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Deep neural networks (DNNs) generate much richer function spaces than shallow networks. Since the function spaces induced by shallow networks have several approximation theoretic drawbacks, this explains, however, not necessarily the…
The state-of-the-art deep neural networks (DNNs) have significant computational and data management requirements. The size of both training data and models continue to increase. Sparsification and pruning methods are shown to be effective…
Advances in image super-resolution (SR) have recently benefited significantly from rapid developments in deep neural networks. Inspired by these recent discoveries, we note that many state-of-the-art deep SR architectures can be…
One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks. Graph neural…
Many measurements in computer vision and machine learning manifest as non-Euclidean data samples. Several researchers recently extended a number of deep neural network architectures for manifold valued data samples. Researchers have…
Single-hidden layer feed forward neural networks (SLFNs) are widely used in pattern classification problems, but a huge bottleneck encountered is the slow speed and poor performance of the traditional iterative gradient-based learning…
In recent years, there has been a surge in applying deep learning to various challenging design problems in communication networks. The early attempts adopt neural architectures inherited from applications such as computer vision, which…
Deep neural networks (DNNs) achieve remarkable performance on a wide range of tasks, yet their mathematical analysis remains fragmented: stability and generalization are typically studied in disparate frameworks and on a case-by-case basis.…
The theoretical analysis of deep neural networks (DNN) is arguably among the most challenging research directions in machine learning (ML) right now, as it requires from scientists to lay novel statistical learning foundations to explain…
Deep neural networks (DNNs) have achieved the state of the art performance in numerous fields. However, DNNs need high computation times, and people always expect better performance in a lower computation. Therefore, we study the human…
This paper introduces MDP homomorphic networks for deep reinforcement learning. MDP homomorphic networks are neural networks that are equivariant under symmetries in the joint state-action space of an MDP. Current approaches to deep…
We study the convergence of gradient flows related to learning deep linear neural networks (where the activation function is the identity map) from data. In this case, the composition of the network layers amounts to simply multiplying the…
Graph Neural Networks (GNNs) have already been widely applied in various graph mining tasks. However, they suffer from the shallow architecture issue, which is the key impediment that hinders the model performance improvement. Although…
Over the past years, there has been significant interest in understanding the implicit bias of gradient descent optimization and its connection to the generalization properties of overparametrized neural networks. Several works observed…
Recent research on deep neural networks (DNNs) has primarily focused on improving the model accuracy. Given a proper deep learning framework, it is generally possible to increase the depth or layer width to achieve a higher level of…
In this paper we propose a generalization of deep neural networks called deep function machines (DFMs). DFMs act on vector spaces of arbitrary (possibly infinite) dimension and we show that a family of DFMs are invariant to the dimension of…
Deep learning's performance has been extensively recognized recently. Graph neural networks (GNNs) are designed to deal with graph-structural data that classical deep learning does not easily manage. Since most GNNs were created using…
While deep neural networks (DNNs) and Gaussian Processes (GPs) are both popularly utilized to solve problems in reinforcement learning, both approaches feature undesirable drawbacks for challenging problems. DNNs learn complex nonlinear…
Convolutional neural networks (CNNs) are deep learning frameworks which are well-known for their notable performance in classification tasks. Hence, many skeleton-based action recognition and segmentation (SBARS) algorithms benefit from…
Convolution Neural Network (CNN) has gained tremendous success in computer vision tasks with its outstanding ability to capture the local latent features. Recently, there has been an increasing interest in extending convolution operations…