Related papers: Positive Competitive Networks for Sparse Reconstru…

Many real world practical problems can be formulated as $\ell_{0}$-minimization problems with nonnegativity constraints, which seek the sparsest nonnegative signals to underdetermined linear systems. They have been widely applied in signal…

A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…

Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of…

The aim of sparse approximation is to estimate a sparse signal according to the measurement matrix and an observation vector. It is widely used in data analytics, image processing, and communication, etc. Up to now, a lot of research has…

Recently, graph neural networks (GNNs) have been widely used for document classification. However, most existing methods are based on static word co-occurrence graphs without sentence-level information, which poses three challenges:(1) word…

In the past two decades we have seen the popularity of neural networks increase in conjunction with their classification accuracy. Parallel to this, we have also witnessed how fragile the very same prediction models are: tiny perturbations…

Noise and inconsistency commonly exist in real-world information networks, due to inherent error-prone nature of human or user privacy concerns. To date, tremendous efforts have been made to advance feature learning from networks, including…

This paper investigates stability conditions of continuous-time Hopfield and firing-rate neural networks by leveraging contraction theory. First, we present a number of useful general algebraic results on matrix polytopes and products of…

Recurrent neural networks (RNNs) are well suited for solving sequence tasks in resource-constrained systems due to their expressivity and low computational requirements. However, there is still a need to bridge the gap between what RNNs are…

Deep learning techniques have been successfully applied in many areas of computer vision, including low-level image restoration problems. For image super-resolution, several models based on deep neural networks have been recently proposed…

The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper, we investigate this issue for the sparse data problem in photoacoustic tomography (PAT). We develop a direct and…

Despite impressive performance, deep neural networks require significant memory and computation costs, prohibiting their application in resource-constrained scenarios. Sparse training is one of the most common techniques to reduce these…

We provide novel guaranteed approaches for training feedforward neural networks with sparse connectivity. We leverage on the techniques developed previously for learning linear networks and show that they can also be effectively adopted to…

Recurrent Neural Networks (RNNs) are powerful tools for solving sequence-based problems, but their efficacy and execution time are dependent on the size of the network. Following recent work in simplifying these networks with model pruning…

Convolutional neural networks (CNNs) have been shown to achieve optimal approximation and estimation error rates (in minimax sense) in several function classes. However, previous analyzed optimal CNNs are unrealistically wide and difficult…

Deep neural networks (DNNs) are computationally/memory-intensive and vulnerable to adversarial attacks, making them prohibitive in some real-world applications. By converting dense models into sparse ones, pruning appears to be a promising…

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…

Sparsifying neural networks often suffers from seemingly inevitable performance degradation, and it remains challenging to restore the original performance despite much recent progress. Motivated by recent studies in robust optimization, we…

In this paper, we consider a class of sparse regression problems, whose objective function is the summation of a convex loss function and a cardinality penalty. By constructing a smoothing function for the cardinality function, we propose a…

Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…