  Deep belief networks are used extensively for unsupervised stochastic
learning on large datasets. Compared to other deep learning approaches their
layer-by-layer learning makes them highly scalable. Unfortunately, the
principles by which they achieve efficient learning are not well understood.
Numerous attempts have been made to explain their efficiency and applicability
to a wide class of learning problems in terms of principles drawn from
cognitive psychology, statistics, information theory, and more recently
physics, but quite often these imported principles lack strong scientific
foundation. Here we demonstrate how one can arrive at convolutional deep belief
networks as potential solution to unsupervised learning problems without making
assumptions about the underlying framework. To do this, we exploit the notion
of symmetry that is fundamental in machine learning, physics and other fields,
utilizing the particular form of the functional renormalization group in
physics.
