of
zero noise.We study the spectrum of the Hessian on an associated classification
task, showing that Swish allows for more consistent performances over a wider
range of network architectures.
