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Deep neural networks are representation learning techniques. During training, a deep net is capable of generating a descriptive language of unprecedented size and detail in machine learning. Extracting the descriptive language coded within…

Convolutional neural networks have been extremely successful in the image recognition domain because they ensure equivariance to translations. There have been many recent attempts to generalize this framework to other domains, including…

Deep learning and convolutional neural networks in particular are powerful and promising tools for cosmological analysis of large-scale structure surveys. They are already providing similar performance to classical analysis methods using…

The paper defines and studies manifold (M) convolutional filters and neural networks (NNs). \emph{Manifold} filters and MNNs are defined in terms of the Laplace-Beltrami operator exponential and are such that \emph{graph} (G) filters and…

Convolutional neural networks (CNNs) have achieved state-of-the-art results on many visual recognition tasks. However, current CNN models still exhibit a poor ability to be invariant to spatial transformations of images. Intuitively, with…

The convolution operator is the fundamental building block of modern convolutional neural networks (CNNs), owing to its simplicity, translational equivariance, and efficient implementation. However, its structure as a fixed, linear,…

Convolutional Neural Networks have revolutionized vision applications. There are image domains and representations, however, that cannot be handled by standard CNNs (e.g., spherical images, superpixels). Such data are usually processed…

Deep convolutional neural networks trained on large datsets have emerged as an intriguing alternative for compressing images and solving inverse problems such as denoising and compressive sensing. However, it has only recently been realized…

Convolutional neural networks are based on a huge number of trained weights. Consequently, they are often data-greedy, sensitive to overtraining, and learn slowly. We follow the line of research in which filters of convolutional neural…

Lossy compression introduces complex compression artifacts, particularly the blocking artifacts, ringing effects and blurring. Existing algorithms either focus on removing blocking artifacts and produce blurred output, or restores sharpened…

Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy and efficiency, the approaches available in the literature…

Toward a deeper understanding on the inner work of deep neural networks, we investigate CNN (convolutional neural network) using DCN (deconvolutional network) and randomization technique, and gain new insights for the intrinsic property of…

Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency…

We introduce a novel weighted convolution operator that enhances traditional convolutional neural networks (CNNs) by integrating a spatial density function into the convolution operator. This extension enables the network to differentially…

Using rough path techniques, we provide a priori estimates for the output of Deep Residual Neural Networks in terms of both the input data and the (trained) network weights. As trained network weights are typically very rough when seen as…

Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…

Convolutional neural networks have shown great success on feature extraction from raw input data such as images. Although convolutional neural networks are invariant to translations on the inputs, they are not invariant to other…

Deep convolutional neural networks (CNNs) used in practice employ potentially hundreds of layers and $10$,$000$s of nodes. Such network sizes entail significant computational complexity due to the large number of convolutions that need to…

Feature extraction with convolutional neural networks (CNNs) is a popular method to represent images for machine learning tasks. These representations seek to capture global image content, and ideally should be independent of geometric…

Deep convolutional neural networks are generally regarded as robust function approximators. So far, this intuition is based on perturbations to external stimuli such as the images to be classified. Here we explore the robustness of…