  With the success of deep neural networks (NNs) in a variety of domains, the
computational and storage requirements for training and deploying large NNs
have become a bottleneck for further improvements. Sparsification has
consequently emerged as a leading approach to tackle these issues. In this
work, we consider a simple yet effective approach to sparsification, based on
the Bridge, or $L_p$ regularization during training. We introduce a novel
weight decay scheme, which generalizes the standard $L_2$ weight decay to any
$p$ norm. We show that this scheme is compatible with adaptive optimizers, and
avoids the gradient divergence associated with $0<p<1$ norms. We empirically
demonstrate that it leads to highly sparse networks, while maintaining
generalization performance comparable to standard $L_2$ regularization.
