Related papers: Robustness, Scott Continuity, and Computability

Hybrid systems - more precisely, their mathematical models - can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of…

This paper studies the design of mechanisms that are robust to misspecification. We introduce a novel notion of robustness that connects a variety of disparate approaches and study its implications in a wide class of mechanism design…

Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…

We investigate a special case of hereditary property in graphs, referred to as {\em robustness}. A property (or structure) is called robust in a graph $G$ if it is inherited by all the connected spanning subgraphs of $G$. We motivate this…

We define a (preorder-enriched) category $\mathsf{Met}$ of quantale-valued metric spaces and uniformly continuous maps, with the essential requirement that the quantales are continuous. For each object $(X,d,Q)$ in this category, where $X$…

This paper studies the robustness of observability of a linear time-invariant system under sensor failures from a computational perspective. To be precise, the problem of determining the minimum number of sensors whose removal can destroy…

We investigate robust Orlicz spaces as a generalisation of robust $L^p$-spaces. Two constructions of such spaces are distinguished, a top-down approach and a bottom-up approach. We show that separability of robust Orlicz spaces or their…

Clustering consists of grouping together samples giving their similar properties. The problem of modeling simultaneously groups of samples and features is known as Co-Clustering. This paper introduces ROCCO - a Robust Continuous…

Adversarial training has been shown to be reliable in improving robustness against adversarial samples. However, the problem of adversarial training in terms of fairness has not yet been properly studied, and the relationship between…

As the issue of robustness in AI systems becomes vital, statistical learning techniques that are reliable even in presence of partly contaminated data have to be developed. Preference data, in the form of (complete) rankings in the simplest…

Robustness of neural networks is commonly quantified via local or global Lipschitz constants. However, Lipschitz continuity can be overly coarse or overly restrictive as global robustness measure, failing to capture nuanced, data-dependent…

The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…

We present knowledge continuity, a novel definition inspired by Lipschitz continuity which aims to certify the robustness of neural networks across input domains (such as continuous and discrete domains in vision and language,…

Submodularity is an important property of set functions and has been extensively studied in the literature. It models set functions that exhibit a diminishing returns property, where the marginal value of adding an element to a set…

In a "structured system" of equations, each equation depends on a specified subset of the variables. In this article, we explore properties common to "almost every" system with a fixed structure and how the properties can be read from the…

We argue that robustness of explanations---i.e., that similar inputs should give rise to similar explanations---is a key desideratum for interpretability. We introduce metrics to quantify robustness and demonstrate that current methods do…

We analyze the properties of weakly compact sets in Lipschitz free spaces. Prior research has established that, for a complete metric space $M$, weakly precompact sets in the Lipschitz free space $\mathcal F(M)$ are tight. In this paper, we…

Here the definitions of nearest neighbor, robustness, concordance, and correlation, all of which feature in (Temple 2023) (henceforth abbreviated (T23)), are adjusted to make them completely mathematical while preserving their significance.…

Inconsistency robustness is "information system performance in the face of continually pervasive inconsistencies." A fundamental principle of Inconsistency Robustness is to make contradictions explicit so that arguments for and against…

Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…