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In this paper, we consider functionals of the form $H_\alpha(u)=F(u)+\alpha G(u)$ with $\alpha\in[0,+\infty)$, where $u$ varies in a set $U\neq\emptyset$ (without further structure). We first show that, excluding at most countably many values of $\alpha$, we have that $\inf_{H_\alpha^\star}G= \sup_{H_\alpha^\star}G$, where $H_\alpha^\star := \arg \min_U H_\alpha$, which is assumed to be non-empty. We further prove a stronger result that concerns the {invariance of the} limiting value of the functional $G$ along minimizing sequences for $H_\alpha$. This fact in turn implies an unexpected consequence for functionals regularized with uniformly convex norms: excluding again at most countably many values of $\alpha$, it turns out that for a minimizing sequence, convergence to a minimizer in the weak or strong sense is equivalent., Comment: 10 pages, expository improvements in the Introduction

High-autonomy vehicle functions rely on machine learning (ML) algorithms to understand the environment. Despite displaying remarkable performance in fair weather scenarios, perception algorithms are heavily affected by adverse weather and lighting conditions. To overcome these difficulties, ML engineers mainly rely on comprehensive real-world datasets. However, the difficulties in real-world data collection for critical areas of the operational design domain (ODD) often means synthetic data is required for perception training and safety validation. Thus, we present A-BDD, a large set of over 60,000 synthetically augmented images based on BDD100K that are equipped with semantic segmentation and bounding box annotations (inherited from the BDD100K dataset). The dataset contains augmented data for rain, fog, overcast and sunglare/shadow with varying intensity levels. We further introduce novel strategies utilizing feature-based image quality metrics like FID and CMMD, which help identify useful augmented and real-world data for ML training and testing. By conducting experiments on A-BDD, we provide evidence that data augmentations can play a pivotal role in closing performance gaps in adverse weather and lighting conditions.

Regulation, legal liabilities, and societal concerns challenge the adoption of AI in safety and security-critical applications. One of the key concerns is that adversaries can cause harm by manipulating model predictions without being detected. Regulation hence demands an assessment of the risk of damage caused by adversaries. Yet, there is no method to translate this high-level demand into actionable metrics that quantify the risk of damage. In this article, we propose a method to model and statistically estimate the probability of damage arising from adversarial attacks. We show that our proposed estimator is statistically consistent and unbiased. In experiments, we demonstrate that the estimation results of our method have a clear and actionable interpretation and outperform conventional metrics. We then show how operators can use the estimation results to reliably select the model with the lowest risk.

We construct a left adjoint $\mathcal{H}^\text{st}\colon \mathbf{Ex}_{\infty} \rightarrow \mathbf{St}_{\infty}$ to the inclusion $\mathbf{St}_{\infty} \hookrightarrow \mathbf{Ex}_{\infty}$ of the $\infty$-category of stable $\infty$-categories into the $\infty$-category of exact $\infty$-categories, which we call the stable hull. For every exact $\infty$-category $\mathcal{E}$, the unit functor $\mathcal{E} \rightarrow \mathcal{H}^\text{st}(\mathcal{E})$ is fully faithful and preserves and reflects exact sequences. This provides an $\infty$-categorical variant of the Gabriel-Quillen embedding for ordinary exact categories. If $\mathcal{E}$ is an ordinary exact category, the stable hull $\mathcal{H}^\text{st}(\mathcal{E})$ is equivalent to the bounded derived $\infty$-category of $\mathcal{E}$., Comment: 22 pages, accepted version

We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections. The aim of this article is twofold: in the first part, we show that even in Euclidean spaces the convergence of the alternating method is not determined by the principal angles between the subspaces involved. In the second part, we investigate the properties of the Oppenheim angle between two linear projections. We discuss, in particular, the question of existence and uniqueness of "consistency projections" in this context., Comment: 15 pages; published in "Linear Algebra and Its Applications". This version corrects a number of misprints