  This paper extends our previous work on regularization of neural networks
using Eigenvalue Decay by employing a soft approximation of the dominant
eigenvalue in order to enable the calculation of its derivatives in relation to
the synaptic weights, and therefore the application of back-propagation, which
is a primary demand for deep learning. Moreover, we extend our previous
theoretical analysis to deep neural networks and multiclass classification
problems. Our method is implemented as an additional regularizer in Keras, a
modular neural networks library written in Python, and evaluated in the
benchmark data sets Reuters Newswire Topics Classification, IMDB database for
binary sentiment classification, MNIST database of handwritten digits and
CIFAR-10 data set for image classification.
