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Convolutional neural networks (CNNs) are able to attain better visual recognition performance than fully connected neural networks despite having much fewer parameters due to their parameter sharing principle. Modern architectures usually…
A well-trained Convolutional Neural Network can easily be pruned without significant loss of performance. This is because of unnecessary overlap in the features captured by the network's filters. Innovations in network architecture such as…
Deep learning (DL) has achieved great success in many applications, but it has been less well analyzed from the theoretical perspective. The unexplainable success of black-box DL models has raised questions among scientists and promoted the…
This work attempts to interpret modern deep (convolutional) networks from the principles of rate reduction and (shift) invariant classification. We show that the basic iterative gradient ascent scheme for optimizing the rate reduction of…
Neural network training is usually accomplished by solving a non-convex optimization problem using stochastic gradient descent. Although one optimizes over the networks parameters, the main loss function generally only depends on the…
While successful for various computer vision tasks, deep neural networks have shown to be vulnerable to texture style shifts and small perturbations to which humans are robust. In this work, we show that the robustness of neural networks…
Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased…
Residual neural networks (ResNets) are a promising class of deep neural networks that have shown excellent performance for a number of learning tasks, e.g., image classification and recognition. Mathematically, ResNet architectures can be…
Convolution is a central operation in Convolutional Neural Networks (CNNs), which applies a kernel to overlapping regions shifted across the image. However, because of the strong correlations in real-world image data, convolutional kernels…
In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the…
Despite the tremendous success in computer vision, deep convolutional networks suffer from serious computation costs and redundancies. Although previous works address this issue by enhancing diversities of filters, they have not considered…
Training deep neural networks is a challenging non-convex optimization problem. Recent work has proven that the strong duality holds (which means zero duality gap) for regularized finite-width two-layer ReLU networks and consequently…
Enhancing quality and removing noise during preprocessing is one of the most critical steps in image processing. X-ray images are created by photons colliding with atoms and the variation in scattered noise absorption. This noise leads to a…
Implicit neural networks have become increasingly attractive in the machine learning community since they can achieve competitive performance but use much less computational resources. Recently, a line of theoretical works established the…
Single image super-resolution (SR) via deep learning has recently gained significant attention in the literature. Convolutional neural networks (CNNs) are typically learned to represent the mapping between low-resolution (LR) and…
Deep convolutional networks have witnessed unprecedented success in various machine learning applications. Formal understanding on what makes these networks so successful is gradually unfolding, but for the most part there are still…
Deep neural networks are powerful tools for solving nonlinear problems in science and engineering, but training highly accurate models becomes challenging as problem complexity increases. Non-convex optimization and sensitivity to…
In deep learning, dense layer connectivity has become a key design principle in deep neural networks (DNNs), enabling efficient information flow and strong performance across a range of applications. In this work, we model densely connected…
The design of metamaterials which support unique optical responses is the basis for most thin-film nanophotonics applications. In practice this inverse design problem can be difficult to solve systematically due to the large design…
While the depth of convolutional neural networks has attracted substantial attention in the deep learning research, the width of these networks has recently received greater interest. The width of networks, defined as the size of the…