  In this work we present a method to improve the pruning step of the current
state-of-the-art methodology to compress neural networks. The novelty of the
proposed pruning technique is in its differentiability, which allows pruning to
be performed during the backpropagation phase of the network training. This
enables an end-to-end learning and strongly reduces the training time. The
technique is based on a family of differentiable pruning functions and a new
regularizer specifically designed to enforce pruning. The experimental results
show that the joint optimization of both the thresholds and the network weights
permits to reach a higher compression rate, reducing the number of weights of
the pruned network by a further 14% to 33% compared to the current
state-of-the-art. Furthermore, we believe that this is the first study where
the generalization capabilities in transfer learning tasks of the features
extracted by a pruned network are analyzed. To achieve this goal, we show that
the representations learned using the proposed pruning methodology maintain the
same effectiveness and generality of those learned by the corresponding
non-compressed network on a set of different recognition tasks.
