  Regularization is a set of techniques that are used to improve the
generalization ability of deep neural networks. In this paper, we introduce
weight compander (WC), a novel effective method to improve generalization by
reparameterizing each weight in deep neural networks using a nonlinear
function. It is a general, intuitive, cheap and easy to implement method, which
can be combined with various other regularization techniques. Large weights in
deep neural networks are a sign of a more complex network that is overfitted to
the training data. Moreover, regularized networks tend to have a greater range
of weights around zero with fewer weights centered at zero. We introduce a
weight reparameterization function which is applied to each weight and
implicitly reduces overfitting by restricting the magnitude of the weights
while forcing them away from zero at the same time. This leads to a more
democratic decision-making in the network. Firstly, individual weights cannot
have too much influence in the prediction process due to the restriction of
their magnitude. Secondly, more weights are used in the prediction process,
since they are forced away from zero during the training. This promotes the
extraction of more features from the input data and increases the level of
weight redundancy, which makes the network less sensitive to statistical
differences between training and test data. We extend our method to learn the
hyperparameters of the introduced weight reparameterization function. This
avoids hyperparameter search and gives the network the opportunity to align the
weight reparameterization with the training progress. We show experimentally
that using weight compander in addition to standard regularization methods
improves the performance of neural networks.
