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Deep reinforcement learning has achieved remarkable performance in various domains by leveraging deep neural networks for approximating value functions and policies. However, using neural networks to approximate value functions or policy…

Convolutional Neural Networks (CNNs) have achieved state-of-the-art performance on a variety of computer vision tasks, particularly visual classification problems, where new algorithms reported to achieve or even surpass the human…

PCA-Net is a recently proposed neural operator architecture which combines principal component analysis (PCA) with neural networks to approximate operators between infinite-dimensional function spaces. The present work develops…

This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…

This paper is devoted to the study of noncommutative maximal operators with rough kernels. More precisely, we prove the weak type $(1,1)$ boundedness for noncommutative maximal operators with rough kernels. The proof of weak type (1,1)…

Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…

A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online…

While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…

Real-world processes operate on objects that are inter-dependent. To accurately reflect the nature of such processes, object-centric process mining techniques are needed, notably conformance checking. However, while the object-centric…

Neural networks (NN) are extensively studied in cutting-edge soft sensor models due to their feature extraction and function approximation capabilities. Current research into network-based methods primarily focuses on models' offline…

We prove several decidability and undecidability results for nu-PN, an extension of P/T nets with pure name creation and name management. We give a simple proof of undecidability of reachability, by reducing reachability in nets with…

With massive amounts of atomic simulation data available, there is a huge opportunity to develop fast and accurate machine learning models to approximate expensive physics-based calculations. The key quantity to estimate is atomic forces,…

Petri Nets is very interesting tool for studying and simulating different behaviors of information systems. It can be used in different applications based on the appropriate class of Petri Nets whereas it is classical, colored or timed…

In Petri net synthesis we ask whether a given transition system $A$ can be implemented by a Petri net $N$. Depending on the level of accuracy, there are three ways how $N$ can implement $A$: an embedding, the least accurate implementation,…

Second-order methods are of great importance for composite convex optimization problems due to their local super-linear convergence rates (under appropriate assumptions). However, the presence of even a simple nonsmooth function in the…

Neural networks (NNs) have emerged as a state-of-the-art method for modeling nonlinear systems in model predictive control (MPC). However, the robustness of NNs, in terms of sensitivity to small input perturbations, remains a critical…

We introduce and study weak o-minimality in the context of complete types in an arbitrary first-order theory. A type $p\in S(A)$ is weakly o-minimal if for some relatively $A$-definable linear order, $<$, on $p(\mathfrak{C})$ every…

The commitment to single-precision floating-point arithmetic is widespread in the deep learning community. To evaluate whether this commitment is justified, the influence of computing precision (single and double precision) on the…

We introduce "weakly chained spaces", which need not be locally connected or path connected, but for which one has a reasonable notion of generalized fundamental group and associated generalized universal cover. We show that in the compact…

Deep Neural Networks (DNNs) are everywhere, frequently performing a fairly complex task that used to be unimaginable for machines to carry out. In doing so, they do a lot of decision making which, depending on the application, may be…