  Promising resolutions of the generalization puzzle observe that the actual
number of parameters in a deep network is much smaller than naive estimates
suggest. The renormalization group is a compelling example of a problem which
has very few parameters, despite the fact that naive estimates suggest
otherwise. Our central hypothesis is that the mechanisms behind the
renormalization group are also at work in deep learning, and that this leads to
a resolution of the generalization puzzle. We show detailed quantitative
evidence that proves the hypothesis for an RBM, by showing that the trained RBM
is discarding high momentum modes. Specializing attention mainly to
autoencoders, we give an algorithm to determine the network's parameters
directly from the learning data set. The resulting autoencoder almost performs
as well as one trained by deep learning, and it provides an excellent initial
condition for training, reducing training times by a factor between 4 and 100
for the experiments we considered. Further, we are able to suggest a simple
criterion to decide if a given problem can or can not be solved using a deep
network.
