Related papers: Robustness, Scott Continuity, and Computability

The distinction between conditional, unconditional, and absolute convergence in infinite-dimensional spaces has fundamental implications for computational algorithms. While these concepts coincide in finite dimensions, the Dvoretzky-Rogers…

Resilience broadly describes a quality of withstanding perturbations. Measures of system resilience have gathered increasing attention across applied disciplines, yet existing metrics often lack computational accessibility and…

Existing methods for verifying access control policies require the policy to be complete and fully determined before verification can proceed, but in practice policies are developed iteratively, composed from independently maintained…

Robust motion planning entails computing a global motion plan that is safe under all possible uncertainty realizations, be it in the system dynamics, the robot's initial position, or with respect to external disturbances. Current approaches…

Despite having high accuracy, neural nets have been shown to be susceptible to adversarial examples, where a small perturbation to an input can cause it to become mislabeled. We propose metrics for measuring the robustness of a neural net…

A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreasing. By Hahn-Banach theorem, a positive strong submeasure is…

Magnitude is a real-valued invariant of metric spaces which, in the finite setting, can be understood as recording the 'effective number of points' in a space as the scale of the metric varies. Motivated by applications in topological data…

This chapter introduces and investigates some fundamental questions on the relationship between accuracy and robustness in both classical and quantum classification algorithms under noisy and adversarial conditions. We introduce and clarify…

Explainability models are now prevalent within machine learning to address the black-box nature of neural networks. The question now is which explainability model is most effective. Probabilistic Lipschitzness has demonstrated that the…

In this paper we prove the existence of a fundamental trade-off between accuracy and robustness in perception-based control, where control decisions rely solely on data-driven, and often incompletely trained, perception maps. In particular,…

Model robustness indicates a model's capability to generalize well on unforeseen distributional shifts, including data corruptions and adversarial attacks. Data augmentation is one of the most prevalent and effective ways to enhance…

We initiate a program of average smoothness analysis for efficiently learning real-valued functions on metric spaces. Rather than using the Lipschitz constant as the regularizer, we define a local slope at each point and gauge the function…

Bubeck and Sellke (2021) pose as an open problem the connection between the law of robustness and robust generalization. The law of robustness states that overparameterization is necessary for models to interpolate robustly; in particular,…

In this work, water distribution systems are regarded as large sparse planar graphs with complex network characteristics and the relationship between important topological features of the network (i.e. structural robustness and loop…

Adversarial robustness, which primarily comprises sensitivity-based robustness and spatial robustness, plays an integral part in achieving robust generalization. In this paper, we endeavor to design strategies to achieve universal…

A robustness measure for incompatibility of quantum devices in the lines of the robustness of entanglement is proposed. The concept of general robustness measures is first introduced in general convex-geometric settings and these ideas are…

We develop a general framework for the probabilistic analysis of random finite point clouds in the context of topological data analysis. We extend the notion of a barcode of a finite point cloud to compact metric spaces. Such a barcode…

A dynamical system is strongly robustly safe provided that it remains safe in the presence of a continuous and positive perturbation, named robustness margin, added to both the argument and the image of the right-hand side (the dynamics).…

Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…

Monadically stable and monadically NIP classes of structures were initially studied in the context of model theory and defined in logical terms. They have recently attracted attention in the area of structural graph theory, as they…