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State-of-the-art neural networks can be trained to become remarkable solutions to many problems. But while these architectures can express symbolic, perfect solutions, trained models often arrive at approximations instead. We show that the…

This survey article is concerned with the application of lattice rules to Deep Neural Networks (DNNs), lattice rules being a family of quasi-Monte Carlo methods. They have demonstrated effectiveness in various contexts for high-dimensional…

Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, current DL methods typically suffer from instability, even when universal approximation properties guarantee the existence…

We propose Deep Companion Learning (DCL), a novel training method for Deep Neural Networks (DNNs) that enhances generalization by penalizing inconsistent model predictions compared to its historical performance. To achieve this, we train a…

One obstacle that so far prevents the introduction of machine learning models primarily in critical areas is the lack of explainability. In this work, a practicable approach of gaining explainability of deep artificial neural networks (NN)…

Background: It is still an open research area to theoretically understand why Deep Neural Networks (DNNs)---equipped with many more parameters than training data and trained by (stochastic) gradient-based methods---often achieve remarkably…

On account of its many successes in inference tasks and denoising applications, Dictionary Learning (DL) and its related sparse optimization problems have garnered a lot of research interest. While most solutions have focused on single…

The problem of approximating smooth, multivariate functions from sample points arises in many applications in scientific computing, e.g., in computational Uncertainty Quantification (UQ) for science and engineering. In these applications,…

The goal in network state prediction (NSP) is to classify the global state (label) associated with features embedded in a graph. This graph structure encoding feature relationships is the key distinctive aspect of NSP compared to classical…

Iterative algorithms solve problems by taking steps until a solution is reached. Models in the form of Deep Thinking (DT) networks have been demonstrated to learn iterative algorithms in a way that can scale to different sized problems at…

Deep neural networks (DNNs) have proven to be highly effective in a variety of tasks, making them the go-to method for problems requiring high-level predictive power. Despite this success, the inner workings of DNNs are often not…

A common machine learning task is to discriminate between normal and anomalous data points. In practice, it is not always sufficient to reach high accuracy at this task, one also would like to understand why a given data point has been…

This paper introduces an SLD-resolution technique based on deep learning. This technique enables neural networks to learn from old and successful resolution processes and to use learnt experiences to guide new resolution processes. An…

Deep learning (DL) has recently been proposed as a novel approach for 21cm foreground removal. Before applying DL to real observations, it is essential to assess its consistency with established methods, its performance across various…

This paper proposes a novel pixel-level distribution regularization scheme (DRSL) for self-supervised domain adaptation of semantic segmentation. In a typical setting, the classification loss forces the semantic segmentation model to…

We propose local distributional smoothness (LDS), a new notion of smoothness for statistical model that can be used as a regularization term to promote the smoothness of the model distribution. We named the LDS based regularization as…

Deep learning (DL) allows computer models to learn, visualize, optimize, refine, and predict data. To understand its present state, examining the most recent advancements and applications of deep learning across various domains is…

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nevertheless, the majority of these studies examine how well deep…

Network slicing promises to provision diversified services with distinct requirements in one infrastructure. Deep reinforcement learning (e.g., deep $\mathcal{Q}$-learning, DQL) is assumed to be an appropriate algorithm to solve the…

We propose a new method of program learning in a Domain Specific Language (DSL) which is based on gradient descent with no direct search. The first component of our method is a probabilistic representation of the DSL variables. At each…