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We derive the fast convergence rates of a deep neural network (DNN) classifier with the rectified linear unit (ReLU) activation function learned using the hinge loss. We consider three cases for a true model: (1) a smooth decision boundary,…

The success of recent deep convolutional neural networks (CNNs) depends on learning hidden representations that can summarize the important factors of variation behind the data. However, CNNs often criticized as being black boxes that lack…

In spatial statistics, fast and accurate parameter estimation, coupled with a reliable means of uncertainty quantification, can be challenging when fitting a spatial process to real-world data because the likelihood function might be slow…

Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…

Traditional deep neural networks (NNs) have significantly contributed to the state-of-the-art performance in the task of classification under various application domains. However, NNs have not considered inherent uncertainty in data…

Recent advances in machine learning have led to a surge in adoption of neural networks for various tasks, but lack of interpretability remains an issue for many others in which an understanding of the features influencing the prediction is…

Guiding the design of neural networks is of great importance to save enormous resources consumed on empirical decisions of architectural parameters. This paper constructs shallow sigmoid-type neural networks that achieve 100% accuracy in…

Recent work by Lakshminarayanan and Singh [2020] provided a dual view for fully connected deep neural networks (DNNs) with rectified linear units (ReLU). It was shown that (i) the information in the gates is analytically characterised by a…

Hierarchical feature learning based on convolutional neural networks (CNN) has recently shown significant potential in various computer vision tasks. While allowing high-quality discriminative feature learning, the downside of CNNs is the…

Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address…

In this work we propose a novel approach to perform segmentation by leveraging the abstraction capabilities of convolutional neural networks (CNNs). Our method is based on Hough voting, a strategy that allows for fully automatic…

An established measure of the expressive power of a given ReLU neural network is the number of linear regions into which it partitions the input space. There exist many different, non-equivalent definitions of what a linear region actually…

Feed-forward, fully-connected Artificial Neural Networks (ANNs) or the so-called Multi-Layer Perceptrons (MLPs) are well-known universal approximators. However, their learning performance varies significantly depending on the function or…

Strong intelligent machines powered by deep neural networks are increasingly deployed as black boxes to make decisions in risk-sensitive domains, such as finance and medical. To reduce potential risk and build trust with users, it is…

Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal approximation ability and robustness to adversarial examples under appropriate conditions. However, SMNNs present some…

This paper introduces an Interpretable Neural Network (INN) incorporating spatial information to tackle the opaque parameterization process of random weighted neural networks. The INN leverages spatial information to elucidate the…

Unet and its variations have been standard in semantic image segmentation, especially for computer assisted radiology. Current Unet architectures iteratively downsample spatial resolution while increasing channel dimensions to preserve…

Probabilistic circuits (PCs) represent a probability distribution as a computational graph. Enforcing structural properties on these graphs guarantees that several inference scenarios become tractable. Among these properties, structured…

Fault detection in rotating machinery is a complex task, particularly in small and heterogeneous dataset scenarios. Variability in sensor placement, machinery configurations, and structural differences further increase the complexity of the…

Implementing quantum gates on quantum computers can require the application of carefully shaped pulses for high-fidelity operations. We explore the use of physics-informed neural networks (PINNs) for quantum optimal control to assess their…