  While deep neural networks (DNNs) have proven to be efficient for numerous
tasks, they come at a high memory and computation cost, thus making them
impractical on resource-limited devices. However, these networks are known to
contain a large number of parameters. Recent research has shown that their
structure can be more compact without compromising their performance. In this
paper, we present a sparsity-inducing regularization term based on the ratio
l1/l2 pseudo-norm defined on the filter coefficients. By defining this
pseudo-norm appropriately for the different filter kernels, and removing
irrelevant filters, the number of kernels in each layer can be drastically
reduced leading to very compact Deep Convolutional Neural Networks (DCNN)
structures. Unlike numerous existing methods, our approach does not require an
iterative retraining process and, using this regularization term, directly
produces a sparse model during the training process. Furthermore, our approach
is also much easier and simpler to implement than existing methods.
Experimental results on MNIST and CIFAR-10 show that our approach significantly
reduces the number of filters of classical models such as LeNet and VGG while
reaching the same or even better accuracy than the baseline models. Moreover,
the trade-off between the sparsity and the accuracy is compared to other loss
regularization terms based on the l1 or l2 norm as well as the SSL, NISP and
GAL methods and shows that our approach is outperforming them.
