  The focus of this paper is the application of classical model order reduction
techniques, such as Active Subspaces and Proper Orthogonal Decomposition, to
Deep Neural Networks. We propose a generic methodology to reduce the number of
layers of a pre-trained network by combining the aforementioned techniques for
dimensionality reduction with input-output mappings, such as Polynomial Chaos
Expansion and Feedforward Neural Networks. The necessity of compressing the
architecture of an existing Convolutional Neural Network is motivated by its
application in embedded systems with specific storage constraints. Our
experiment shows that the reduced nets obtained can achieve a level of accuracy
similar to the original Convolutional Neural Network under examination, while
saving in memory allocation.
