  It is often the case that the performance of a neural network can be improved
by adding layers. In real-world practices, we always train dozens of neural
network architectures in parallel which is a wasteful process. We explored
$CompNet$, in which case we morph a well-trained neural network to a deeper one
where network function can be preserved and the added layer is compact. The
work of the paper makes two contributions: a). The modified network can
converge fast and keep the same functionality so that we do not need to train
from scratch again; b). The layer size of the added layer in the neural network
is controlled by removing the redundant parameters with sparse optimization.
This differs from previous network morphism approaches which tend to add more
neurons or channels beyond the actual requirements and result in redundance of
the model. The method is illustrated using several neural network structures on
different data sets including MNIST and CIFAR10.
