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Adversarial robustness is considered as a required property of deep neural networks. In this study, we discover that adversarially trained models might have significantly different characteristics in terms of margin and smoothness, even…
Recently, deep unfolding methods that guide the design of deep neural networks (DNNs) through iterative algorithms have received increasing attention in the field of inverse problems. Unlike general end-to-end DNNs, unfolding methods have…
Deep neural networks and in particular, deep neural classifiers have become an integral part of many modern applications. Despite their practical success, we still have limited knowledge of how they work and the demand for such an…
In this paper, a shallow Ritz-type neural network for solving elliptic equations with delta function singular sources on an interface is developed. There are three novel features in the present work; namely, (i) the delta function…
Learning in non-stationary environments is one of the biggest challenges in machine learning. Non-stationarity can be caused by either task drift, i.e., the drift in the conditional distribution of labels given the input data, or the domain…
We introduce a graceful approach to probabilistic inference called bounded conditioning. Bounded conditioning monotonically refines the bounds on posterior probabilities in a belief network with computation, and converges on final…
While achieving unmatched performance on many well-defined tasks, deep learning models have also been used to solve visual abstract reasoning tasks, which are relatively less well-defined, and have been widely used to measure human…
We propose a novel framework to solve risk-sensitive reinforcement learning (RL) problems where the agent optimises time-consistent dynamic spectral risk measures. Based on the notion of conditional elicitability, our methodology constructs…
Distributionally robust optimization (DRO) is a widely used framework for optimizing objective functionals in the presence of both randomness and model-form uncertainty. A key step in the practical solution of many DRO problems is a…
We consider embedding a predictive machine-learning model within a prescriptive optimization problem. In this setting, called constraint learning, we study the concept of a validity domain, i.e., a constraint added to the feasible set,…
Variational Quantum Algorithms have emerged as promising tools for solving optimization problems on quantum computers. These algorithms leverage a parametric quantum circuit called ansatz, where its parameters are adjusted by a classical…
We consider the problem of automatically proving resource bounds. That is, we study how to prove that an integer-valued resource variable is bounded by a given program expression. Automatic resource-bound analysis has recently received…
Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes…
In this paper, we propose a novel solution for non-convex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of…
Deep learning models are increasingly deployed in safety-critical tasks where predictions must satisfy hard constraints, such as physical laws, fairness requirements, or safety limits. However, standard architectures lack built-in…
The existence of adversarial data examples has drawn significant attention in the deep-learning community; such data are seemingly minimally perturbed relative to the original data, but lead to very different outputs from a deep-learning…
We propose a novel deep learning (DL) approach to solve one-dimensional non-linear elliptic, parabolic, and hyperbolic problems on graphs. A system of physics-informed neural network (PINN) models is used to solve the differential…
Can neural networks solve math problems using first a principle alone? This paper shows how to leverage the fundamental theorem of the calculus of variations to design deep neural networks to solve functional optimization without requiring…
In this paper, we focus on exploiting neural networks for the analysis and planning stage in self-adaptive architectures. The studied motivating cases in the paper involve existing (legacy) self-adaptive architectures and their adaptation…
This research focuses on enhancing reinforcement learning (RL) algorithms by integrating penalty functions to guide agents in avoiding unwanted actions while optimizing rewards. The goal is to improve the learning process by ensuring that…