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We here present a stepping stone towards a deeper understanding of convolutional neural networks (CNNs) in the form of a theory of learning in linear CNNs. Through analyzing the gradient descent equations, we discover that the evolution of…
It is widely acknowledged that trained convolutional neural networks (CNNs) have different levels of sensitivity to signals of different frequency. In particular, a number of empirical studies have documented CNNs sensitivity to…
The convolutional layers are core building blocks of neural network architectures. In general, a convolutional filter applies to the entire frequency spectrum of the input data. We explore artificially constraining the frequency spectra of…
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…
Convolutional neural networks (CNNs) in recent years have made a dramatic impact in science, technology and industry, yet the theoretical mechanism of CNN architecture design remains surprisingly vague. The CNN neurons, including its…
Convolutional Neural Networks (CNNs) have shown remarkable performance in general object recognition tasks. In this paper, we propose a new model called EnsNet which is composed of one base CNN and multiple Fully Connected SubNetworks…
Deep learning has established many new state of the art solutions in the last decade in areas such as object, scene and speech recognition. In particular Convolutional Neural Network (CNN) is a category of deep learning which obtains…
Despite the phenomenal success of deep neural networks in a broad range of learning tasks, there is a lack of theory to understand the way they work. In particular, Convolutional Neural Networks (CNNs) are known to perform much better than…
It is widely believed that the practical success of Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) owes to the fact that CNNs and RNNs use a more compact parametric representation than their Fully-Connected Neural…
Recent efforts have shown machine learning to be useful for the prediction of nonlinear fluid dynamics. Predictive accuracy is often a central motivation for employing neural networks, but the pattern recognition central to the network…
We describe the class of convexified convolutional neural networks (CCNNs), which capture the parameter sharing of convolutional neural networks in a convex manner. By representing the nonlinear convolutional filters as vectors in a…
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 (CNNs) have achieved impressive results on imbalanced image data, but they still have difficulty generalizing to minority classes and their decisions are difficult to interpret. These problems are related…
Successful training of convolutional neural networks is often associated with sufficiently deep architectures composed of high amounts of features. These networks typically rely on a variety of regularization and pruning techniques to…
Deep Convolutional Neural Network (CNN) is a special type of Neural Networks, which has shown exemplary performance on several competitions related to Computer Vision and Image Processing. Some of the exciting application areas of CNN…
Previous work has shown that DNNs with large depth $L$ and $L_{2}$-regularization are biased towards learning low-dimensional representations of the inputs, which can be interpreted as minimizing a notion of rank $R^{(0)}(f)$ of the learned…
We propose a generalized convolutional neural network (CNN) architecture that first decomposes the input signal into subbands by an adaptive filter bank structure, and then uses convolutional layers to extract features from each subband…
Deep Convolutional Neural Networks (CNNs) have been widely used in various domains due to their impressive capabilities. These models are typically composed of a large number of 2D convolutional (Conv2D) layers with numerous trainable…
Convolutional Neural Networks (CNNs) are known to be significantly over-parametrized, and difficult to interpret, train and adapt. In this paper, we introduce a structural regularization across convolutional kernels in a CNN. In our…
We consider Convolutional Neural Networks (CNNs) with 2D structured features that are symmetric in the spatial dimensions. Such networks arise in modeling pairwise relationships for a sequential recommendation problem, as well as secondary…