  The aim of this work is to enable inference of deep networks that retain high
accuracy for the least possible model complexity, with the latter deduced from
the data during inference. To this end, we revisit deep networks that comprise
competing linear units, as opposed to nonlinear units that do not entail any
form of (local) competition. In this context, our main technical innovation
consists in an inferential setup that leverages solid arguments from Bayesian
nonparametrics. We infer both the needed set of connections or locally
competing sets of units, as well as the required floating-point precision for
storing the network parameters. Specifically, we introduce auxiliary discrete
latent variables representing which initial network components are actually
needed for modeling the data at hand, and perform Bayesian inference over them
by imposing appropriate stick-breaking priors. As we experimentally show using
benchmark datasets, our approach yields networks with less computational
footprint than the state-of-the-art, and with no compromises in predictive
accuracy.
