  It is commonly believed that the hidden layers of deep neural networks (DNNs)
attempt to extract informative features for learning tasks. In this paper, we
formalize this intuition by showing that the features extracted by DNN coincide
with the result of an optimization problem, which we call the `universal
feature selection' problem, in a local analysis regime. We interpret the
weights training in DNN as the projection of feature functions between feature
spaces, specified by the network structure. Our formulation has direct
operational meaning in terms of the performance for inference tasks, and gives
interpretations to the internal computation results of DNNs. Results of
numerical experiments are provided to support the analysis.
