Related papers: Robustness, Scott Continuity, and Computability
Ensuring neural network robustness is essential for the safe and reliable operation of robotic learning systems, especially in perception and decision-making tasks within real-world environments. This paper investigates the robustness of…
The concept of robustness of regulatory networks has been closely related to the nature of the interactions among genes, and the capability of pattern maintenance or reproducibility. Defining this robustness property is a challenging task,…
A key property for systems subject to uncertainty in their operating environment is robustness, ensuring that unmodelled, but bounded, disturbances have only a proportionally bounded effect upon the behaviours of the system. Inspired by…
The measure contraction property, $\mathsf{MCP}$ for short, is a weak Ricci curvature lower bound conditions for metric measure spaces. The goal of this paper is to understand which structural properties such assumption (or even weaker…
Soft set theory is an important and emerging area within soft computing, owing to its attribute-oriented mathematical framework and its wide applicability in diverse domains, including science and social sciences. The theoretical…
Robustness is a standard correctness property which intuitively means that if the input to the program changes less than a fixed small amount then the output changes only slightly. This notion is useful in the analysis of rounding error for…
Motivated by persistent homology and topological data analysis, we consider formal sums on a metric space with a distinguished subset. These formal sums, which we call persistence diagrams, have a canonical 1-parameter family of metrics…
We define robust abstractions for synthesizing provably correct and robust controllers for (possibly infinite) uncertain transition systems. It is shown that robust abstractions are sound in the sense that they preserve robust satisfaction…
Diversities are a generalization of metric spaces, where instead of the non-negative function being defined on pairs of points, it is defined on arbitrary finite sets of points. Diversities have a well-developed theory. This includes the…
Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…
Neural networks are becoming increasingly prevalent in software, and it is therefore important to be able to verify their behavior. Because verifying the correctness of neural networks is extremely challenging, it is common to focus on the…
Robustness is a critical aspect of machine learning models. Existing robustness evaluation approaches often lack theoretical generality or rely heavily on empirical assessments, limiting insights into the structural factors contributing to…
In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that…
Certifiable robustness gives the guarantee that small perturbations around an input to a classifier will not change the prediction. There are two approaches to provide certifiable robustness to adversarial examples: a) explicitly training…
An abstract chordal metric is defined on linear control systems described by their transfer functions. Analogous to a previous result due to Jonathan Partington ("Robust control and approximation in the chordal metric", in Robust Control,…
We introduce the post-processing preorder and equivalence relations for general measurements on a possibly infinite-dimensional general probabilistic theory described by an order unit Banach space $E$ with a Banach predual. We define the…
Lasso, or $\ell^1$ regularized least squares, has been explored extensively for its remarkable sparsity properties. It is shown in this paper that the solution to Lasso, in addition to its sparsity, has robustness properties: it is the…
We introduce a metric for evaluating the robustness of a classifier, with particular attention to adversarial perturbations, in terms of expected functionality with respect to possible adversarial perturbations. A classifier is assumed to…
We investigate the statement "the order topology of every countable complete linear order is compact" in the framework of reverse mathematics, and we find that the statement's strength depends on the precise formulation of compactness. If…
It is ``folklore'' that the solution to a set reachability problem for a dynamical system is only noncomputable because of non-robustness reasons. A robustness condition that can be imposed on a dynamical system is the requirement of the…