Related papers: Certifying Robustness via Topological Representati…

Deep networks realize complex mappings that are often understood by their locally linear behavior at or around points of interest. For example, we use the derivative of the mapping with respect to its inputs for sensitivity analysis, or to…

Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be…

Recent works show that Graph Neural Networks (GNNs) are highly non-robust with respect to adversarial attacks on both the graph structure and the node attributes, making their outcomes unreliable. We propose the first method for certifiable…

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…

In data-based control, dissipativity can be a powerful tool for attaining stability guarantees for nonlinear systems if that dissipativity can be inferred from data. This work provides a tutorial on several existing methods for data-based…

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…

Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…

Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…

Learning graphs from data automatically has shown encouraging performance on clustering and semisupervised learning tasks. However, real data are often corrupted, which may cause the learned graph to be inexact or unreliable. In this paper,…

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…

We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…

In adversarial machine learning, the popular $\ell_\infty$ threat model has been the focus of much previous work. While this mathematical definition of imperceptibility successfully captures an infinite set of additive image transformations…

The highly non-linear nature of deep neural networks causes them to be susceptible to adversarial examples and have unstable gradients which hinders interpretability. However, existing methods to solve these issues, such as adversarial…

Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering. Traditional stability and receptivity…

Recently, it has been widely known that deep neural networks are highly vulnerable and easily broken by adversarial attacks. To mitigate the adversarial vulnerability, many defense algorithms have been proposed. Recently, to improve…

As the representations output by Graph Neural Networks (GNNs) are increasingly employed in real-world applications, it becomes important to ensure that these representations are fair and stable. In this work, we establish a key connection…

Establishing Lipschitz stability estimates is crucial for ensuring the mathematical robustness of neural network (NN) approximations in machine learning (ML)-based parameter estimation, particularly in physics-informed settings. In this…

Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its performance critically depends on the choice of the uncertainty set. While large sets ensure reliability, they often lead to overly…

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…

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…