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A burgeoning line of research leverages deep neural networks to approximate the solutions to high dimensional PDEs, opening lines of theoretical inquiry focused on explaining how it is that these models appear to evade the curse of…
In this technical note, we introduce and analyze AWNN: an adaptively weighted nearest neighbor method for performing matrix completion. Nearest neighbor (NN) methods are widely used in missing data problems across multiple disciplines such…
Hypergraphs serve as an effective model for depicting complex connections in various real-world scenarios, from social to biological networks. The development of Hypergraph Neural Networks (HGNNs) has emerged as a valuable method to manage…
Training neural networks to satisfy universal constraints over continuous domains poses unique challenges. Common examples include Lyapunov Neural Networks (Lyapunov NNs) and Physics-Informed Neural Networks (PINNs), where analytical…
In this paper, we study approximation properties of single hidden layer neural networks with weights varying on finitely many directions and thresholds from an open interval. We obtain a necessary and at the same time sufficient measure…
Neural network pruning techniques reduce the number of parameters without compromising predicting ability of a network. Many algorithms have been developed for pruning both over-parameterized fully-connected networks (FCNs) and…
Adaptive inference is an effective mechanism to achieve a dynamic tradeoff between accuracy and computational cost in deep networks. Existing works mainly exploit architecture redundancy in network depth or width. In this paper, we focus on…
The computational properties of neural systems are often thought to be implemented in terms of their network dynamics. Hence, recovering the system dynamics from experimentally observed neuronal time series, like multiple single-unit (MSU)…
Analog neural networks are highly effective to solve some optimization problems, and they have been used for target localization in distributed multiple-input multiple-output (MIMO) radar. In this work, we design a new relaxed energy…
Neural networks (NNs) are known for their high predictive accuracy in complex learning problems. Beside practical advantages, NNs also indicate favourable theoretical properties such as universal approximation (UA) theorems. Binarized…
The solution of partial differential equations (PDES) on irregular domains has long been a subject of significant research interest. In this work, we present an approach utilizing physics-informed neural networks (PINNs) to achieve…
A common explanation for the failure of deep networks to generalize out-of-distribution is that they fail to recover the "correct" features. We challenge this notion with a simple experiment which suggests that ERM already learns sufficient…
A recent work by Ramanujan et al. (2020) provides significant empirical evidence that sufficiently overparameterized, random neural networks contain untrained subnetworks that achieve state-of-the-art accuracy on several predictive tasks. A…
Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…
One of the most common and universal problems in science is to investigate a function. The prediction can be made by an Artificial Neural Network (ANN) or a mathematical model. Both approaches have their advantages and disadvantages.…
Artificial neural networks (ANNs) have been successfully applied to solve a variety of classification and function approximation problems. Although ANNs can generally predict better than decision trees for pattern classification problems,…
The significance of learning constraints from data is underscored by its potential applications in real-world problem-solving. While constraints are popular for modeling and solving, the approaches to learning constraints from data remain…
In recent years, the researches about solving partial differential equations (PDEs) based on artificial neural network have attracted considerable attention. In these researches, the neural network models are usually designed depend on…
We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the…
This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or…