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.
Convolutional Neural Network (CNN) is one of the most important architectures in deep learning. The fundamental building block of a CNN is a trainable filter, represented as a discrete grid, used to perform convolution on discrete input data. In this work, we propose a continuous version of a trainable convolutional filter able to work also with unstructured data. This new framework allows exploring CNNs beyond discrete domains, enlarging the usage of this important learning technique for many more complex problems. Our experiments show that the continuous filter can achieve a level of accuracy comparable to the state-of-the-art discrete filter, and that it can be used in current deep learning architectures as a building block to solve problems with unstructured domains as well.
The focus of this work is on 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 in 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 motivation behind compressing the architecture of an existing Convolutional Neural Network arises from its usage in embedded systems with specific storage constraints. The conducted numerical tests demonstrate that the resulting reduced networks can achieve a level of accuracy comparable to the original Convolutional Neural Network being examined, while also saving memory allocation. Our primary emphasis lies in the field of image recognition, where we tested our methodology using VGG-16 and ResNet-110 architectures against three different datasets: CIFAR-10, CIFAR-100, and a custom dataset.
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