Related papers: ECLipsE: Efficient Compositional Lipschitz Constan…

We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…

We introduce in this paper an optimal first-order method that allows an easy and cheap evaluation of the local Lipschitz constant of the objective's gradient. This constant must ideally be chosen at every iteration as small as possible,…

Recent research has established that the local Lipschitz constant of a neural network directly influences its adversarial robustness. We exploit this relationship to construct an ensemble of neural networks which not only improves the…

Deep learning architectures have proved versatile in a number of drug discovery applications, including the modelling of in vitro compound activity. While controlling for prediction confidence is essential to increase the trust,…

The robustness of neural networks to adversarial examples has received great attention due to security implications. Despite various attack approaches to crafting visually imperceptible adversarial examples, little has been developed…

With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a…

DNNs have been quickly and broadly exploited to improve the data analysis quality in many complex science and engineering applications. Today's DNNs are becoming deeper and wider because of increasing demand on the analysis quality and more…

Let $F$ be a set-valued mapping from an $N$-element metric space $({\mathcal M},\rho)$ into the family of all closed half-planes in ${\bf R}^2$. In this paper, we provide an efficient algorithm for a Lipschitz selection of $F$, i.e., a…

The configuration of latent representations plays a critical role in determining the performance of deep neural network classifiers. In particular, the emergence of well-separated class embeddings in the latent space has been shown to…

Robustness estimation is critical for the design and maintenance of resilient networks, one of the global challenges of the 21st century. Existing studies exploit network metrics to generate attack strategies, which simulate intentional…

Neural ordinary differential equations (NODEs) are an effective approach for data-driven modeling of dynamical systems arising from simulations and experiments. One of the major shortcomings of NODEs, especially when coupled with explicit…

Although Deep Neural Networks (DNNs) have shown incredible performance in perceptive and control tasks, several trustworthy issues are still open. One of the most discussed topics is the existence of adversarial perturbations, which has…

Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…

Attention is a powerful component of modern neural networks across a wide variety of domains. In this paper, we seek to quantify the regularity (i.e. the amount of smoothness) of the attention operation. To accomplish this goal, we propose…

Deep neural networks are known to be fragile to small adversarial perturbations. This issue becomes more critical when a neural network is interconnected with a physical system in a closed loop. In this paper, we show how to combine recent…

We present a theoretical and experimental investigation of the quantization problem for artificial neural networks. We provide a mathematical definition of quantized neural networks and analyze their approximation capabilities, showing in…

The neural network with $1$-Lipschitz property based on $\ell_\infty$-dist neuron has a theoretical guarantee in certified $\ell_\infty$ robustness. However, due to the inherent difficulties in the training of the network, the certified…

Learning operators between infinitely dimensional spaces is an important learning task arising in wide applications in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric…

We propose a general technique for extracting a larger set of stable information from persistent homology computations than is currently done. The persistent homology algorithm is usually viewed as a procedure which starts with a filtered…

While much attention of neural network methods is devoted to high-dimensional PDE problems, in this work we consider methods designed to work for elliptic problems on domains $\Omega \subset \mathbb{R} ^d, $ $d=1,2,3$ in association with…