  We study the space of functions computed by random-layered machines,
including deep neural networks and Boolean circuits. Investigating the
distribution of Boolean functions computed on the recurrent and layer-dependent
architectures, we find that it is the same in both models. Depending on the
initial conditions and computing elements used, we characterize the space of
functions computed at the large depth limit and show that the macroscopic
entropy of Boolean functions is either monotonically increasing or decreasing
with the growing depth.
